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Forces Chapter 6 Pg. 117-147 6.1: Force and Motion Objectives Define a force Differentiate between contact and long-range forces Recognize the significance of Newton’s 2nd law of motion and use it to solve problems Explain Newton’s 1st law and use it to describe objects at equilibrium. Force and Motion Force – a push or pull on a object The object is known as the “system” The world around the object is the “environment” “F” is used to represent the magnitude or size of the force. HOW MANY FORCES CAN YOU NAME? Contact vs. Long-Range Forces Contact forces act on objects only when they come into contact with the object. They have to be touching the object. Friction is a contact force. Long-range forces can act on objects without having contact. Magnetic force is an example Force of Gravity – long-range force that acts on all objects. Attracts forces to each other. Forces have Agents Each force has an identifiable cause called an “agent” This is essentially what is is causing the force; if you cannot name the agent, the force does not exist. What is the agent of a ball falling to the ground? The first step to solving any problem is creating a force diagram or pictorial model of the event. We need to identify the system, the environment and all the forces acting upon the system. Some will be contact forces, some will be long-range or constant forces as well Forces have Agents Drawing pictorial models Identify the system and circle it Identify every place the system and environment are touching. Identify the contact forces Identify the long-range forces Replace object in model with a dot Use arrows to represent the forces Length of the arrow should equal magnitude of the force. Label the forces with “F” to identify the agent Try Practice Problem 1 on pg. 119 Newton’s 2nd Law of Motion States: The acceleration of an object equals the net force on that object divided by its mass. Gravity and friction influence almost everything, so if we can avoid those by performing experiments it is helpful. The best way to do so is study horizontal forces because gravity does not affect horizontal forces We can also perform the experiment with low friction wheels, on ice, or another low friction surface. Newton’s 2nd Law How do we exert a controlled force on an object? Stretching object work well, like a rubber band. The further you stretch the object, the greater the force exerted. Look at figure 6.2a on pg. 120 of the text. Determine acceleration of the object in 6.2b, but calculating the slope of the graph. How Acceleration Depends on Force You could repeat the experiment of the rubber band and low friction cart and continue to stretch the rubber band further. You can still determine the acceleration of the object no matter the stretch. The force and acceleration are proportional and create a linear relationship. The larger the force the greater the acceleration F = ka Force = k (slope of line) x acceleration How Does Acceleration Depend on the Object What happens if we increase mass of the object the force is being exerted on by 2-fold? 3-fold? You will find that if we double the mass of the object the acceleration will become ½ of what it was originally. This is because Force = mass x acceleration or F=ma This concept is simple: The heavier an object, the more force it takes to move it. Combining Forces What happens when we have more than once force exerting a push/pull on an object? Forces can act in the same direction, in opposite directions, and at directions that are angles of each other. We should use a free-body diagram to draw multiple forces A free-body diagram uses a dot with vectors drawn in the direction of the individual forces Look at Figure 6-4 to see examples Combining Forces The total force is always equal to the sum of all the individual forces acting upon the object. The sum of 2 or more forces is called the net force. The net force is the key: A = Fnet / m Measuring Force: The Newton The Newton (N) is the net unit of force 1 Newton is 1kgm/s2 F =ma : m =kg a = m/s2 Solve Practice Problems 2-6 on pg. 122 Newton’s 1st Law of Motion An object at rest will stay at rest unless acted upon by a force. An object in motion will stay in motion (in a straight line at a constant speed) unless acted upon by a force These two statements make up Newton’s 1st Law of Motion. But wait…….this does not always happen on Earth does it? NOPE!!!! Why? Because we are constantly being acted upon by a variety of forces that you do not even know about . Inertia Newton’s 1st law is often called the “law of inertia” Inertia is the tendency of an object to resist change. Things at rest want to stay resting Things moving want to stay moving Equilibrium If the sum of the forces on an object equal zero then the object is at equilibrium. Two states of equilibrium: Object is at rest Object is moving at a constant velocity Remember Rest is simply a special case of constant velocity = 0 Newton’s 1st law defines net forces as anything that disrupts an objects equilibrium Common sense: it is something that changes an objects velocity Physical Models: Free-Body Diagrams Look at Table 6-2 on pg. 123 This table shows a variety of forces and how they are defined. KNOW THEM!!!!! These forces are added, subtracted, etc to determine net force. BEING ABLE TO DRAW FORCE DIAGRAMS IS HUGELY IMPORTANT!!!!!!!!!!!!!!!!!! Try to draw force diagrams for Practice Problems 7- 11 on pg. 124 Common Misconceptions about Forces Friction dominates our world, so Newton’s laws are hard to visualize. Also, some every day words are also used interchangeably with words from physics; this causes issues: When you throw a ball, the force of the hand remains on the ball Forces are needed to keep an object moving Inertia is a force Air does not exert a force The quantity ma is a force Assignment 6.1 Review Pg. 125 Questions 1-5 Will grade tomorrow. 6.2: Using Newton’s Laws Objectives Describe how the weight and the mass of an object are related Differentiate between the gravitational force weight and what is experienced as apparent weight. Define the friction force Distinguish between static and kinetic friction Describe simple harmonic motion Explain how the acceleration due to gravity influences motion Using Newton’s 2nd Law Aristotle believed the heavier the object, the faster it falls. Galileo understood this, but knew to understand true motion, we must ignore certain factors, mainly air resistance/drag. We are trying to understand the forces that causes objects to fall/ move, so we ignore certain “Earth” factors. Mass and Weight No evidence Galileo actually dropped two balls from the Tower of Pisa (yes the leaning one), but his theory is very simple. He said that if Aristotle was correct then dropping two cannon balls from a given height would result in both falling at the same rate, however fastening them together and dropping them would result in them falling at 2x the first rate. Galileo said that this was incorrect and theorized that all object in free fall gain speed at the same rate, no matter what their weight is. We now know this to be true and the force that causes this acceleration is GRAVITY Mass and Weight The simplest way to picture the force of gravity (Fg) is to use Newton’s 2nd law (F= ma) For gravity this gives us Fg = mg The direction of both components is downward This means the magnitude of the force is equal to the force times the acceleration, which we also call weight This hold true on Earth at 9.8m/s2, but the force of gravity is different on different planets Scales Measure weight or the force you are exerting downward. Old scales use springs to counteract your force and then that is read by the scale. New scales have sensors that do this exact same thing This means your weight would be different on other planets because of the difference in the force of gravity Force and Motion Problem Solving 1. Read the problem carefully. Visualize the situation and 2. 3. 4. 5. 6. 7. 8. create a pictorial model Circle the system and choose your coordinate system Decide what quantities are known (givens) and which quantities you need to find (unknown). Assign symbols to your unknown. Create a motion diagram that shows the direction of the force and create a free-body diagram that shows the net force on the object Use Newton’s laws to link acceleration and net force Rearrange the equation to solve for a or F(net). Newton’s 2nd law uses vectors so it must be solved using X and Y directions Substitute the given quantities with their units in the equation and solve Check your results to make sure they make sense Example Problems P. 128 and 129 of textbook Try Practice Problems on pg. 129 (12 and 13) on your own. Apparent Weight The force exerted by the scale is measuring apparent weight. What happens if you stand one foot on and one foot off the scale? What happens in the elevator scenarios? What happens if the cable holding the elevator breaks and the acceleration is equal to – g? The scale would show your weight as zero. Does that mean you actually weigh nothing? No, it means there are no contact forces pushing up on you. The Friction Force Friction is the contact force that opposed motion. You attempt to push a large, heavy box across the floor. The laws of physic say that the box should move, but it does not move. Why? You push harder, the box still does not move; this means some force must exist between the box and the surface it is sitting on to counteract the force you are exerting on the box. This force is called the Static Friction Force This force acts in response to other forces Static and Kinetic Friction Finally you push hard enough for the box to move; I guess we overcame friction…… Not so fast, friction is still at play What happens when you stop pushing the box? The box stops moving? It slides a little bit then stops moving? This force that acts between two objects (surfaces) that are in relative motion is called the Kinetic Friction Force A Model for Friction Forces Friction forces are Complicated, but we can simplify them. The friction force is proportional to the magnitude of the force pushing one surface against another. That force, perpendicular to the surface, is the Normal force. The equation we use is: Force of Friction (kinetic) = kinetic coefficient of friction times the Normal force Ffk = μkFN A Model for Friction The static friction force relates to the normal force using this expression: 0≤ Ffs≥μsFN This tells you that the static friction force can range from zero to μs (static friction coefficient) times the Normal force. The static friction coefficient times the normal force is the maximum friction force that can be overcome, because higher than this the object begins to move. A Model for Friction The previous equations solve for the magnitude of the forces only. The friction force and normal force are at right angles to each other. Table 6-3 on pg. 131 shows several coefficients of friction that we will use to solve upcoming problems. Notice all listed coefficients are below 1.0 but that does not mean that all possible coefficients are below 1.0 Example Problems Look at Example Problems with Solutions on pg. 131-132 Try to Solve Practice Problems 14-16 Causes of Friction All surfaces, no matter how smooth they appear, are rough at a microscopic level. When you push an object across another object the high points of the surfaces temporarily bond You must break those bonds for the object to move This is the source of Static Friction As the object moves, there are still electrostatic attractions between the high points of the surfaces; this causes weak kinetic friction. Air Drag and Terminal Velocity As an object moves through air or a fluid, there is a friction-like force that exerted on that object. The big difference is that with air and fluids, the speed and shape of the object matter. The larger the object, the faster it is moving, or the more surface area = increase in the force. This is Drag When the drag force equals the force of gravity results in a constant velocity known as Terminal Velocity. The more aerodynamic an object the greater the possible terminal velocity Periodic Motion Playground swings sway back and forth in the same path, this is an example of vibrational motion Other examples are a pendulum in a clock, springs, and guitar strings. All of these have a zero, equilibrium point and are pulled away from this zero point, then restored to the zero point. When the force that restores equilibrium is directly proportional to the displacement of the object this is called Simple Harmonic Motion Periodic Motion Simple harmonic motion has 2 quantities represented T – the period The period is the time needed to complete one cycle of motion. Amplitude Amplitude is the maximum distance the object moves from the zero (equilibrium) point. Mass on a Spring Picture an object dangling from a spring Two forces are exerted on this object: the downward force of gravity and the upward force of the spring, which depends on how much the spring is stretched. Springs obey Hooke’s law The spring will work to match the force of the object it is connected to, thus putting the object at equilibrium. When we pull the object down, the spring will produce an upward force When we push the object up, the spring will produce a downward force. Mass on a Spring The further the spring is stretched or compressed, the stronger the restoring force exerted by the spring. Now when released, does the block just return back to equilibrium? No, inertia is too great causing the object to move past it’s equilibrium point and either compress or stretch the spring temporarily. This restarts the process. The period of vibration/oscillation “T” depends on the mass of the object and the strength of the spring, but not on the amplitude of the motion Pendulum Contains two parts: the bob (heavy end mass) and the rod/string with a length “l” The bob is pulled to one side, when released, the bob swings back and forth. A force of “T” is exerted by the rod and gravity exerts a force on the bob The sum of these two forces: FT and Fg produces the net force. The net force is always restoring, thus acting in the opposite direction of the displacement of the bob. Pendulum When the angle is small, the motion is linear and thus simple harmonic motion. The period of a pendulum of length “L” is given as: T = 2π √l/g The period depends only on the length of the rod and the acceleration due to gravity, not on the mass of the bob Resonance Mechanical resonance is the addition of small forces to a vibrating/oscillating object that will increase the amplitude The time interval for application of forces is equal to the period of oscillation What the?? Think of this…..you are on a swing, how do you make the swing to higher and higher?? You pump your legs and the highest points the swing reaches……this is resonance Assignment 6.2 Section Review Questions 1-5 Pg. 136 of textbook Due next class 6.3: Interaction Forces Objectives: Explain the meaning of interaction pairs of forces and how they are related by Newton’s third law List the four fundamental forces Draw the environment in which each fundamental force can be observed. Explain the tension in ropes and strings in terms of Newton’s third law Identifying Interaction Forces Certain forces will be dependent on other forces: Think of playing catch. A baseball is thrown with a force, then the person catching it exerts a force on the ball with his/her glove to stop it. The ball strikes with force, and has a force exerted on it by the glove. We will now bring the environment into play and see how different forces interact. Systems and the Environment So far, we have only looked at scenarios with a single system (object). What we will examine now are situations that have two systems that are interacting upon each other. Remember the system is the object effected by a force The environment is everything around that object that is not the system. Think back to the playing catch scenario…what are the systems? What are the forces interacting upon them? Newton’s Third Law Interaction pair – two forces that are in opposite directions and have equal magnitude. The forces of playing catch: F –ball on glove and F – glove on ball are interaction pairs. These forces summarize Newton’s Third Law of Motion; states “all forces come in pairs and that the forces in pairs act upon different objects that are of equal magnitude and in opposite directions Read pg. 139 to yourself: Car on Road Scenario. Problem Solving Strategy 1. Separate the Systems from the Environment 2. Draw a Pictorial Model with coordinate systems 3. 4. 5. 6. for each system and draw a physical model which includes free-body diagrams for each system. Connect interaction pairs with dashed lines Use Newton’s 2nd law to relate net force and acceleration for each system. Newton’s 3rd law equates the magnitudes of the force pairs and gives relative directions Solve the problems and check units, signs and magnitude to make sure they make sense. Example Problem Look at Example Problem on pg.140-141 Try Practice Problems 20-21 on your own Four Fundamental Forces Gravitational Interaction Based on the attraction between two objects due to the mass of the objects Electromagnetic Interaction Magnetic forces and electric forces Holds atoms and molecules together Responsible for all contact forces Strong Nuclear Interaction Acts between protons and neutrons in nuclei Weak Nuclear Interaction Responsible for radioactive decay http://www.neok12.com/video/Types-ofForces/zX747d7003674a6f79434459.htm Assignment Read Chapter 6, Section 3 Will attempt to finish the section tomorrow Forces of Ropes and Strings We have already touched on tension but let us discuss some more so we can relate it to Newton’s 3rd Law of Motion. Say we have a rope that is attached to a bucket. At a certain force the rope will break, however up to that point it means we have forces holding the rope together. Now we bring in Newton….What is means is that there is a Force that the top of the rope exerts on the bottom of the rope and a Force that the bottom of the rope exerts on the top of the rope This gives us 2 opposing forces so it obeys Newton’s 3rd Law Forces of Ropes and Strings The origin of tension is, of course, electromagnetic and the result of attraction between the molecules and atoms of the rope. The tension of the ropes is measurable, but the bucket is not moving so it is in equilibrium. This means that the two interaction forces of the rope are pulling in opposite directions at the same magnitude. This means that the Force of Tension (top on bottom) – the force of gravity = 0 Or that the Force of Tension (top on bottom) = Force of Gravity Force of Ropes and Strings Tension is also at work in a Tug-of-War. Two teams are pulling in opposite directions. If both forces are equal than the rope will not move. Now what is the Tension on the rope?? To figure this out we have to divide the rope into two halves: Left and Right Neither side is moving so this means the net force on both sides is 0. They are interaction pairs so they must be equal and opposite, this means the tension in the rope is equals the force with which each team pulled Assignment 6.3 Review Pg. 143 Questions 1-3 Due Next Class