Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Coriolis force wikipedia , lookup
Newton's theorem of revolving orbits wikipedia , lookup
Nuclear force wikipedia , lookup
Rigid body dynamics wikipedia , lookup
Electromagnetism wikipedia , lookup
Fictitious force wikipedia , lookup
Fundamental interaction wikipedia , lookup
Mass versus weight wikipedia , lookup
Centrifugal force wikipedia , lookup
Classical central-force problem wikipedia , lookup
Freshman Physics Name __________________________ Hour______ Unit 4. Forces Primary Authors: Meera Chandrasekhar and Dorina Kosztin Department of Physics and Astronomy, University of Missouri, Columbia Unit 4: Forces Page 1 Freshman Physics Lab 1: Reading Page: Reading Page: Reading Page: 4.1. Practice: Reading Page: 4.2. Practice: Reading Page: 4.3. Practice: 4.4. Practice: Reading Page: 4.5. Practice: Reading Page: 4.6. Practice: 4.7. Practice: 4.8. Practice: Reading Page: 4.9. Practice: 4.10. Practice: 4.11. Practice: Reading Page: 4.12. Practice: 4.13. Practice: 4.14. Practice: 4.15. Practice: 4.16. Practice: Unit 4: Forces Name __________________________ Hour______ Table of Contents Broom Ball – The Game Lab ................................................................................... 3 What is a Force? ........................................................................................................ 5 Type of Forces ........................................................................................................... 7 Drawing and Analyzing Forces ............................................................................. 9 Force Challenge ...................................................................................................... 13 Measuring Weight .................................................................................................. 15 Gravitational Force and Mass .............................................................................. 19 Forces as vectors ..................................................................................................... 21 Forces as Vectors .................................................................................................... 25 Force Addition and Balancing Forces ............................................................... 27 Drawing Force Diagrams ..................................................................................... 31 Force Diagrams I .................................................................................................... 33 Newton’s First Law ................................................................................................ 35 Force Diagrams II .................................................................................................. 37 Broom Ball Lab Revisited ..................................................................................... 39 Newton’s First Law ................................................................................................ 41 Newton’s Third Law .............................................................................................. 43 Identifying Pairs of Forces.................................................................................... 47 Identifying Pairs of Forces II ............................................................................... 53 Newton’s Third Law Problems ........................................................................... 55 Newton’s Second Law ........................................................................................... 57 Newton’s Second Law Problems ........................................................................ 59 Newton’s Third and Second Laws with Blocks ............................................... 63 Balanced Forces ...................................................................................................... 65 Force Diagrams related to Motion...................................................................... 71 Force Diagrams, Motion Diagrams and Newton’s Laws .............................. 75 Page 2 Freshman Physics Name __________________________ Hour______ LAB 1: BROOM BALL – THE GAME LAB Purpose: What is a force and what does it do? Materials: Broom with flexible bristles and a plastic casing at the top of the bristle end. Bowling ball and soccer ball or basket ball Large pail containing sand Course marked off with tape on the floor (see diagram below). Blue painters’ masking tape or electrical tape work best for tape removal after the activity. Start/Stop No touch zone pail The rules of the game: 1. Broom Ball is played as a relay race. 2. There are two teams. Half of each team will be stationed at each end of the course. 3. The bowling ball should be at rest at one end of the course and the soccer ball will be at rest at the other end. Each student will run the course from whichever end he/she is one way using the bowling ball, and coming back using the soccer ball. 4. The ball may be manipulated only with the bristles of the broom. If any part of the broom other than the bristles touches the ball that is a penalty. If the ball touches any obstacle in the room, such as walls, pail, furniture, a student foot, etc. that is a penalty. 5. The clock starts when the first player takes off. Everybody should follow the course. You must go all the way around the large pail (360 degrees), through the no touch zone without touching the ball with the broom, around the corner and bring the ball to a complete stop in the starting box, before the next player takes off reversing the course. 6. After the last team member has completed the course the watch is stopped and a time penalty is added to the total time for each penalty while the ball was in play. 7. The team with the shortest time wins. Unit 4: Forces Page 3 Freshman Physics Name __________________________ Hour______ Post-lab discussion 1. What three things are the most difficult when it comes to handling the ball? 2. Was there a difference between handling the bowling ball and the soccer ball? Explain. 3. How can a player use the broom to overcome the difficulties mentioned in question 1? (What strategies would you recommend to a teammate?) 4. How does the ball move in the no-touch zone? 5. What causes the motion of the ball in the no-touch zone? Unit 4: Forces Page 4 Freshman Physics Name __________________________ Hour______ Reading Page: What is a Force? People often think of force as something you apply using your muscles. When you push or pull on an object, you apply a force on it. You also apply force when you throw a baseball or kick a soccer ball, or sit on a soccer ball. Therefore, a force is nothing else than a push or a pull. When you apply a force on an object, its shape can change, as it might when you sit on a soccer ball, or on a sofa, or when you squeeze an orange. These are soft objects; but even rigid objects, such as a wall or a car, can be deformed (have their shape changed) if enough force is applied, such as with a sledgehammer or in a collision with another car. Contact Forces Vs Field Forces Forces cause not only deformations (changes in shape), they can also cause motion – if you push or pull on a cart, it may move. When you played the broom ball game, you had to push the bowling ball with the broom to make it move, stop or change its direction. You had to push harder on the bowling ball than on the soccer ball because the bowling ball was heavier than the soccer ball. If you push a cart on a rough surface, or if the cart is very heavy, you will need more force to move it than on a smooth surface. If you sit on a chair, the chair holds you up (you are not falling through it) and applies a force to you: the longer you sit in that chair, the more you will feel that force. These forces are examples of contact forces – they arise from physical contact between the applier of the force (called the agent) and the receiver of the force (called the receiver). Field forces or long range forces, also called non-contact forces or forces at a distance, are another class of forces. These forces do not involve physical contact between the agent and the receiver, but act through space, through a field. For example, the force of gravity the Earth applies to us is what keeps us on the planet Earth and does not let us fly out in space. The effect of the gravitational force on all objects on the surface of the Earth can be described through a gravitational field. The Moon goes around the Earth because of the gravitational force between them; the solar system is kept together by the same force. The Moon itself has a gravitational field, applies a gravitational force to objects on its surface. Another example of a field force is the magnetic force: you feel a magnet being attracted or repelled by another magnet even if the two magnets do not touch each other. The third example of a field force is the electric force, often observed as static electricity, which causes your socks to stick to your sweaters when you take them out of the dryer or the hair on your head to stick to your brush or to stand up after brushing it. While it is convenient to classify forces as field forces and contact forces, on a microscopic level the distinction is not so clear. For example, the force of friction might seem like a contact force, but it is caused by repulsive forces between electric charges, which are field forces. It might seem like there are a lot of forces in nature – gravitational force, friction forces, electric forces, magnetic forces, push and pull forces, elastic forces …the list is not short. These forces are macroscopic descriptions of phenomena. These descriptions are useful in designing, say, roller coasters, furniture, bridges, or highways. The atomic origins of these forces, however, can be traced to just four forces in nature: Unit 4: Forces Page 5 Freshman Physics Name __________________________ Hour______ 1. The gravitational force, which describes the attraction between objects, is based on the mass of each object and the distance between them, and holds galaxies, stars, and planets together. 2. The electromagnetic force, which describes the attraction and repulsion between objects due to the charge on each object and the distance between them, is responsible for the binding of atoms and molecules. 3. The nuclear strong force is responsible for the binding of neutrons and protons into nuclei. 4. The nuclear weak force is a short-range nuclear force that produces instability in certain nuclei. Each of these forces is described by a constant, a number, which gives the “strength” of this force. Ranked using these constants, the strengths of the forces are, in order, strong, electromagnetic, weak and gravitational. The strong and weak forces have a very short range of action, of the order of the radii of nuclei. These invisible forces keep things together, but are hard to observe except in the research laboratory. In everyday life, when we are not dealing with atomic-scale phenomena, the only forces that impact us are the two long-range forces: gravity and the electromagnetic force. While the gravitational force may be “weakest,” when one factors in the large masses involved (such as that of earth, planets or stars), the gravitational force becomes a dominant force in everyday life. Close behind is the electromagnetic force, which causes static, gives us electrical power, makes cell-phones work, and makes for the conveniences of modern-day life. Unit 4: Forces Page 6 Freshman Physics Name __________________________ Hour______ Reading Page: Type of Forces The most common forces we deal with in everyday life and will study in this class are: Gravitational Forces Gravitational forces occur because objects have mass. Gravitational forces have the largest effect when exerted by a large mass, such as the earth, sun, planets or the moon. Gravitational forces always attract objects. People, trains, and buildings remain “stuck” to the earth because the gravitational force due to the earth’s mass attracts them. Even when you lift an object off the earth, the moment you let go, it falls back to the earth because of the earth’s gravitational attraction. When you go sliding, the force of gravity is responsible for bringing you down that slide. When you throw a ball up into the air, it always comes back down because of the force of gravity acting on it. Have you ever held up a heavy object and felt it pulling down toward the earth? That’s the gravitational force of the earth attracting it! This force acts at a distance, it is a field force and we say that it acts through a gravitational field. In everyday life, people refer to the gravitational force the earth exerts on all objects as the weight of that object. (Note: In everyday language we use the words mass and weight interchangeably, but scientists distinguish between mass, which measures how much “stuff” an object has, and weight, which measures the force with which the earth attracts that mass.) Friction Forces Friction is often observed when we rub objects together, or when we slide an object on a surface. It is much easier to drag a box across a smooth surface than across a rough one. Also, it is much easier to walk (have better traction) if your shoes have treads on the bottom than if they have a smooth bottom. Generally, rough surfaces hinder the motion of an object more than a smooth surface does. Although friction may appear to be caused by surface texture, it is actually caused by electrical forces between molecules. Frictional forces between two objects depend on the type of surfaces that are in contact with each other: the rougher the surface, the bigger the friction. One method of reducing friction is to modify the texture of the contact surface by applying lubricants, such as oil or graphite. While friction is often considered a hindrance, there are situations where friction is necessary – compare walking on a dry sidewalk with walking on it on an icy day! Also, put grease on the handle of your spoon and then try and hold it when you eat; it is much more difficult! Elastic force (also known as stretching or compressing force) When you stretch a rubber band, you have to pull on it with a force. But the rubber band appears to pull back – in fact, you have to continuously apply the pulling force to keep the rubber band stretched. When you go bungee jumping, at the bottom of your jump the bungee cord starts extending and at one point starts pulling you back up. This “pulling back” is a manifestation of the elastic force that exists in the bungee cord or rubber band. If you let go, the rubber band will go back to its original length too. This elastic force also appears when you compress a spring – for example, when you push the “Jack in the Box” back in its box, the spring is compressed and when you open the lid, the elastic force in the spring (due to its compression) makes the toy pop-up from the box and brings the spring back to its unstretched length. Objects that stretch or compress when a force is applied to them, and then go back to their Unit 4: Forces Page 7 Freshman Physics Name __________________________ Hour______ original form when the force is removed are called elastic. A force is called elastic force if once removed allows the object to recover its original form, length, shape. This can happen to things other than springs, for example, a tree branch can be pulled down and it retracts to its original position. Have you ever pulled the tip of a ruler back like a catapult and hit a ball? There’s the elastic force at work again. Tension (also known as stretching force or pulling force) Stretching forces or “tension” also occurs when you have something that is held taut. For example, when you play tugof-war, the string/rope the two teams pull on is stretched taut and each team applies a force to its end. The force that shows up in the string/rope as the result of its stretching is called tension force. A picture hanging on the wall has tension force in the string used to hang it. If the picture is very heavy and the string is not strong enough to support the tension force, the string will break. Normal or Support Force When you sit on your chair, your own weight pushes down on the chair. If so, why don’t you fall through the chair? Easy – because the chair is supporting you. How does it do it? Well, the strong material that makes up your chair deforms the chair a bit, and the molecules of the material that make up the chair feel their bonds deform a bit too. Just as a spring that is compressed pushes back at you, the springy bonds between the molecules push back too – and that is the origin of the normal or support force provided by the chair. The amount of support force is just enough to leave you sitting where you are. If it were a bit less, you would fall through the chair. If it were more, it would push you upward. The chair supports you with an equal and opposite force. If you think about the molecular origin of this force, it makes sense – if the person was heavy and deformed the chair a lot, the bonds between molecules would be deformed a lot, and the chair would push back a lot. If it were a light person – small deformation, smaller push-back, smaller support force. Support forces are pretty clever – they appear only when they are needed, and only in as much amount as needed. If the person got up from the chair, the deformation of the bonds is gone, and the support force vanishes! The support force is often called the normal force – normal being perpendicular. Support forces are always perpendicular to the surface at the point where the object touches it. (If they were in any other direction they would make the object slide in that direction!). Commonly used symbols to denote the forces we discussed above are: Symbol Name of the Force Type of Force Direction of force Perpendicular to the surface that FN or Fn Normal force Contact force applies it Gravitational force Non-contact force Always oriented down toward the FG or Fg (or weight) (field force) earth Along the surface in contact; opposes Ff Friction force Contact force the relative motion of the two surfaces FT Tension force Contact force Along the rope, always pulling Along the spring, always opposing the Fe Elastic force Contact force deformation of the spring Note: any other contact force that is not one of the forces listed above can be called “applied force” and denoted with FA. Unit 4: Forces Page 8 Freshman Physics Name __________________________ Hour______ Reading Page: Drawing and Analyzing Forces A force is always applied by an object or the result of a phenomenon. The object that applies the force is called the agent. This force is also applied to an object that experiences the force, called the receiver. And finally, something happens because the agent applied a force to the receiver – the effect. Let’s see how we can apply this analysis to forces. A force is a push or a pull and as such when describing a force we must specify not only its magnitude (how strong the force is) but also the direction of the force (pushing or pulling?). As such we can represent a force graphically by using an arrow. We place the tail of the arrow on the object that the force acts on, the receiver, and orient the arrow such that we show the direction of the force. The length of the arrow should represent the magnitude of the force. Whenever analyzing forces acting, follow the steps below: 1. Determine the object that is the receiver (has forces applied to it). 2. Identify the agents (objects that apply forces to the receiver). 3. For each agent, identify the force it applies. (Note: remember that we live on Earth and therefore Earth (agent) always applies a force (gravity) to every single object (receiver) on its surface). 4. Represent the direction of the force with an arrow starting on the receiver. 5. Describe the effect of the identified forces on the receiver. g Example 1 Examine the picture of the Moon going around the Earth: The Moon goes around the Earth because the Earth (the agent) applies a force to the Moon (the receiver) and as a result the Moon moves around the Earth (the effect). The force applied by the Earth is the force of gravity (Note: This analysis is somewhat simplified in the sense that we have separated out the agent and the receiver. To produce the attractive gravitational force you need at least two masses; technically the Earth and the Moon are both agents, and they are both receivers. However, at this time we chose to examine the Moon as the receiver.) Example 2 Frequently there is more than one force acting on an object. Let’s look at the picture of the child on the slide. In this case we consider forces acting on the child, therefore the child is the receiver. A B C Receiver: Child Force: Force of Gravity Agent: Earth Effect/s: Child slides down Receiver: Child Force: Normal Force Agent: Slide Effect/s: Supports the child Receiver: Child Force: Friction Force Agent: Slide Effect/s: Slows down the child Unit 4: Forces Page 9 Freshman Physics Name __________________________ Hour______ The child slides down on the slide because the force of gravity applied by the earth (agent) has the effect of bringing him down (figure A). The child is also in contact with the slide, thus the slide is another agent applying forces on the child. The normal force applied by the slide (agent) has the effect of holding the child from falling through the slide (figure B). The friction force applied by the slide (agent) has the effect of slowing down the child (figure C). So as you can see, there are three forces acting on the child (receiver) and they are the result of the interaction between the child and Earth (long range forces) and the child and slide (contact forces). Example 3: Here’s another example of several forces at play: A man pulls on the leash of a dog. In this case we can choose either the dog or the man as being the receiver. Let’s start with the dog as receiver. All forces, and their agents and effects are listed in the table below. The effect of all these forces combined is that the dog does not move as the man pulls on its leash. All forces acting on this dog are balanced. Receiver: Dog Force: Force of Gravity Agent: Earth Effect/s: Tends to bring to dog down Receiver: Dog Force: Normal Force Agent: Ground Effect/s: Holds up the dog Receiver: Dog Force: Friction Force Agent: Ground Effect/s: Stops the dog from sliding Receiver: Dog Force: Tension Force Agent: Rope Effect/s: Pulls on the dog How are things changing if the selected receiver is the man? Look in the table below for all the forces acting on the man, their agents and effects. Receiver: Man Force: Force of Gravity Agent: Earth Effect/s: Tends to bring to man down Receiver: Man Force: Normal Force Agent: Ground Effect/s: Holds up the man Receiver: Man Force: Friction Force Agent: Ground Effect/s: Stops the man from sliding Receiver: Man Force: Tension Force Agent: Rope Effect/s: Pulls on the man The effect of all these forces combined is that the man does not move as he pulls on the leash. All forces acting on this man are balanced. Unit 4: Forces Page 10 Freshman Physics Name __________________________ Hour______ Example 4: Now let’s go back to the broom ball lab. How did the ball move in the “no touch” zone? It moved with constant speed. Were there any forces acting on the bowling ball when moving through the “no touch” zone? Yes, there were! The force of gravity was pulling down on the ball and the normal force was supporting the ball. The two forces balanced each other, and as a result, the ball moved with constant speed. Thus we can say that if forces acting on an object are balanced, the object can be either at rest or moving with constant speed. FN Fg Unit 4: Forces Page 11 Freshman Physics Name __________________________ Hour______ Notes: Unit 4: Forces Page 12 Freshman Physics Name __________________________ Hour______ 4.1. Practice: Force Challenge Directions: Follow the 5 steps in the “Analyzing Forces” reading page. Identify one receiver and one force acting on it. Make sure you don’t use the force of gravity for every example. In some cases, the receiver or agent is already identified for you. A. C. E. Receiver: B. Receiver: Force: Force: Normal Agent: Earth Agent: Effect/s: Effect/s: Receiver: D. Receiver: tire Force: Force: Agent: Rope Agent: Effect/s: Effect/s: Receiver: panda F. Receiver: Thesaurus book Force: Force: Agent: Agent: Dictionary Effect/s: Effect/s: G. I. Unit 4: Forces Receiver: bicycle seat H. Receiver: Force: Force: Normal Agent: boy Agent: Effect/s: Effect/s: Receiver: balloon J. Receiver: ball Force: Force: Agent: Agent: Effect/s: Effect/s: Page 13 Freshman Physics K. M. O. Q. S. Unit 4: Forces Name __________________________ Hour______ Receiver: L. Receiver: ball Force: Force: Agent: Agent: Effect/s: Effect/s: Receiver: N. Receiver: girl Force: Force: Agent: Agent: Effect/s: Effect/s: Receiver: toolbox P. Receiver: chair Force: Force: Agent: Agent: Effect/s: Effect/s: Receiver: doorknob R. Receiver: Force: Force: Agent: Agent: Effect/s: Effect/s: Receiver: T. Receiver: Force: Force: Agent: Agent: Effect/s: Effect/s: Page 14 Freshman Physics Name __________________________ Hour______ Reading Page: Measuring Weight One of the simplest methods of measuring a force is to use a spring scale. If you pull on the hook of a spring scale with a force, the spring inside the scale stretches. The amount a spring stretches is proportional to the amount of force applied. For example, if we apply a force of 40 N and we find that a spring gets 8 cm longer than its original length, then we know that if we apply 20 N of force, it should get 4 cm longer. This allows us to construct a scale (10 N = 2 cm of stretch). Once we have a scale, we can measure other amounts of force. A common use of a spring scale is to measure weight, the amount of gravitational force applied by the earth. In everyday language we think that weight is a measure of how much “stuff” an object contains. Scientists distinguish between mass, which measures how much “stuff” an object has, and weight, which measures the force with which the earth attracts that mass. Since the force with which the earth attracts all objects scales with the mass of the object, the mass and weight of an object are proportional to one another. The mathematical relationship between the gravitational force applied by Earth (or weight) and the mass of the object is: 𝐹𝑜𝑟𝑐𝑒 𝑜𝑓 𝐺𝑟𝑎𝑣𝑖𝑡𝑦 (𝑜𝑟 𝑤𝑒𝑖𝑔ℎ𝑡 ) 𝑁 = 9.8 𝑚𝑎𝑠𝑠 𝑘𝑔 This is also known as the “gravitational field strength” or the acceleration due to gravity and it is denoted with the letter “g”. We can then rewrite the above mathematical relationship using symbols, as: g Fg m where g = 9.8 N/kg on Earth From the above expression, we can calculate the gravitational force Fg (or weight) on Earth as: Fg mg or Weight (in N) = mass (in kg) x 9.8 (in N/kg) The numerical factor of 9.8 will change if we use different units. For example, in the cm-mg-sec system, Weight (dynes) = mass (mg) x 980 (dyne/mg) In the British system, Weight (lbs) = mass (slugs) x 32 (lb/slug) Because weight and mass are related just by a numerical factor, we can use the same device to measure both and just mark the device with the appropriate scales. Spring scales often have markings to measure both mass and weight. When you go to the store to buy apples, and you want to check how much mass the apples have, you are using a spring scale. The reading of the scale is in lb (pounds) which is a unit of force. Unit 4: Forces Page 15 Freshman Physics Name __________________________ Hour______ A bathroom scale is another device to measure weight – a person has to stand on it, his/her mass is pulled down toward the earth due to the earth’s gravity, and the person pushes down on the scale. A spring inside the scale gets compressed due to this force, and rotates a dial or displays a number that displays this force. The force may be displayed in pounds of force, or it may be rescaled and displayed as kilograms of mass. Or it could equally have been displayed as slugs of mass or newtons of force! Marking equivalent units is not unusual – many car speedometers have speed displayed as km/hour and miles/hour; thermometers may also read Celsius or Fahrenheit. Spring scales are a bit different in that the two units are for different factors – mass and weight, but the principle is the same. In a digital balance (like the ones used in class), the weight of the object compresses a spring or a strain gauge inside the balance. The amount of compression is related to the mass of the object. In a classical beam balance, the weight in the left pan is balanced by the weight in the right pan. How can you tell mass and weight apart? Mass and weight have different units. Weight is a force and it is measured in units of newtons (abbreviated N) in the metric system, or pounds (lb) in the British system. Mass is a measure of how much stuff an object contains and it is measured in units of grams or kilograms (g or kg) in the metric system and slugs in the British system. Mass will remain the same on the Earth or the Moon or anywhere else. Weight, however, is the force with which the object is attracted. If the object were on the Moon, it would be attracted by a different amount of force than on the Earth, since the gravitational field strength of the Moon is smaller than the gravitational field strength of the Earth (the mass of the moon is smaller than that of the earth, and the object is also closer to the center of the moon). So its weight would be different (in fact it would be about 1/6 as much). Below you have a table with the gravitational field strength of each planet in the Solar System: Planet Gravitational Strength Unit 4: Forces Earth Moon Sun Mars Jupiter Pluto 9.8 N/kg 1.6 N/kg 273.4 N/kg 3.7 N/kg 25.8 N/kg 0.6 N/kg Page 16 Freshman Physics Name __________________________ Hour______ 4.1. Practice: Gravitational Force and Gravitational Strength 1. Many unit conversion tables contain the following conversion: 1 kg = 2.2 pounds. Explain what is wrong with this “equation.” Write a statement that includes the terms “1 kg” and “2.2 pounds” that is correct. 2. It is commonplace to find statements on food cans such as “Net Weight: 16 oz. (454g)” Why do most people find this acceptable? Why do “physics types” object to such statements? 3. When you step on a bathroom scale here is US, your weight is given in pounds. Is this a correct unit for such a scale? What would happen to the reading on this device if you were to stand on it while on the moon? Is this what the scale should read? Why are all these standards and measurements used so often? Unit 4: Forces Page 17 Freshman Physics Unit 4: Forces Name __________________________ Hour______ Page 18 Freshman Physics 4.2. Practice: Name __________________________ Hour______ Gravitational Force and Mass 1. A box has a mass of 8.00 kg. Knowing that the gravitational field strength on Earth is 9.8 N/kg, calculate the force of gravity on the box. 2. A box of cereal has a mass of 250 g. What is the force of gravity on the box, knowing that the gravitational field strength on Earth is 9.8 N/kg? 3. The Earth exerts a gravitational force of 500 N on Amy. What is Amy’s mass in kg? 4. The Earth exerts a gravitational force of 850 N on John. What is John’s mass in g? 5. A rock has a mass of 5.00 kg on the moon. What is the mass of the rock on the earth? 6. The gravitational field strength on the Moon is 1.6 N/kg. If a rock on the moon weighs 200 N, how much does the same rock weigh on the earth? Unit 4: Forces Page 19 Freshman Physics Name __________________________ Hour______ 7. Using the information provided below, fill out the table: g (N/kg) 9.8 N/kg Mass on Earth (m) A. 9.8 N/kg 1.6 N/kg 273.4 N/kg 3.7 N/kg 25.8 N/kg Weight on Earth (Fg) Weight on Moon Weight on Sun Weight on Mars Weight on Jupiter 0.2 kg B. 6000 N C. D. 45000 N 30 N E. F. 500 N 89000 N 8. If you were to drop a 5 kg rock on your toe, would you rather be on Mars or on Jupiter? Explain. 9. Do you think it is easier or harder to hammer a nail into a floorboard on the Moon than on Earth? Explain. Unit 4: Forces Page 20 Freshman Physics Name __________________________ Hour______ Reading Page: Forces as vectors The word “force” makes us think of pushing, pulling, holding up, dragging down – all phrases that have a feeling of direction associated with them. You can push away from yourself, or pull toward you. Other forces that one encounters, like the force of friction may not intuitively tell us the direction involved – until we realize that friction always slows things down. Friction resists motion – so it has a direction too! All forces have a direction associated with them. They belong to the family of vectors, for which we need to know both the amount and the direction. A vector is a physical quantity for which both the amount and the direction should be specified. A scalar has only the amount specified, but not the direction. Not all things in nature are vectors. For example, mass (e.g., 56 grams) does not have a direction. To say “56 grams south” does not mean anything. Thus mass is always a scalar – it does not have a vector equivalent. Similarly, temperature is always a scalar (34°C north east is meaningless). In contrast, a force can be push or pull, up or down, left or right – thus forces are vectors. Some physical quantities, like speed and velocity have different names for the scalar and vector forms. Others, like force, do not have scalar counterparts. The direction of a vector can be specified in many ways. We can represent a force graphically by using an arrow. We place the tail of the arrow on the object that the force acts on, the receiver, and orient the arrow such that we show the direction of the force. The length of the arrow should represent the magnitude of the force and the arrow should indicate the direction of the force. Let’s look at an example and see how we can use this new information when representing forces. In the picture on the left you have a bear sitting at rest on a very smooth table. If the bear is the receiver, then there are two forces acting on the bear. The force of gravity, Fg, (agent: Earth) is always oriented vertically down. The normal force, FN, (agent: table) is always oriented perpendicular to the surface that applies it, in this case, perpendicular to the table, and upward. The two forces are represented by two arrows, each one indicating the direction of the force. The lengths of the two arrows indicate the strength (magnitude) of each force. In this case, because the bear is sitting on the table at rest, the two forces balance each other out, which means their lengths are the same. Why is it useful or necessary to have vectors? Because just giving the force amount information does not paint the whole picture! I am telling you now that an additional force of 50 N is applied to the bear, so you know the amount of force applied. Is that enough information to determine what happens to the bear? No, you also need to know in which direction this force is applied. If the force is upward, the bear will lift off the table, if it is to the right, the bear will move to the right. So as you can see, the direction of the force is also very important to specify. Now, if the pulling force of 50 N is applied to the right, how can you keep the bear from moving to the right? Of course, you must Unit 4: Forces Page 21 Freshman Physics Name __________________________ Hour______ apply a force that is also 50 N oriented to the left, meaning you must balance the forces along the horizontal direction. Do you remember how the bowling ball form Broom Ball Lab moved in the “no touch” zone? The only forces acting on the bowling ball were the force of gravity and the normal force, and they balance each other out. There were no forces along the horizontal direction, and still the ball moved with a constant speed. So we can say that when all forces acting on an object are balanced, the object is either at rest or moving with a constant speed. The direction of a vector can be specified in many ways. Here are some: Unit 4: Forces Page 22 Freshman Physics Name __________________________ Hour______ Examples: Adding Forces in 2D Rita and Manny pull on a sack of candy. Rita pulls toward the north with a force of 26 N, while Manny pulls toward the east with a force of 40 N. Draw the total force on the sack. 1. Set up your graph paper: Define the northeast-south-west directions with a compass rose. The axes on the graph paper should be along north-south and east-west. Choose your scale – decide how many cm will represent 10 N. Mark off the axes. In the figure we show marks every 10 cm. (box 8) 2. Set the sack at the center of the graph paper as before. Draw Manny’s force, 40 N toward the east (let’s call it force ⃗A). Draw Rita’s force, 26 ⃗ ). (Box 9). N toward the north (force B 3. To add vectors, we add them one after another. This means that you draw force ⃗A, and at the end of force ⃗A, draw force ⃗B. Since we represent force ⃗A as going from 0 to 40 (which is where the tip of the arrowhead is ⃗ is placed at the “40” mark, drawn), force B which is the end point of force ⃗A. To do so, ⃗ so it still points north, (and is we move force B still the same length) but its starting point is at the tip of force ⃗A. The arrows representing the vectors need to be placed tip-to-tail. (Box 10). 4. The vector that represents the sum of ⃗A and ⃗B now starts from the tail (the beginning) of the first vector to the tip (the end) of the last one. The total force ⃗A + ⃗B is shown by the dashed arrow in box 11. Note: ⃗ you would In order to find the length of ⃗A + B need to use Pythagorean theorem. We will not be using this at this level. Unit 4: Forces Page 23 Freshman Physics Name __________________________ Hour______ A Note On Defining Angles: After you have drawn your vector diagram for adding forces, your answer must define both the amount of the force and the angle it makes. Here are two common conventions for defining angles: Convention #1 – useful when your vector diagram is drawn with a North-East-South-West grid. Two equivalent methods of defining the angle of the vector (dashed line): Measure your angle starting from one of the axes. We started from the east and measured the angle in the northward direction (see arrow). The angle is defined as 35˚ North of East or 35˚ North from East. This angle is between the east axis and the vector. OR: The angle can be measured starting from the north axis and measured in the eastward direction (see arrow). This angle is defined as 55˚ East of North or 55˚ East from North. This angle is between the north axis and the vector. Convention #2: Useful when you have an x-y Cartesian grid. Two equivalent methods of defining the angle of the vector (dashed line): As with convention #1, measure your angle starting from any one of the four axes. Usually one starts from one of the nearby axes. Above, we start at the +x axis and measure 30˚ in the clockwise (CW) direction. The angle is defined as 30˚ CW from +x, and is the angle between the +x axis and the vector. Unit 4: Forces OR: The same angle can be measured starting from the -y axis: start from the -y axis and measure the angle in the counter-clockwise (CCW) direction (see arrow). This angle is defined as 60˚ CCW from -y, and is the angle between the -y axis and the vector. Page 24 Freshman Physics Name __________________________ Hour______ 4.3. Practice: Forces as Vectors 1) Knowing that the size of one square is 10 N by 10 N, draw force vectors to represent the following: a) 20 N south b) 45 N south c) 15 N east N W E S 2) What is different about these two vectors: a force that is 5 Newtons, west, and a force that is 25 Newtons, north? Explain in words and draw the arrows. 3) Karina is pulling on her toy truck with a force of 25 N. At the same time, her brother Lovell pulled on it with a force of 20 N. Can you think of three different diagrams (scenarios) that represent the forces described above? Explain what happens in each scenario as the result of the two forces acting on the truck. Unit 4: Forces Page 25 Freshman Physics Name __________________________ Hour______ 4) If you want everybody to interpret the forces on the truck the same way, what important piece(s) of information should you specify? 5) Can you figure out the total force acting on these objects? (Show what you understood by total force and how you figured it out, this can be an equation.) 6) If all the forces acting upon an object are balanced, then the object: a) must not be moving. b) must be moving with a constant velocity. c) must not be accelerating. d) none of these Unit 4: Forces Page 26 Freshman Physics 4.4. Practice: Name __________________________ Hour______ Force Addition and Balancing Forces 1. Describe the angles below in words (i.e., 12˚ North of West, etc). Give two equivalent descriptions for each angle. a) Original angle Equivalent angle Equivalent angle b) Original angle Equivalent angle Equivalent angle c) Original angle Equivalent angle Equivalent angle Unit 4: Forces Page 27 Freshman Physics Name __________________________ Hour______ 2. Describe the angles below in words (i.e., 12˚ CW of +y, etc). Give two equivalent descriptions for each angle. a) Original angle Equivalent angle Equivalent angle b) Original angle Equivalent angle Equivalent angle c) Original angle Equivalent angle Equivalent angle Unit 4: Forces Page 28 Freshman Physics Name __________________________ Hour______ 3. Draw diagrams on graph paper, mark the angles and figure out equivalent descriptions (e.g., 30˚ North of East is equivalent to 60˚ East of North) for: a) 24˚ North of East d) 34˚ CCW from –x b) 52˚ West of South e) 60˚ CW from -y c) 38˚ South of East f) 25˚ CCW from +y 4. (a) Shawna pulls on a mule with a force of 8.0 N toward the north, while Tammy pulls on it with a force of 4.0 N toward the east. Draw a diagram of the forces and show the resultant vector of the two directions. (b) If the mule is stubborn and does not want to move, in which direction, and with how much force, must it resist (give the two specific directions and draw the resultant vector). 5. Julie pushes a box with a force of 2.0 N toward the west, while Martha pushes it with a force of 4.0 N toward the north. Draw a diagram of the forces. Draw the total (resultant vector) of these two forces on the box? 6. Farmer Tim is trying to get his pony loaded on a train, and has a crane helping him lift the pony. He pushes on a pony with a force of 800 N to the right, while a crane pulls on the pony with a force of 2000 N upward. (a) Draw a diagram of the forces. Show the vector sum (resultant) of the two forces. (b) If Jackie wanted the pony not to move, what must Jackie’s force be? Unit 4: Forces Page 29 Freshman Physics Unit 4: Forces Name __________________________ Hour______ Page 30 Freshman Physics Name __________________________ Hour______ Reading Page: Drawing Force Diagrams What is a force diagram? A force diagram (often called a free-body diagram) is a tool to represent all the forces acting on an object. In some situations it might be easy to identify all the forces that act on an object. However, situations tend to get complicated quickly, especially if there are both contact and long-range forces. Therefore it is a good idea to have a process that helps us identify all the forces in situation. Here is a method that works well: 1. Draw a picture of the problem, showing the object and everything in the environment that touches the object – ropes, tables, springs are all part of the environment. 2. Identify the receiver – which is the object or objects of interest – by drawing a closed curve around the receiver, with the object inside the curve and everything else (environment) outside the curve. 3. Locate every point in the receiver at the boundary of the curve where the environment touches the receiver and identify by name all the contact forces at each point of contact (there may be more than one force), then give each one an appropriate symbol. 4. Identify any long-range forces acting on the receiver. Name the force and write its symbol in the picture. 5. Draw the force diagram. Start by representing the receiver with a dot. Draw all forces with the tail on the dot and keep the direction of those forces the same. Example 1: A flamingo stands on the ground. Draw the force diagram for the flamingo. 1. The picture 2. Identify the receiver with a closed curve around it. 5. Make the force diagram Fg 3. Identify all contact forces. 4. Identify all long range forces. Force of gravity, Fg Normal force, FN Unit 4: Forces FFNg Normal force, FN Page 31 Freshman Physics Name __________________________ Hour______ Example 2: A sled on level ground is being pulled by a rope. Draw the force diagram for the sled. 1. The picture 2. Identify the receiver with a closed curve around it. 5. Make the force diagram FN FT 3. Identify all contact forces. 4. Identify all long range forces. Ff Fg Example 3: A dog is being pulled by her leash on level ground. Draw the force diagram for the dog. Note: one might think that we need to have four normal forces, and four friction forces, one for each paw. However, we are going to represent the dog by a point in the force diagram, so it is all right to represent the normal force and the friction force at one point (paw) only. 1. The picture 2. Identify the receiver with a closed curve around it. 5. Make the force diagram FN FT 3. Identify all contact forces. 4. Identify all long range forces. Tension force, FT Tension force, FT Ff Fg Friction force, Ff Friction force, Ff Force of gravity, Fg Unit 4: Forces Page 32 Freshman Physics Name __________________________ Hour______ 4.5. Practice: Force Diagrams I Identify your receiver with a dotted line. Be aware that if you cannot identify the agent for a force, it means that there is no force! 1. Draw a force diagram for a bird sitting motionless on a branch. 2. Draw a force diagram for a lamp that is suspended from the ceiling. 3. Draw a force diagram for Sarah as she clears a high jump. 4. Draw a force diagram for the ball used as a book end. 5. Draw a force diagram for the skier and skies during his jump. Ignore air resistance. 6. Draw a force diagram for the sled and boxes together. Note that the child pulls on the sled at an angle. Unit 4: Forces Page 33 Freshman Physics Name __________________________ Hour______ 7. Draw a force diagram for the picture hanging on the wall. 8. Draw a force diagram for Henry who hangs motionless from a tree branch. 9. Draw a force diagram for the toolbox. 10. Draw a force diagram for the chair that the cowboy sits on. 11. Draw a force diagram for a balloon floating stationary in the air. 12. Draw a force diagram for the worker sitting motionless on a sloped roof. Unit 4: Forces Page 34 Freshman Physics Name __________________________ Hour______ Reading Page: Newton’s First Law To explain in the most general way how force and motion are connected Newton came up with three physics laws. NEWTON’S FIRST LAW Newton's first law of motion is also known as the law of inertia. It states that: An object moving with constant velocity continues to do so unless acted upon by a nonzero net force. This law may sound simple but it has many nuances that must be clarified in order to be understood. 1) The phrase “moving with constant velocity” in the statement of this law means that the object is traveling in a straight line, with constant speed, i.e. it is neither speeding up, nor slowing down, nor changing direction. This law says that the natural state of motion is that of constant velocity. Since the law does not distinguish the constant velocity of zero (at rest) from any other constant velocity, it says that all constant velocities are equivalent. Newton’s First Law can be restated as: An object in constant velocity motion, or at rest, will continue its constant velocity motion, or remain at rest, unless acted upon by a net force. 2) Newton’s First Law can seem counterintuitive: in real life objects in motion stop moving sooner or later. Prior to Newton, people believed that the “natural state” of an object was at rest. Example: push your physics textbook across the table. As long as you keep pushing it (applying a force to it), the book will move and as soon as you stop pushing, it will start slowing down and eventually stop moving. It may seem that the only force acting on your book is the force applied. In reality there is another force that acts on the book: the force of friction between the book and the table. The book comes to a stop once the pushing force is gone not because rest is its “natural state” but because the force of friction is still there acting on the book. If the same book was pushed along a smooth icy surface it would travel much farther before it stops. Now imagine an ideal case where there is no friction: the book would continue to move forever as a result of one push from your hand. 3) The word inertia describes the tendency of all objects to continue with their previous motion when the net force is zero. We correlate the inertia of an object with its mass. Mass can be thought of as a measure of the matter content of an object; but for motion, mass is a measure of its inertia. It is harder to make an object with a lot of mass (lot of inertia) deviate from its path than an object with less mass (and less inertia). Unit 4: Forces Page 35 Freshman Physics Name __________________________ Hour______ Newton’s First Law can be restated as: An object with a lot of inertia (i.e. a lot of mass) is harder to deviate from its trajectory (i.e. it takes a lot of force to change its motion) than an object with less inertia. 4) Now let’s get back to the example of your book moving forever if there is no friction acting on it. Newton’s First Law actually says two things: a) in the absence of a net force, an object keeps moving as it was moving and b) in the presence of a net force, a body changes its motion. Unit 4: Forces Page 36 Freshman Physics Name __________________________ Hour______ 4.6. Practice: Force Diagrams II Identify your receiver with a dotted line. Be aware that if you cannot identify the agent for a force, it means that there is no force! Draw a force diagram in the space provided and discuss if forces acting on the receiver are balanced or not. Force Diagram Are forces balanced or not? A. Draw a force diagram for the hockey player sliding at constant speed across the ice. B. Draw a force diagram for the bowling ball after it left Dan’s hand. C. Draw a force diagram for the ascending balloon. Unit 4: Forces Page 37 Freshman Physics Name __________________________ Hour______ D. Draw a force diagram for Allie (and sled) speeding down the hill. E. Draw a force diagram for Dan who slides down the slide. Unit 4: Forces Page 38 Freshman Physics Name __________________________ Hour______ 4.7. Practice: Broom Ball Lab Revisited Broom ball is the physics game you played at the beginning of this unit. The objective is to use a broom to cause a bowling ball to move along a specific course in the smallest amount of time without leaving the boundaries of the course. Consider the course shown below, where you start at A and stop at H. Assignment: For each of the lettered positions (A through H) on the diagram above, you will be asked to do the following: 1. Draw the force applied by the broom on the ball. 2. Draw the direction of the velocity of the ball at that position. 3. Describe the motion of the ball as one or more of the following: at rest, speeding up, slowing down, constant speed, changing directions. Unit 4: Forces Page 39 Freshman Physics Name __________________________ Hour______ After completing the table above, answer the following questions: 1. At which points is the direction of the force the same as the direction of motion (direction of the velocity)? 2. What is the effect of a force applied in the same direction as the direction of motion of the object? 3. Between what points did the direction of the force change? Did the direction of motion also change between those points? Is there a connection between these two changes? 4. At which points is the direction of the force different than the direction of motion (direction of the velocity)? 5. What is the effect of a force applied in a different direction than the direction of motion? 6. Was there a place where no force was applied by the broom? How did the ball move at that place? Explain your answer. Unit 4: Forces Page 40 Freshman Physics Name __________________________ Hour______ 4.8. Practice: Newton’s First Law 1. A sheet of paper can be withdrawn from under a container of milk without toppling it if the paper is jerked quickly. This best demonstrates that a) the milk carton has no acceleration. b) gravity tends to hold the milk carton secure. c) the milk carton has inertia. d) none of the above. Explain your answer: 2. A school bus is moving at constant velocity. Inside the bus, a student drops a tennis ball from his hand. The ball hits the floor a) exactly below the student’s hand. b) ahead of the student’s hand. c) behind the student’s hand. d) more information is needed to solve this problem. e) none of the above. Explain your answer: 3. If your automobile runs out of fuel while you are driving, the engine stops but you do not come to an abrupt stop. The concept that most explains why this occurs is a) inertia. b) gravity. c) acceleration. d) resistance. Explain your answer: 4. According to Newton's law of inertia, a rail road train in motion should continue going forever even if its engine is turned off. We never observe this because railroad trains a) move too slowly. b) are much too heavy. c) must go up and down hills. d) always have forces that oppose their motion. Explain your answer: Unit 4: Forces Page 41 Freshman Physics Name __________________________ Hour______ 5. Whirl a rock at the end of a string and it follows a circular path in a horizontal plane. If the string breaks, the tendency of the rock is to a) continue to follow a circular path. b) follow a straight-line path. c) increase its speed d) revolve in a smaller circle Explain your answer: 6. When a rocket ship accelerating in outer space runs out of fuel it a) accelerates for a short time, then slows down to a constant velocity. b) accelerates for a short time, slows down, and eventually stops. c) no longer accelerates. Explain your answer: 7. Compared to a 1-kg block of solid iron, a 2-kg block of solid iron has twice as much a) inertia. b) mass. c) volume. d) all of the above. e) none of the above. Explain your answer: 8. If one object has twice as much mass as another object, it also has twice as much a) inertia. b) velocity. c) acceleration due to gravity. d) all of the above. Explain your answer: Unit 4: Forces Page 42 Freshman Physics Name __________________________ Hour______ Reading Page: Newton’s Third Law What is the connection between forces acting on two objects interacting with each other? Let’s consider the simple interaction between a hammer and a nail. The hammer exerts a force on the nail as it drives it into the wall. At the same time, the nail exerts a force on the hammer. If you are not sure that it does, imagine hitting the nail with a banana or a glass hammer. It is the force of the nail on the banana that pokes holes into it or shatters the glass. Let’s look now at the picture on left: a mom is pulling on her son, trying to get him away from his computer. The mom interacts with her son, and her son interacts with the computer. We have already learned how to identify all the forces acting on the boy, or on the mom or on the computer. But how do we deal with objects that interact with each other, such as the mom and the boy, or the boy and the computer? Newton’s Third Law explains how two objects/systems interact with each other. Every time an object A pushes or pulls on an object B, object B pushes or pulls back on object A. When the mom pulls on the boy, the boy pulls back (and she feels this in her arms). The two objects, mom and boy, are interacting. An interaction is the mutual influence of two systems on each other. The boy and mom are also interacting with the ground/earth. Let’s analyze all forces acting on the mom: And now let’s analyze all forces acting on the boy: The pulling force applied by the mom on the boy is the action force, and the pulling force applied by boy on his mom’s arms is the reaction force. Although we name one force the action and the other force the reaction for convenience, these two forces occur simultaneously and one cannot strictly specify which one is the “action” and which one is the “reaction”. An action/reaction pair of forces exists as a pair, or not at all. Also, paired action and reaction forces have (a) the same magnitude, (b) act in opposite directions and (c) act on different objects. But how about the rest of the forces acting on the boy and mom? Are they part of an action/reaction pair? Yes, all forces in the universe are part of action/reaction pairs – there are no forces that act alone. If you look only at the forces acting on the boy it may seem that these forces are isolated but that is because we have chosen our system to be one single object: the boy. All Unit 4: Forces Page 43 Freshman Physics Name __________________________ Hour______ forces acting on the boy arise from his interaction with the environment (which is outside for the chosen system). To be able to identify all the action reaction forces we must consider the expanded system which consists of boy, his mom and the ground. Let’s now identify all the action reaction pairs that act in the system. In the diagram below the action reaction forces are connected through a dotted line. For each force applied on the boy, there is a force the boy applies to another object. The same holds true for the mom. All interaction forces between boy and mom, boy and ground, and mom and ground are contact forces. The exception is the weight applied by earth, which is a long range force. How do action reaction pairs work for long range forces? If you let a ball fall, it will move down toward the earth because the earth pulls on it with a force called weight, the action force. But does the ball pull on the earth? Is there a “reaction” force acting on the earth? Indeed there is. The ball also attracts the earth with the same amount of force – the weight of the object. Does the earth then fall toward the ball? Yes, it does. But since the earth is huge and the ball is very small what one observes is a larger effect on the small ball. A similar effect occurs with two magnets: two magnets attract or repel each other through a long range force that can act at a distance. If you hold a magnet in each hand, you can feel the force acting on each magnet because long range forces come in pairs too. Unit 4: Forces Page 44 Freshman Physics Name __________________________ Hour______ There is only one force in the boy + mom + ground diagram for which a force pair is not drawn: the friction force applied by the keyboard on the boy’s fingers. Is there no pair for this force? Yes, there is: the force with which the boy’s fingers act on the keyboard. We have not drawn the reaction for that force intentionally. Whenever we deal with Newton’s Third Law we must define the system of interacting object. In our case the system was boy + mom + ground/earth. The computer was an external object to our system and thus the force applied by the computer to the boy’s fingers is considered an external force. Newton’s Third Law states that: 1. Every force occurs as one member of an action/reaction pair of forces. 2. The two members of an action/reaction pair act on two different objects. 3. The two members of an action/reaction pair point in opposite directions, and are equal in magnitude. Rules to follow when identifying action/reaction pairs: 1. Identify the objects that are systems of interest. Other objects whose motion you don’t care about are part of the environment. 2. Draw each object separately. Place them in the correct position relative to other objects. Don’t forget to include objects like the earth that may not be mentioned in the problem. 3. Identify every force. Draw the force vector on the object on which it acts. Label each with a subscripted label. The usual force symbols can be used. 4. Identify the action/reaction pairs. A force goes with a force. Connect the two force vectors of each action/reaction pair with a dotted line. When you’re done, there should be no unpaired forces. 5. Draw a free-body diagram for each object within the system. Include only the forces acting on the objects in your system, not forces that the objects in your system exert on other objects. Newton’s third law is one of the fundamental symmetry principles of the universe. Since we have no examples of it being violated in nature, it is a useful tool for analyzing situations which are somewhat counter-intuitive. For example, when a small truck collides head-on with a large truck, your intuition might tell you that the force on the small truck is larger. Not so! Both cars experience the same force. But why does the small car sustain much more damage than the truck? That has to do with Newton’s Second Law! Unit 4: Forces Page 45 Freshman Physics Name __________________________ Hour______ Notes: Unit 4: Forces Page 46 Freshman Physics Name __________________________ Hour______ 4.9. Practice: Identifying Pairs of Forces 1. Wherever there is an action force, there must be a reaction force which a) always acts in the same direction. b) is slightly smaller in magnitude than the action force. c) is slightly larger in magnitude than the action force. d) is exactly equal in magnitude. Explain: 2. An archer shoots an arrow. Consider the action force to be exerted by the bowstring against the arrow. The reaction to this force is the a) combined weight of the arrow and bowstring. b) air resistance against the bow. c) friction of the ground against the archer's feet. d) grip of the archer's hand on the bow. e) arrow's push against the bowstring. Explain: 3. A player catches a ball. Consider the action force to be the impact force of the ball against the player's glove. The reaction to this force is the a) player's grip on the glove. b) force the glove exerts on the ball. c) friction of the ground against the player's shoes. d) muscular effort in the player's arms. e) none of these Explain: 4. A player hits a ball with a bat. The action force is the impact force of the bat against the ball. The reaction to this force is the a) air resistance on the ball. b) weight of the ball. c) force that the ball exerts on the bat. d) grip of the player's hand against the ball. e) weight of the bat. Explain: Unit 4: Forces Page 47 Freshman Physics Name __________________________ Hour______ 5. For all the pictures shown below: a) Select two objects that interact with each other. b) Draw force diagrams for each object separately, clearly labeling each force with the receiver and agent’s name. c) Identify the action reaction pair of forces for the two interacting objects. Example Object 1: Cake & Object 2: Plate Force Diagram for cake: Force Diagram for plate: Applied Action force: normal force on cake by plate Reaction force: applied force on plate by cake A. _____________ Force Diagram for Force Diagram for & _______________ Action Force: Reaction Force: B. ____________ & Force Diagram for Force Diagram for _____________ Action Force: Reaction Force: Unit 4: Forces Page 48 Freshman Physics C. ____________ & Name __________________________ Hour______ Force Diagram for Force Diagram for _____________ Action Force: Reaction Force: D. ______________ & Force Diagram for Force Diagram for ________________ Action Force: Reaction Force: E. _______________ & Force Diagram for Force Diagram for _______________ Action Force: Reaction Force: Unit 4: Forces Page 49 Freshman Physics Name __________________________ Hour______ 6. Use choices (A – G) for cases 1 and 2 below for when a large truck and a small car collide. A) The truck exerts a greater amount of force on the car than the car exerts on the truck. B) The car exerts a greater amount of force on the truck than the truck exerts on the car. C) Neither exerts a force on the other; the car gets smashed simply because it is in the way of the truck. D) The truck exerts a force on the car but the car doesn't exert a force on the truck. E) The truck exerts the same amount of force on the car as the car exerts on the truck. F) Not enough information is given to pick one of the answers above. G) None of the answers above describes the situation correctly. Case 1: Which choice describes the forces when the truck is much heavier than the car. _______They are both moving at the same speed when they collide. _______The car is moving much faster than the heavier truck when they collide. _______The truck is moving much faster than the car when they collide. _______The car is standing still when the truck hits it. _______The heavier truck is standing still when the car hits it. Case 2: Which choice describes the forces when the truck is a small pickup truck and has the same mass as the car. _______They are both moving at the same speed when they collide _______The car is moving much faster than the truck when they collide. _______The truck is moving much faster than the car when they collide. _______The car is standing still when the truck hits it. _______The truck is standing still when the car hits it. Unit 4: Forces Page 50 Freshman Physics Name __________________________ Hour______ 7. Use choices (A – F) for cases 1 below for when a large truck breaks down and receives a push back to town from a small compact car. A) The force of the car pushing against the truck is equal to that of the truck pushing back against the car. B) The force of the car pushing against the truck is less than that of the truck pushing back against the car. C) The force of the car pushing against the truck is greater than that of the truck pushing back against the car. D) The car's engine is running so it applies a force as it pushes against the truck, but the truck's engine isn't running so it can't push back with a force against the car. E) Neither the car nor the truck exerts any force on each other. The truck is pushed forward simply because it is in the way of the car. F) None of these descriptions is correct. Case 1: Which choice describes the forces between the car and the truck. _______The car is pushing on the truck, but not hard enough to make the truck move. _______The car, still pushing the truck, is speeding up to get to cruising speed. _______The car, still pushing the truck, is at cruising speed and continues to travel at the same speed. _______The car, still pushing the truck, is at cruising speed when the truck puts on its brakes and causes the car to slow down. Unit 4: Forces Page 51 Freshman Physics Name __________________________ Hour______ 8. Farmer Brown hitches Old Dobbin to his wagon one day, then says, "OK, Old Dobbin, let's go!" Old Dobbin turns to Farmer Brown and says "Do you remember how Newton's Third Law says that every action force has an equal and opposite reaction force?”. Ignoring Farmer Brown's impatience, he continues, "If the wagon's pull is always equal and opposite of my pull, then the net force will always be zero, so the wagon can never move! Since it is at rest, it must always remain at rest, according to Newton’s 1st law! So, get over here and unhitch me! I have just proven that Newton's Laws say that it is impossible for a horse to pull a wagon!" At this point, Farmer Brown throws up his hands in dismay and turns to you. "Please help me!" he says, "I really should have paid more attention in physics class! I know that Newton's Laws are correct, and I know that horses really can pull wagons.” Help Farmer Brown by drawing separate force diagrams for the wagon, the horse, and the horse and the wagon together. Then explain in words the flaw in the horse’s reasoning. (Your answer should include three force diagrams with an explanation for each.) Unit 4: Forces Page 52 Freshman Physics Name __________________________ Hour______ 4.10. Practice: Identifying Pairs of Forces II For each of the following problems, draw a physical diagram; construct a separate force diagram for each object, labeling each force with its type, agent and receiver. Circle any Newton’s 3rd law pairs that occur in your force diagrams. 1. One book lies on top of another book, which rests on a table. System: the two books. Physical Diagram Force Diagram: top book Force Diagram: bottom book Fon book A by book B Fon book B by table book A book B Fon book A by Earth Fon book B by book A Fon book B by Earth 2. A person exerts an upward force to hold a bag of groceries. System: person’s hand and bag of groceries. Physical Diagram Force Diagram: hand Force Diagram: bag of groceries 3. A broom is pushing against a bowling ball and makes it move. System: broom and bowling ball Physical Diagram Force Diagram: broom Force Diagram: bowling ball 4. You are pushing a box across a very rough floor. System: you and the box. Physical Diagram Force Diagram: you Force Diagram: box Unit 4: Forces Page 53 Freshman Physics Name __________________________ Hour______ 5. (a) Eric holds a ball in his hand, and is in the process of throwing the ball upward. System: hand and ball. Physical Diagram Force Diagram: hand Force Diagram: ball (b) The ball just left Eric’s hand. System: ball and hand. Physical Diagram Force Diagram: hand Force Diagram: ball (c) The ball is on its way down. System: ball and hand. Physical Diagram Force Diagram: hand Force Diagram: ball (d) The ball has just hit the ground, and is slowing down. System: ball and ground. Physical Diagram Force Diagram: hand Force Diagram: ball Unit 4: Forces Page 54 Freshman Physics Name __________________________ Hour______ 4.11. Practice: Newton’s Third Law Problems 1. While driving down the road, an unfortunate butterfly strikes the windshield of your car. You are thinking: this is a case of Newton's third law of motion! The butterfly hit the car windshield and the car windshield hit the butterfly. Which of the two forces is greater: the force on the butterfly or the force on the car’s windshield? Explain. 2. Andy goes hunting for the first time. He has just learned Newton’s Third Law and is now ready to explain to his dad why the gun recoils when it is fired. He tells his dad that the recoil is the result of action-reaction force pairs. As the gases from the gunpowder explosion expand, the gun pushes the bullet forwards and the bullet pushes the gun backwards. His dad has a question for Andy (and you must answer it): How are the forces that act on the gun and on the bullet related and why? 3. A karate chop delivers a blow of 3000 N to a board that breaks. The force that acts on the hand during this event is a) zero. b) 1500 N. c) 3000 N. d) 6000 N. Explain: 4. Arnold Strongman and Suzie Small each pull very hard on opposite ends of a rope in a tug-ofwar. The greater force on the rope is exerted by a) Arnold, of course. b) Suzie, surprisingly. c) both exert the same force. Explain: Unit 4: Forces Page 55 Freshman Physics Name __________________________ Hour______ 5. A big truck and a small car traveling at the same speed have a head-on collision. The impact force is a) greater on the small car. b) greater on the big truck. c) the same for both. Explain: 6. A 10.0 N force is pulling vertically up on the ring of spring scale that weighs 2.0 N. If an 8.0 N mass is attached to the bottom hook of the scale, the scale reading would be a) 0 N. b) 2.0 N. c) 8.0 N. d) 10.0 N e) 12.0 N Explain: 7. A horse pulling a wagon forward exerts 500 N of force on the heavy wagon. The wagon pulls back on the horse with an equal force. a) The wagon moves forward because these forces are not an action-reaction pair. b) The wagon moves forward because there is an unbalanced force on the wagon. c) The wagon moves forward because the horse pulls on the wagon a brief time before the wagon reacts. d) The wagon cannot move because these forces are equal and opposite. Explain: Unit 4: Forces Page 56 Freshman Physics Name __________________________ Hour______ Reading Page: Newton’s Second Law Newton’s first law told us what happens when no net external force acts: a) Things that are sitting still will not move on their own, they need an outside force to make them move. b) Things that are moving in a straight line will not stop, slow down or speed up on their own, they need an external force to change their motion. c) Things that are moving in a straight line will not change direction unless a force makes them do so. So it is pretty clear that if a net external force does act, a) Things that are sitting still can begin to move. b) Things that are moving can be made to slow down, speed up or even stop. c) Things that are moving in one direction can be made to change direction. In the previous activity we saw that a net external force changes the motion of an object by making it accelerate. How does that go along with the statements above? Things that are sitting still can begin to move: the object had a velocity of zero to begin with, and after a force is applied, it accelerates to a higher velocity. Things that are moving can be made to slow down (force is applied to change a high velocity to low velocity) speed up or even stop. Things that are moving in one direction can be made to change direction – this is also a change in velocity, namely, the amount of velocity may not have changed, but the direction has, so there is a net acceleration. We also saw in the previous activity that the amount of mass affects the force applied. In other words, for two masses to have the same acceleration, the larger mass needs a larger force. In equation form, Force = (mass) x (acceleration) or in equation form F ma A lot of the applications of Newton’s second law deal with the fact that several forces can act on an object, but if the forces don’t all balance out then there is a net external force. This net force causes acceleration – and the acceleration will be along the direction of that net force. If all forces balance out, the object will either be at rest (or in equilibrium) or move with a constant velocity. In the examples below all forces are drawn and a motion diagram is associated to each example. Example 1: A Teddy Bear sits on a table. Unit 4: Forces The weight acts downward, and the normal force acts upward. They balance each other out; the bear does not move. We know the two forces are equal because; a) if FG > FN the bear would fall downward b) if FN > FG the bear would fly upward c) since it stays put, FN = FG Page 57 Freshman Physics Name __________________________ Hour______ Example 2: A bear sitting on a table is pushed gently to the right but does not move. In the vertical direction: The weight acts downward, the normal force upward. They balance each other out; bear does not move in the vertical direction. In the horizontal direction: The pushing force Fpush to the right is opposed by the force of friction, Ff; Since there is no motion along the horizontal direction, the pushing force must balance the force of friction: Fpush = Ff. Example 3: The bear is being pulled on a table and moves to the right with constant speed. Vertical: The weight acts downward, the normal force upward. They balance each other out; bear does not move along the vertical direction. Horizontal: Since the bear moves to the right, the force of friction acts toward the left since friction always opposes motion. Constant velocity means that there are no net forces acting in the horizontal direction. Therefore the pulling force and the force of friction balance each other: F(pull) = Ff Example 4: The bear is being pulled on a Vertical: table and moves to the right with The weight acts downward, the normal force upward. constant acceleration. They balance each other out; bear does not move along the vertical direction. Horizontal: Since the bear accelerates to the right, the force of friction acts toward the left since friction always opposes motion. Acceleration to the right means that the net force acting in the horizontal direction is to the right. Therefore the pulling force must be stronger than the force of friction for the bear to accelerate to the right. FN a Ff F(pull) Fnet = ma where Fnet = Fpull - Ff Fg Unit 4: Forces Page 58 Freshman Physics Name __________________________ Hour______ 4.12. Practice: Newton’s Second Law Problems 1. A 10-kg brick and a 1-kg book are dropped in a vacuum. The force of gravity on the 10-kg brick a) is the same as the force on the 1-kg book. c) is one-tenth as much. b) is 10 times as much d) is zero. Explain your answer: 2. If an object's mass is decreasing while a constant force is applied to the object, would its acceleration decrease, increase, or remain the same? Explain. 3. An object is propelled along a straight-line path in space by a force. If the object sweeps up extra particles and its mass becomes twice as much, its acceleration a) quadruples. d) halves. b) doubles. e) none of these c) stays the same. Explain your answer: 4. The force of friction on a sliding object is 10 newtons. Would the applied force needed to maintain a constant velocity be more than 10 N, less than 10 N or 10 N? Explain. 5. A 10-N falling object encounters 4 N of air resistance. The net force on the object is a) 6 N upwards. d) 10 N downwards. b) 4 N upwards. e) none of these. c) 6 N downwards. Explain your answer: 6. A 10-N falling object encounters 10 N of air resistance. The net force on the object is a) 0 N. d) 10 N. b) 4 N. e) none of these c) 6 N. Explain your answer: Unit 4: Forces Page 59 Freshman Physics Name __________________________ Hour______ 7. An apple weighs 1 N. When held at rest above your head, what is the net force on the apple? 8. An apple at rest weighs 1 N. Tammy throws it up in the air. a) What is the net force on the apple on its way up? What is the direction of the acceleration? b) What is the net force on the apple during the time is falling? What is the direction of the acceleration? 9. A 1-kg rock that weighs 9.8 N is thrown straight upward at 20 m/s. Neglecting air resistance, would the net force that acts on it when it is half way to the top of its path be less than 9.8 N, 9.8 N, or more than 9.8 N? 10. Which case has zero acceleration? a) A car stopped in front of your house. b) A child biking past your house at constant velocity. c) Sledding down a very steep hill. d) B and C only e) A and B only Explain your answer: 11. Whenever the net force on an object is zero, would its acceleration be less than zero, zero, or more than zero? Explain. 12. Your car is coasting on level ground at 60 km/h and you apply the brakes until the car slows to 40 km/h. If you suddenly release the brakes now, would the car tend to momentarily regain its higher initial speed, continue moving at 40 km/h, or decrease in speed if no other forces act? Explain. Unit 4: Forces Page 60 Freshman Physics Name __________________________ Hour______ 13. When you hang from a pair of gym rings, the upward support forces of the rings will always a) each be half your weight. c) add up to equal your weight. b) each be equal to your weight. Explain your answer: 14. A car has a mass of 2000 kg and accelerates at 2 meters per second per second. What is the magnitude of the net force exerted on the car? 15. A tow truck exerts a force of 3000 N on a car, accelerating it at 2 meters per second per second. What is the mass of the car? 16. A girl pulls on a 10-kg wagon with a constant horizontal force of 30 N. If there are no other horizontal forces, what is the wagon's acceleration in meters per second per second? 17. A force of 1 N accelerates a mass of 1 kg at the rate of 1 m/s2. The acceleration of a mass of 2 kg acted upon by a net force of 2 N is a) half as much. c) the same. b) twice as much. d) none of these Explain your answer: 18. An object following a straight-line path at constant speed a) has a net force acting upon it in the c) has no forces acting on it direction of motion. d) none of these b) has zero acceleration. Explain your answer: Unit 4: Forces Page 61 Freshman Physics Name __________________________ Hour______ 19. A man weighing 800 N stands at rest on two bathroom scales so that his weight is distributed evenly over both scales. The reading on each scale is a) 200 N. d) 1600 N. b) 400 N. e) none of these c) 800 N. Explain your answer: 20. When a woman stands at rest with both feet on a scale, it reads 500 N. When she gently lifts one foot, the scale reads a) less than 500 N. c) 500 N. b) more than 500 N. Explain your answer: 21. A 10-N block and a 1-N block lie on a horizontal frictionless table. To provide them with equal horizontal acceleration, we would have to push with a) equal forces on each block. b) 10 times as much force on the heavier block. c) 10 squared or 100 times as much force on the heavier block. d) 1/10 as much force on the heavier block. e) none of these Explain your answer: 22. A block is dragged without acceleration in a straight-line path across a level surface by a force of 6 N. What is the force of friction between the block and the surface? a) less than 6 N c) 6 N b) more than 6 N d) need more information to say 23. Suppose a particle is being accelerated through space by a 10-N constant force. Suddenly the particle encounters a second force of 10 N in the opposite direction from the first force. The particle with both forces acting on it a) is brought to a rapid halt. b) decelerates gradually to a halt. c) continues at the speed it had when it encountered the second force. d) theoretically tends to accelerate toward the speed of light. e) none of these Unit 4: Forces Page 62 Freshman Physics Name __________________________ Hour______ 4.13. Practice: Newton’s Third and Second Laws with Blocks For each of the situations below compare the forces exerted by the blocks on each other as they move on a table with some friction. Note: the 100 g block experiences twice as much frictional force as the 50 g block. For each of the problems A through F, select from the following choices: a) block A exerts a greater force b) block B exerts a greater force c) the forces are equal Also draw separate force diagrams for block A, for block B, and for a system that includes both blocks. Block A Block B Block A+B together 1. Both blocks move with constant speed to the left 2. Both blocks move with constant speed to the left 3. Both blocks move with constant speed to the left. 4. Both blocks move with constant acceleration to the left. 5. Both blocks move with constant acceleration to the right. Unit 4: Forces Page 63 Freshman Physics Unit 4: Forces Name __________________________ Hour______ Page 64 Freshman Physics Name __________________________ Hour______ 4.14. Practice: Balanced Forces 1. Draw force diagrams for the following situations: An object lies motionless on a flat, horizontal surface. Two equal forces in opposite directions along the horizontal act on an object that lies motionless on a flat surface. 2. A swing is suspended by two ropes. Amy and Ryan sit together on the swing. The swing’s weight is 60 N. Amy’s weight is 520 N and Ryan’s is 640 N. Draw a diagram indicating all forces acting on your system (Amy, Ryan, swing). If the tension in the two support ropes are equal, calculate those tensions. Unit 4: Forces Page 65 Freshman Physics Name __________________________ Hour______ 3. Qi and Jared sit on a board that is suspended by two cables. Qi weighs 590 N and Jared weighs 850 N. The board weighs 180 N. The tension in one of the ropes is 670 N. Draw a diagram for all forces acting on the system (Qi, Jared, board). a) Calculate all the downward forces. b) Calculate all the upward forces. d) Use the idea that the net force is zero to calculate the tension in the second rope. 4. Draw force diagrams for the following situations: a) An object is suspended from the ceiling by a rope. Unit 4: Forces Page 66 Freshman Physics Name __________________________ Hour______ b) An object is suspended from the ceiling by two parallel ropes. c) The tension in the cable is 100 N. Find the mass of the tire. d) The tension in the cable on the left is 30 N. Draw a force diagram and then calculate the mass of the ball. Hint: how is the tension in the second cable compared to the tension in the first one? Unit 4: Forces Page 67 Freshman Physics Name __________________________ Hour______ e) Draw the force diagrams and figure out the tension in each cable for case (a) and case (b). (a) (b) f) An owl is sitting on a branch in a tree. The owl’s mass is 1.2 kg. Draw a force diagram of the owl and calculate the normal force acting on it. Unit 4: Forces Page 68 Freshman Physics Name __________________________ Hour______ g) The force with which the balance beam pushes up on the gymnast is 450 N. Knowing that the gymnast is in equilibrium on the beam (all forces acting on her are balanced), draw a force diagram and find the gymnast’s mass. 5. A block is sitting at rest on a level floor. The normal force on the block is 3.00 N. Draw a picture, identify the system, define the system with a curve, draw a force diagram and then calculate the mass of the block. Unit 4: Forces Page 69 Freshman Physics Unit 4: Forces Name __________________________ Hour______ Page 70 Freshman Physics Name __________________________ Hour______ 4.15. Practice: Force Diagrams related to Motion 1. Draw a force diagram for each one of the cases shown below: Indicate the direction of the acceleration for each object. A. Equilibrium B. Equilibrium C. Friction prevents sliding D. Equilibrium E. Equilibrium F. Equilibrium G. Rock is sliding on a frictionless incline H. Rock is falling. No air resistance. I. Rock is falling with constant speed. Air resistance is present. J. Rock is sliding at constant speed on a frictionless surface K. Rock is slowing down because of friction. L. Rock pulled by a rope moves horizontally at constant velocity. There is friction with ground. Unit 4: Forces Page 71 Freshman Physics Name __________________________ Hour______ M. Rock is rising in a parabolic N. Rock is at the top of a trajectory. parabolic trajectory. O. Rock is tied to a rope and pulled so that it accelerates horizontally. 2. For the following problems, draw a picture of the system described and a force diagram. Picture A. Draw the force diagram for: Book Verbal description A book is at rest on a table top. B. Backpack A student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. C. Book A rightward force is applied to a book in order to move it across a desk at constant velocity. D. Skydiver A skydiver is descending with a constant velocity. Consider air resistance. Unit 4: Forces Page 72 Freshman Physics Name __________________________ Hour______ Picture E. Draw the force diagram for: Person F. Bird G. Pot H. Child I. Skier Unit 4: Forces Verbal description Page 73 Freshman Physics Unit 4: Forces Name __________________________ Hour______ Page 74 Freshman Physics Name __________________________ Hour______ 4.16. Practice: Force Diagrams, Motion Diagrams and Newton’s Laws 1. For each of the situations below, draw a picture and then the force diagram. A. A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book. B. A force is applied to the right to drag a sled across looselypacked snow with a rightward acceleration. Diagram the forces acting upon the sled. C. A football is moving upwards towards its peak after having been booted by the punter. Diagram the forces acting upon the football as it rises upward towards its peak. D. A car is coasting to the right and slowing down. Diagram the forces acting upon the car. E. An egg falls from a nest in a tree. Neglect air resistance. Diagram the forces acting on the egg as it falls. Unit 4: Forces Page 75 Freshman Physics Name __________________________ Hour______ 2. In the following problems you are given a representation of the motion that occurs. Fill in the rest of the table. A. Picture of motion (the points are drawn at equal 1 second time intervals) Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram: Verbal description of motion: B. Picture of motion (the points are drawn at equal 1 second time intervals) Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram: Verbal description of motion: Unit 4: Forces Page 76 Freshman Physics Name __________________________ Hour______ C. Picture of motion (the points are drawn at equal 1 second time intervals) Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram: Verbal description of motion: D. Picture of motion (the points are drawn at equal 1 second time intervals) Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram Verbal description of motion Unit 4: Forces Page 77 Freshman Physics Name __________________________ Hour______ E. Picture of motion Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram: Verbal description of motion F. Picture of motion Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram Verbal description of motion Unit 4: Forces Page 78 Freshman Physics Name __________________________ Hour______ G. Picture of motion Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram: Verbal description of motion and force diagram H. Picture of motion Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram Verbal description of motion Unit 4: Forces Page 79 Freshman Physics Name __________________________ Hour______ I. Picture of motion Motion diagram (including position, velocity and acceleration) Position, velocity and acceleration vs time graphs Force diagram Verbal description of motion Unit 4: Forces Page 80 Freshman Physics Name __________________________ Hour______ 3. In the following table you are given either the motion diagram, force diagram, verbal description, or a graph. Fill in the rest of the table. A. Motion Diagram Force Diagram (you must label all forces) Verbal Description Position, velocity and acceleration vs time graphs B. Motion Diagram Force Diagram (you must label all forces) Verbal Description: You throw a ball up into the air. Describe what happens from the instant it leaves your hand up until it reaches its highest point. Position, velocity and acceleration vs time graphs Unit 4: Forces Page 81 Freshman Physics Name __________________________ Hour______ C. Motion Diagram of an airplane on a runway Force Diagram (you must label all forces) Verbal Description Position, velocity and acceleration vs time graphs D. Motion Diagram Force Diagram (you must label and draw all forces) Verbal Description: A box is pulled up a ramp that has no friction. Continue the description of its motion: Position, velocity and acceleration vs time graphs Unit 4: Forces Page 82 Freshman Physics Name __________________________ Hour______ E. Motion Diagram Force Diagram (you must label and draw all forces) Verbal Description: Position, velocity and acceleration vs time graphs 4. The motion of a cart in three different situations is described below . a) A cart is released from the top of a frictionless ramp. Which of the following best describes the situation after the cart was released? Explain your reasoning. b) After the cart reaches the bottom of the ramp, a boy gives it a shove and sends it moving up the ramp. Which of the following best describes the situation just after the cart was shoved? Explain your reasoning. c) After it was shoved upward in the previous problem, the cart reaches the highest point it can reach on the ramp. Which of the following best describes the situation at the instant when the cart is at its highest point? Explain your reasoning. Unit 4: Forces Page 83 Freshman Physics Unit 4: Forces Name __________________________ Hour______ Page 84 Freshman Physics Review:Forces Name __________________________ Hour______ What is a force? A force is nothing else than a push or a pull applied by one object to another. Type of Forces Symbol FN or Fn FG or Fg Ff FT Fe Name Normal force Gravitational force (or weight force) Friction force Tension force Elastic force Type of force Contact force Non-contact force (field force) Contact force Contact force Contact force Analyzing forces Steps to follow when analyzing forces acting on an object: 1. Determine the object that is the receiver (has forces applied to it). 2. Identify the agents (objects that apply forces to the receiver). 3. For each agent, identify the force it applies. (Note: remember that we live on Earth and therefore Earth (agent) always applies a force (gravity) to every single object (receiver) on its surface). 4. Represent the direction of the force with an arrow starting on the receiver. 5. Describe the effect of the identified forces on the receiver. Force Diagrams Steps to follow when drawing force diagrams: 1. Draw a picture of the problem, showing the object and everything in the environment that touches the object – ropes, tables, springs are all part of the environment. 2. Identify the system – which is the object or objects of interest – and draw a closed curve around the system. The object should be inside the curve and everything else outside the curve. 3. Locate every point in the system at the boundary of the curve where the environment touches the system. These are the points where the environment exerts contact forces on the system. 4. Identify by name all the contact forces at each point of contact (there may be more than one force), then give each one an appropriate symbol. 5. Identify any long-range forces acting on the object. Name the force and write its symbol in the picture. 6. Indicate the object by a point and draw the force diagram. Calculating forces Force of gravity on Earth can be determined from: Fg mg where g = 9.8 N/kg. Elastic force can be calculated from: Fe k x where k = elastic constant and x is the stretch or compression of the spring. Netwon’s Laws: Unit 4: Forces Page 85 Freshman Physics Name __________________________ Hour______ Newton’s first law tells us what happens when no net external force acts on an object: a) Things that are sitting still will not move on their own, they need an outside force to make them move. b) Things that are moving in a straight line will not stop, slow down or speed up on their own, they need an external force to change their motion. c) Things that are moving in a straight line will not change direction unless a force makes them do so. Newton’s second law tells us what happens when a net external force does act on an object: a) Objects that are sitting still can begin to move: the object had a velocity of zero to begin with, and after a force is applied, it accelerates to a higher velocity. b) Objects that are moving can be made to slow down (force is applied to change a high velocity to low velocity), speed up, or stop. c) Objects that are moving in one direction can be made to change direction – this is also a change in velocity, namely, the amount of velocity may not have changed, but the direction has, so there is a net acceleration. Newton’s second law also gives us the connection between the net force, mass and acceleration: Force = (mass) x (acceleration) or in equation form F ma Newton’s Third Law explains how two objects/systems interact with each other. Every time an object A pushes or pulls on object B, object B pushes or pulls back on object A. Forces in nature always act in pairs; one force is called action and the other one reaction. The two forces are always equal, in opposite directions and act on different objects. Unit 4: Forces Page 86