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
Classical mechanics wikipedia , lookup
Newton's theorem of revolving orbits wikipedia , lookup
Fundamental interaction wikipedia , lookup
Fictitious force wikipedia , lookup
Centrifugal force wikipedia , lookup
Rigid body dynamics wikipedia , lookup
Classical central-force problem wikipedia , lookup
Unit II: Newton’s Laws Subunit A: Balanced Forces Equations Variables, Units NOTES: Unit II-A Objectives What you should know when all is said and done 1. State and use Newton’s first law to explain the motion of an object: a. Describe the motion of a moving object on which balanced forces are acting. b. Describe the motion of a stationary object on which balanced forces are acting. c. Describe the balanced forces acting on a moving object commonly encountered. 2. Given a diagram or a written description of the forces acting on an object: a. Draw a force diagram (using vectors) for the object. b. Resolve forces into x and y components, then find the vector sum of the forces. c. State whether the velocity of the object is constant or changing. 3. Given a diagram or description of an object in equilibrium, including the forces acting on the object, determine the magnitude and direction of the unknown force required to keep the object from accelerating. 4. State Newton’s third law and apply it to situations in which you are trying to determine all the forces acting on an object. 5. If a moose were chasing you through the woods, its enormous mass would be very threatening. But if you zigzagged, then its great mass would be to your advantage. Explain why. Unit II-A: Balanced Forces Worksheet 1 6. 7. 1. Inertia can best be described as Inertia can bestwhich be described as _____. A) the force keeps moving objects moving an stationary objects at rest. a. the force which keeps moving objects moving objects at rest. B) the willingness of an object to eventually lose an its stationary motion b. C) thethe willingness of causes an object eventually force which allto objects to stoplose its motion c. the force which causes all objects to stop D) the tendency of any object to resist change and keep doing whatever its doing d. the tendency of any object to resist change and keep doing whatever its doing Mass and velocity values for afor variety of objects are are listed below. Rank thethe objects from smallest to 2. Mass and velocity values a variety of objects listed below. Rank objects from greatest inertia. _______ < _______ < _______ < _______ smallest to greatest inertia. _______ < _______ < _______ < _______ 3. Two bricks are resting on edge of the lab table. Shirley Sheshort stands on her toes and spots the two bricks. She acquires an intense desire to know which of the two bricks are most massive. Since Shirley is vertically challenged, she is unable to reach high enough and lift the bricks; she can however reach high enough to give the bricks a push. Discuss how the process of pushing the bricks will allow Shirley to determine which of the two bricks is most massive. What difference will Shirley observe and how can this observation lead to the necessary conclusion? © The Physics Classroom, 2009 Page 1 4. Would Shirley Sheshort be able to conduct this same study if she was on a spaceship in a location in space far from the influence of significant gravitational forces? _______ Explain your answer. 5. If a moose were chasing you through the woods, its enormous mass would be very threatening. But if you zigzagged, then its great mass would be to your advantage. Explain why. 6. Several forces act upon an object. The vector sum of these forces ends up being 0 Newtons. The object is described as being A) weightless B) at equilibrium C) stationary D) disturbed 7. Which of the following is always true of an object that is at equilibrium? A) The net force acting upon it is 0 Newtons. B) The individual forces acting upon it are balanced. C) The object is at rest. D) The object has no acceleration. E) The object has a constant (unchanging) velocity. F) There are no forces acting on it. 8. The following statements were made about an Ewok. In which case could you conclude that the Ewok is at equilibrium? A) The Ewok is at rest. B) The Ewok has a constant velocity. C) The Ewok is moving. D) The Ewok has a constant speed. E) The Ewok is stationary. F) The acceleration of the Ewok is 0 m/s2. G) The individual forces acting on the Ewok are balanced. H) There are no forces acting on the Ewok. I) All the forces acting on the Ewok are equal in magnitude. Newton's Laws 9. These graphs describe the motion of Carson Busses at various times during his trip to school. 5. Indicate These graphs describe thevehicle motion is ofbeing Carson Busses at various times during his trip to aschool. whether Carson's acted upon by an unbalanced force. Give reason in Indicate whether Carson's vehicle is being acted upon by an unbalanced force. Give a reason in terms of a description of what the car is doing (speeding up, slowing down, or constant velocity). terms of a description of what the car is doing (speeding up, slowing down, or constant velocity). 6. Unbalanced Force? Yes or No? Unbalanced Force? Yes or No? Unbalanced Force? Yes or No? Reason/Description: Reason/Description: Reason/Description: A free-body diagrams show all the individual forces acting upon an object. The net force is the vector sum of all these forces (! F). Determine the net force and state if there is an acceleration. a. ! F= Accel'n? 7. b. ! F= Yes or No Accel'n? c. ! F= Yes or No Accel'n? Yes or No During an in-class discussion, Anna Litical suggests to her lab partner that the dot diagram for the motion of the object in # 6b could be UNIT II-A: Balanced Forces Reading: Force Diagrams Forces can intuitively be thought of as pushes and pulls. For example, you exert a force (a push or a pull) on a door to open it. Gravity exerts a force on you (a pull) which holds you to the surface of the earth. Friction with the surface of a hill exerts a force on your car that keeps it from sliding when parked. Note that in every situation, forces are an interaction between two objects--you can't touch without being touched. In order to analyze the reason behind the behavior of an object (or the dynamics), we will refer to the object under consideration as the system, and everything else in the environment that might in any significant way affect the system as the surroundings. This analysis process can often times be greatly simplified by using a technique of constructing force diagrams (sometimes called free-body diagrams or FBDs) to assist you in selecting the relevant forces and appropriately representing these forces with vector notations. To make a force diagram for problem analysis, all forces will be categorized as either contact or long-range forces. Contact forces are all forces acting on the system under analysis that result from the contact between the system and its surroundings at the systems boundaries. These forces include applied forces, forces of static and kinetic friction, tension forces and normal forces. Long-range forces result from the systems interaction with a force field of some kind, such as magnetic, electric, or gravitational fields. Here are some of the ones we will use in class: Contact Forces: When two surfaces touch each other, forces perpendicular to the surfaces are called Normal forces (here "normal" is a mathematical term meaning perpendicular) and forces parallel to the surfaces in contact are Frictional. The Friction force that allows us to step forward or keeps car wheels from spinning can be called traction. When we touch things a combination of both normal and frictional forces are present. For simplicity, we can call a combination force a push or a pull. A push or pull force can be labeled simply as an Applied force. Extended or linked materials such as a string or chain exert Tension forces on an object. When an object interacts with a fluid, such as water or air, propelling forces are called thrust, resistive forces are called drag, floating forces are called buoyant, and steering (or Bernoulli's) forces are called lift. When two objects interact without touching, they exert forces through a force field. Earth, for example, exerts a gravitational force on the Moon even though the Earth and Moon do not touch. Other non-contact forces include electric and magnetic forces. When we label forces, we want to indicate the type of interaction between the objects, what object the force is acting on and what object the force is by. Therefore, we will use the following notation: Fkind Such as the Force due to gravity, Fg, the force of Tension, FT, or the Normal Force, FN. Consider the analysis of forces acting on a log as a tractor pulls it at a constant speed. (Figure 2 below) The analysis proceeds as follows: 1. Shrink the system to a point at the center of coordinate axes with one axis parallel to the direction of motion. 2. Represent all relevant forces (across the system boundary) by a vector labeled with an appropriate symbol. As an illustration of this process, consider the forces acting on a log being pulled by a tractor follows: Step 1 Since the shape of the object is unimportant, shrink it to a point. Place it at the intersection of a set of coordinate axes with one of the axes parallel to the direction of motion as shown in figure 4. Step 2 Proceed around the system boundary line and identify all points at which there is contact between the system (log) and its surroundings. Construct qualitative vectors (indicate directions and relative magnitudes) to represent these forces. The contact forces would be kinetic friction, Fk (parallel to the supporting surface), the normal force, FN (the component of force that is perpendicular to the supporting surface), and the tension force of the rope, FT. The long-range force(s), in this case would be only the force of gravity, Fg. See Figure 4 at left. Step 3 Indicate which forces (if any) are equal in magnitude to other forces. The problem states that the tractor pulls the log at constant velocity, so we know that the net force has to be zero. In other words, the forces up must equal the forces down, and the forces left must equal the forces right. In the diagram below these equalities have been marked with hashes like those used to indicate congruences in geometry. Now, it should be easy to determine the net force on the object. To do this, consider the force in each direction (x or y) separately. That is, x-axis FT and Fk y-axis Fg and FN In this case, the two forces in the x-direction are equal, but opposite, so they sum to zero. Also note that the two forces in the y-direction sum to zero. Therefore, you can conclude that this object will not accelerate in either direction. That leaves two possibilities: it is either motionless, or it is moving at constant velocity. For a more complicated problem, consider the block at rest on a ramp. As before, we use a point to represent the object. Note that we have rotated the coordinate axes as shown above so that the x-axis is parallel to the surface of the ramp (the likely direction of motion). Next, break any force vector that is not parallel to the coordinate axes (in this case, the force of gravity, Fg) into its x and y components. See the diagram at right. Note that the x-component and y-component form the sides of a right triangle with the original force vector, Fg as the hypotenuse. In this case, the y-component balances out the normal force, so the object does not accelerate up or down. The x-component of Fg is opposed by the force of static friction. If these forces have the same magnitude, the object will stay put. To determine the magnitudes of Fx and Fy, you need to use some simple trigonometry. There are just a few points to keep in mind. 1. The angle θ should be drawn so that it is included in the triangle formed by the three vectors. 2. The side opposite the angle has magnitude equal to the original vector times the sine of the angle. 3. The side adjacent to the angle has magnitude equal to the original vector times the cosine of the angle. Remember Newton’s 1st Law: If ΣF = 0, then v = 0, and If v = 0, then ΣF = 0 The S.I. unit for force is named after Sir Isaac Newton himself. All forces are measure in Newtons. Symbol Name of Force FA FG FN FT 1. Ff 2. Agent/Interaction Unit II-A: Balanced Forces Worksheet 2 For each situation below, write a list of relevant objects in the system and draw the system behavior diagram. On separate paper, write a sentence justifying why you choose to include each of the objects in your list. Situation 1. The object lies motionless 2. The object slides at a constant speed without friction. 3. The object slows due to kinetic friction. 4. The object slides without friction. 5. Static friction prevents sliding. 6. The object is suspended from the ceiling by a single rope. List of Objects Force Diagram 7. The object is suspended from the ceiling by the two ropes. 8. The object is held motionless by the two ropes. 9. The object is motionless. 10. The object is motionless. 11. The object is being pulled at a constant velocity by a string attached as shown. 12. The object is being pulled (constant velocity) by a string attached as shown. 13. The object is being pushed by a person as shown and is moving at a constant velocity. 14. The object falls at a constant speed because of a parachute. 15. The object falls. (No air resistance) 16. The object rises after being thrown into the air. 17. The object is at the top of its path after it was thrown into the air. Unit II-A: Balanced Forces Worksheet 3 1. Free-body diagrams for four situations are shown below. For each situation, determine the net force acting upon the object. Situation A Situation B FN = 3 Fk = 5 N FN = 3 N Fg = 3 FA = 5 Fk = 5 N N N Fg = 3 N N Situation D Situation C Fair = 30 FN = 10 N N Fg = 15 Fg = 10 N force is known for each 2. Free-body diagrams for four situations are shown below. The net NN situation. However, the magnitudes of a few of the individual forces are not known. Analyze each situation individually and determine the magnitude of the unknown forces. Free Particle Model Worksheet 1a: Force Diagrams In each of the following situations, represent the object with a particle. Sketch all the forces acting upon the object, making the length of each vector represent the magnitude of the force. Also use Create a marks forceto diagram theare object all caps! congruency indicate whichon vectors equal inin magnitude. 3. A CAT is at rest 4. A student sitting 1. Draw a force diagram for the motionless cat on a rug. Label the forces and use equality marks on aonrug. a CHAIR. the force vectors. 5. BOBO the Panda is hanging from a branch. 6. Sammy the snail sitting on TIM THE TURTLE standing on top of a table. 2. Draw a force diagram for the skater, moving at constant speed across frictionless ice. Label the forces and use equality marks on the force vectors. Newton's Laws 5. These graphs describe the motion of Carson Newton's Laws Busses at various times during his trip to school. Name: Indicate whether Carson's vehicle is being acted upon by an unbalanced force. Give a reason in terms of a description of what the car is doing (speeding up, slowing down, or constant velocity). 7. An EGG is free-falling from a nest in a tree. Neglect air resistance. 8. SLICK STEVE slidingRecognizing Forces down a slide at a constant Read from Lesson 2 of the Newton's Laws chapter at The Physics Classroom: speed. http://www.physicsclassroom.com/Class/newtlaws/u2l2a.html http://www.physicsclassroom.com/Class/newtlaws/u2l2b.html MOP Connection: Newton's Laws: sublevel 4 Unbalanced Force? There are several Unbalanced Force? Force? fill in the list provide described For each situation, 9. Calvin pulling 10.situations A horse pulling below.Unbalanced Yes or No? Yes or No? Yes of or the No?situation you used to determ which forces are present and stating which features Hobbes on a SLED a WAGON up a hill or absence of the To facilitate utilize the Net Force Help Sheet. Up Reason/Description: Reason/Description: (flat surface)Reason/Description: at a atforce. a constant speed.this exercise, this assignment, check your answers using the available Web page. constant speed. http://www.physicsclassroom.com/morehelp/recforce/recforce.htm 6. A free-body diagrams show all the individual forces acting upon an object. The net force is the vector sum of all these forces (! F). Determine the net force and state if there is an acceleration. Description of b. Situation Force Present c. (P) 11. A rightward force a. 12. A rightward force or Absent (A)? applied a TABLE applied to Label a BOOK 4.is Draw a forceto diagram for a chandelier that is suspended from the is ceiling by a chain. the andto usemove equalityitmarks on the force vectors. Gravity in forces order in order to move it across across the floor with a rightward acceleration. Consider frictional forces. ! F= a desk at constant velocity. Consider frictional forces. Spring: ! F= Tension ! F= P or A? P or A? P or A? 13. A SKYDIVER is 14. A CAR driving or A? Accel'n? Yes or No Accel'n? Yes or No Normal: Accel'n? P Yes or No descending with a at a constant velocity. 1. A block hangs at rest constant velocity. 7. During an in-class discussion, Anna Litical to her fromsuggests the ceiling bylab a partner that the dot diagram for the Consider air resistance. Friction P or A? motion of the object in # 6b could be piece of rope. Consider the forces acting on the block. Air Res.: P or A? Anna's partner objects, arguing that the object in # 6b could not have any horizontal motion if there are only vertical forces acting upon well it. Who16. is right? ____________ Explain. A BUCKET raised from A well BLOCK hangs from a spring 5.15. Draw a force diagramisforbeing the bucket of water that isabeing raised from the at constant Gravity P or A? speed. Label the forces and use equality marks on the force vectors. at a constant speed. from the ceiling. 8. P ortoA? During an in-class discussion, Aaron Agin asserts that the object in #Spring: 6a must be moving the left since the only horizontal force acting upon it is a "left-ward" force. Is he right? ______ Explain. Tension P or A? Normal: P acting or A? an diagramsbelow belowdepict depict the the magnitude and direction of the individual forces acting upon 17.9.TheThe diagrams magnitude and direction of individual forces upon 2. A block hangs from thethe object. Whichall objects could be moving ceiling to the right? Circle all that apply. by a spring. an object. Choose that apply. Consider the forces acting on the block when it is at rest (at its equilibrium position). Friction P or A? Air Res.: P or A? 6. Draw a force diagram for a skydiver who has just left the plane and is still speeding up. Label the forces and use equality marks on the force vectors. A) Which objects could be moving to the right? B) Which objects could be speeding up? The Physics 2009 C) ©Which objectsClassroom, could be stationary? © The Physics Classroom, 2009 Page 4 Explan Unit II-A: Balanced Forces Worksheet 4 1. The standard metric unit for mass is _____ and the standard metric unit for weight is _____. 2. An object's mass refers to ______ and an object's weight refers to _______. A) the amount of space it takes up B) the force of gravitational attraction to Earth C) how dense an object is D) the amount of stuff present in the object 3. When an astronaut lands on the moon, which of the following are more than, less, than, or the same as on Earth: A) The astronaut’s mass B) The astronaut's weight C) The astronaut’s inertia 4. Which weighs more, a pound of feathers or a pound of bricks? Which has more mass? 5. The value of g in the British system is 32 ft/sec2. The unit of force is pounds. The unit of mass is the slug. Use your weight in pounds to calculate your mass in units of slugs. 6. You might be wondering about your metric weight. Using conversion factors, convert your weight in pounds to units of N. (Use 1 N = 0.22 pounds, and okay, you can lie…) 7. When an elevator is ascending at a constant velocity, there are two forces acting on it, gravity and the cable pulling on it. Which of these is greater? Why do you say so? 8. When you go roller-blading (if you don’t then try to imagine that you do), you must keep pushing with your feet in order to maintain a constant speed. Explain why this is, talk about the forces acting on you in your explanation. 9. Do chickens weigh more here on earth or on the moon? Do they have more mass here or there? 10. A shopping cart sits in a parking lot. Sophie Shopper walks up to it and begins pushing it towards the door at a constant speed. Because of the way the handle is attached, Sophie must push downward at an angle on the cart. Describe what happens to the normal (or support) force acting on the cart before and after Sophie begins pushing. 11. An armadillo weighs has a mass of 15 kg. Find its weight. 12. Wile E. Coyote has a new plan to catch the Roadrunner involving a 100 kg box of TNT. In preparation he starts pushing it at a constant velocity to the edge of a cliff. Friction has a force of 200 N. A) With how much force should Wile E. Coyote be pushing? B) What is the support force of the ground on the box? 13. A car’s engine pushes with 45N to the right. If it is at equilibrium, how much air friction is there and what is the car’s acceleration? 14. Spaceman Spiff weighs 350 N on Earth when decked out in full astronaut gear. How much would he weigh on planet Zorg, where the gravitational field strength is 20 N/kg? 15. Find the normal force from a level table on a 2-kg pineapple. 16. A wagon rolls at a constant speed of 2 m/s on level ground. Marvin Mole (mass = 3.5 kg) rides in the 10 kg wagon. A) What is the combined weight (force of gravity) of Marvin and the wagon? B) What is the normal force (support force) that acts on Marvin (only) in the wagon? C) What normal force (support) acts on the wagon carrying Marvin? ction of the two components by circling two h component (or effect) is greatest in magnitude. Components: E W N S Components: E Greatest magnitude? ______ W N Greatest magnitude? ______ Force and Vector Applications S Components: E W N S Greatest magnitude? ______ Name: Each diagram displays a vector. Thehave anglecombined between the vector of and the nearest 17. Burl and Paul weights 1300 N. The coordinate tensions inaxes theissupporting ropes that marked as theta (! ). If ! is gradually increased to 90 degrees, the magnitudes of the components support the scaffold they stand on add to 1700 N. Find the weight of the scaffold. would change. Which component would increase horizontal (E/ W) or vertical (N/ S)? Equilibrium Situations Using- Vector Components to Analyze Read from Lesson 3 of the Vectors and Motion in Two-Dimensions chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/vectors/u3l3b.html http://www.physicsclassroom.com/Class/vectors/u3l3c.html ! E W N S Components: E Connection: W N S MOP Forces in Two Dimensions: sublevels 3 and 4 ! nitude? ______ Greatest magnitude? ______ Many physical situations involve forces exerted at angles to the coordinate axes. A proper analysis of 18. Harry gives his little sister a !piggyback Harry has a mass of 40 kg and his lie little sister these situations demands that theride. forces be resolved into components which along the horizontal and ween the vector and the nearest coordinate axes is vertical axes. This involves the useforce of trigonometric has a mass of 20 kg. Calculate the support supplied byfunctions. the floor. d to 90 degrees, the magnitudes of the components 1. For the following situations, draw and label the force components as the projection onto the axes. ase - horizontal (E/ W) or vertical (N/ S)? Then use trigonometric functions to determine the magnitude of each component. Label the Increasing component? Increasing component? Increasing component? magnitudes of the component on the diagram. PSYW E E Mauer W pulls N up with S a force of E N Yuss S yanks on Spot's dog chain with Lon 75 N atW b. Jean an angle of 45° to the horizontal on the a force of 12 N at an angle of 60° to the handle his manual lawn mower. horizontal. For the following situations, draw and label theofforce components of the given vector. Then use trigonometric functions to determine the magnitude of each component. Label the magnitudes of given vector. Then 19. For the following situations, draw and label the force components of the ! the component on the diagram. PSYW use trigonometric functions to determine the magnitude of each component. Label the a.! W S a. magnitudes of thea component A 5.0 N force is exerted upon dog chain on b. the A diagram. baseball is hit by a bat with a force of N force is exerted upon a dog chain at an angle of 65° above the horizontal. at an angleA) of A 65°5.0 above the horizontal. 325 N at a direction of 105°. ng component? W N N S Increasing component? E W N S force components of the givenUse vector. Then use your noodle (that's your brain) to logically think through the following two questions. tude of each component. Label the magnitudes of 2. Which of the following statements is ALWAYS 3. The following statements were made about an true of an object at equilibrium? object. In which case could you conclude that a. a force The object is at rest. the object is at equilibrium? b. A baseball is hit by a bat with of a. The object is at rest. 325 N at a direction of 105°. b. The object is maintaining its state of motion. The object has a constant velocity. B) A baseball is hit by a bat with a force of 325 N at a direction of b. 105°. c. The object's velocity is not changing. c. The object is moving. d. The net force on the object is 0 Newtons. d. The object has a constant speed. e. The object is NOT accelerating. e. The object is stationary. f. The individual forces acting on the object f. The acceleration of the object is 0 m/ s/ s. are balanced. g. The individual forces acting on the object he Physics Classroom, 2009 Page 4 g. All individual forces acting on the object are balanced. are equal in magnitude. 4. Three forces - F1, F2 , and F3 - are acting upon an object. and direction areobject. shownTheir at the 20. Three forces Their - F1, relative F2, andmagnitude F3 - are acting upon an right. The xand y-components are also shown. relative magnitude and direction are shown at the right. The x- and ythe Complete following mathematical by components are Complete also shown. the followingstatements mathematical placing > , < , and = symbols in the blanks. statements by placing >, <, and = symbols in the blanks. F1x ____ F2x F1y ____ F3 F1x ____ F2x F2y Page 4 ____ F3 F1y ____ F3 F2y ____ F3 F1y + F2y ____ F3 F1y + F2y ____ F3 © The Physics Classroom, 2009 Page 5 Unit II-A: Balanced Forces 3. The figure below is a snapshot looking down on a bowling ball moving at constant velocity from Worksheet 5is given a short, sharp hit in a left to right on a smooth, level floor. At the position shown, the ball direction perpendicular to the ball's initial motion. 3. The figure below a snapshot looking down a bowling moving at constant velocity from 1. The figure below is aissnapshot looking down on on a bowling ballball moving at constant velocity left to right on a smooth, level floor. At the position shown, the ball is given a short, sharp hit in a from left to right on a smooth, level floor. At the position shown, the ball is given a short, sharp direction perpendicular to the ball's initial motion. hit in a direction perpendicular to the ball's initial motion. A)On Onthe thediagram, diagram,draw draw a path might follow after Explain your reasoning for a. a path thatthat thethe ballball might follow after thethe hit.hit. Explain your reasoning for drew. the path you drew. the path you a. On the diagram, draw a path that the ball might follow after the hit. Explain your reasoning for the path you drew. b. of of thethe ball bebe equal to, greater than,than, or smaller B)Immediately Immediatelyafter afterthe thehit, hit,will willthe thespeed speed ball equal to, greater or smaller than than the ball's velocity before the hit? Explain your reasoning. the ball's velocity before the hit? Explain your reasoning. b. Immediately after the hit, will the speed of the ball be equal to, greater than, or smaller than the ball's velocity before the hit? Explain your reasoning. c. How will the velocity of the ball behave as time goes by after the blow? That is, will either C) How will the velocity of the ball behave as time goes by after the blow? That is, will either the the magnitude or the direction of the velocity change? If so, how? magnitude or the direction of the velocity change? If so, how? c. How will the velocity of the ball behave as time goes by after the blow? That is, will either the magnitude or the direction of the velocity change? If so, how? 4. You push a grocery cart along a level floor in the presence of friction effects a 10-kg between2. theYou cartpush and the floor.shopping cart at a constant velocity of 0.5 m/s as you leisurely stroll HEB looking for toilet paper. Finding a screaming deal, you pick up 4 4. You push a grocery aalevel floor in the2presence of friction effects packages thatdiagrams you estimate toalong have mass of about kg each (you like the extra a. Draw force forcart you, the cart, and the floor/earth. Fully label between the cart and the floor. thick kind). all vectors. A) Write the equation for the forces acting in the vertical direction and calculate the a. Draw force diagrams for you, the cart, and the floor/earth. Fully label normal force the floor is providing. all vectors. you cart B) Write the equation for the forces acting in the horizontal direction. If friction is resisting you cart with 10 N of force, you how hard must you push? floor/Earth floor/Earth 3. Determine the tension in each cable in case A and case B if the ball has a mass of 5 kg. Case A Case B Free Particle Model Works Quantitative Force Analysis & Ve 1. Determine the tension in each cable below. Draw a force diag the problem. Case A - ball suspended on one cable Case B - ball suspen 4. Determine tension in each cable. (Hint: There is more than one way to define the system.) 2. Determine tension in each cable. 7kg 4kg 3. Find the horizontal and vertical components of the tension i 5. Find the horizontal and vertical components of the Tension in the fishing line if the tension is 100 N. 5 5̊ 6. A 2000 kg elephant stands on a ramp. Draw a force diagram to determine the components of the elephant’s weight parallel and perpendicular to the ramp. ©2009 Modeling Instruction Program 1 Physics Tip: When a sign is hung at equilibrium, the downward pull of gravity must be balanced by the upward pull of the wires (cables, strings, etc.). In most cases, the wires are oriented diagonally such that the tension force has both a horizontal and vertical component. If the sign is hung symmetrically, then each wire pulls with the same amount of force and at the same angle. The vertical component of the tension will be the same in each wire. And if there are two wires, each wire must supply sufficient up pull to balance one-half the weight of the sign. 7. The three identical signs below are supported by wires at three different angle orientations. Since each sign has asigns weight of 10.0 N, each wire mustatexert verticalangle component of force of 5. The three identical below are supported by wires three adifferent orientations. Since 5.0 N. Use a trigonometric function to determine the tension in each wire. A diagram of each each sign has a weight of 10.0 N, each wire must exert a vertical component of force of 5.0 N. Use a situation is shown.function to determine the tension in each wire. A diagram of each situation is shown. trigonometric If hanging the above sign with a given wire, which one of the above angles would provide for the safest arrangement? _____________ Explain. If hanging the above sign with a given wire, which one of the above angles would provide for the 6. Suppose that a student pulls with two large forces (F1 and F2) in order to lift a 1-kg book by two safest arrangement? Explain. cables. If the cables make a 1-degree angle with the horizontal, then what is the tension in the cable? 8. A normal force is a force which is always directed A) upwards B) sideways C) perpendicular to the surface the object is contacting 9. An object is upon a surface. The normal force is equal to the force of gravity A) in all situations B) only when the object is at rest C) only when the object is accelerating D) only when there is no vertical acceleration E) only when there is no vertical acceleration AND FN and Fg are the only vertical forces © The Physics Classroom, 2009 Page 6 Unit II-A: Balanced Forces Worksheet 6 For each of the problems below, carefully draw a force diagram of the system before attempting to solve the problem. 1. A person pulls on a 50 kg desk with a 200-N force acting at a 30º angle above the horizontal. The desk does not move. A) Draw a force diagram for the desk. B) Write the equation that describes the forces that act in the x direction. C) Write the equation that describes the forces that act in the y direction. D) Determine the x and y components of the force of tension. E) Determine the value of the frictional force. Do the same for the normal force. 2. Suppose that the person in the previous problem were pushing down at a 30º angle with 200 N of force. The desk still does not move. A) Draw a force diagram for the desk. B) Write the equation that describes the forces that act in the x direction. C) Write the equation that describes the forces that act in the y direction. D) Determine the value of the frictional force. Do the same for the normal force. 3. a. Draw a force diagram for the block held at rest. 25 T1 b. Write the equation that describes the forces that act in the x direction. T2 c. Write the equation that describes the forces that act in the y direction. d. Suppose that the magnitude of T1 is 50 N. Determine the magnitude of T2. e. Determine the weight of the box. What is its mass? 4. Draw the force diagram for the box, which rests motionless on the ramp. 20 a. Write the equation that describes the forces that act in the x direction. b. Write the equation which describes the forces which act in the y direction. c. If the mass of the box is 8.0 kg, determine the value of the normal force. Unit II-A: Balanced Forces Worksheet 7 1. A) Draw a force diagram for each block held at rest. B) Write the equation for the forces acting in the x-direction for the larger block. C) Write the equation for the forces acting in the y-direction for each block. D) How does the tension on the smaller block compare to the tension on the larger block? E) Calculate the amount of friction required to hold the system at rest. 2. The sign shown hangs outside the physics classroom, advertising the most important truth to be found inside. The sign (mass = 50 kg) is supported by a diagonal cable and a rigid horizontal bar. A) Draw a force diagram for the sign. B) Write the equation describing the forces acting horizontally on the sign. C) Write the equation describing the forces acting vertically on the sign. D) Calculate the Tension in the cable. E) Calculate the amount of force the bar applies to the sign. 3. You were so excited about your Thanksgiving ski trip that you over-packed your duffle bag. The bag (and all your stuff) has a mass of 80 kg. You drag the heavy bag at a constant velocity by exerting a force of 400 N at an angle of 45 degrees to the floor. A) Draw a force diagram for your duffle bag. B) Write the equation describing the forces acting horizontally on the duffle bag. C) Write the equation describing the forces acting vertically on the duffle bag. D) Calculate the frictional force acting against your duffle bag. E) Calculate the normal force acting on your duffle bag. 4. Your little brother is pushing his Thomas the Tank Engine along the train track. He pushes downward at an angle of 20 degrees to the floor with a force of 5 N in order to make the train go at a constant velocity. The train has a mass of 0.2 kg. A) Draw a force diagram for the train. B) Write the equation describing the forces acting in the horizontal direction. C) Write the equation describing the forces acting in the vertical direction. D) Calculate the friction acting on the train. E) Calculate the normal force supporting the train. 5. A box of Girl Scout cookies is being unloaded from a truck using an inclined plane that forms a 37-degree angle with the ground as shown in the diagram. The box has a mass of 10 kg. It is allowed to slide down the ramp at a constant speed. A) Draw a force diagram for the box. B) Write the equation describing the forces acting parallel to the ramp (in the horizontal direction). C) Write the equation describing the forces acting perpendicular to the ramp (in the vertical direction). D) Calculate the amount of friction resisting your next snack. E) Calculate the normal force keeping your snack from crumbling to the ground. Unit II-A: Balanced Forces Worksheet 8 For each of the problems below, carefully draw a force diagram of the system before attempting to solve the problem. 1. The cable at left exerts a 30 N force. a. Write the equation for the sum of the forces in the x-direction. What is the value of T2? b. Write the equation for the sum of the forces in the y-direction. What is the force of gravity acting on the ball? 7. Draw aforce force diagram the child on the swin 2. You pull back your 15-kg brother in preparation for a swinging time. HowLabel much mustandforuse the force vectors equality marks on you apply to hold him motionless at an angle of 25 degrees to the vertical? 3. The object hung from the cable has a weight of 25 N. Write the equation for the sum of the forces in the y-direction. What is the tension in the cable? 8. Draw a force diagram for the climber who has equality marks on the vectors. 4. Tarzan prepares to swing and much to his dismay, gets his loincloth stuck on a branch. He's left hanging with the vine pulling upward at a 40-degree angle and his loincloth pulling him horizontally to the right. A) If Tarzan’s mass is 75 kg, calculate the tension in the vine. 7. Tarzan prepares to swing and much to his disma hanging with the vine pulling upward at a 40-degre to the right. a. Draw a angled fo are equal B) Calculate the force of the branch on his loincloth (let’s hope it holds!). b. Write an equation for the vertical forces c. Write an equation for the horizontal forc 5. The box on the frictionless ramp is held at rest by the tension force. The mass of the box is 20 kg. d. Tarzan's mass is 75 kg. Calculate his we e. Use the appropriate equation for the forc A) What is the value of the tension force? f. Determine the tension in his loincloth. B) What is the value of the normal force? ©2009 Modeling Instruction Program 6. In the system below the pulley and ramp are frictionless and the block is in static equilibrium. What is the mass of the block on the ramp? 3 7. A man pulls a 25 kg box at constant speed across the floor. He applies a 250 N force at an angle of 30. A) Sum the forces in the x-direction. What is the value of the frictional force opposing the motion? B) Sum the forces in the y-direction. What is the value of the normal force? 8. A man pushes a 2.0 kg broom at constant speed across the floor. The broom handle makes a 50 angle with the floor. He pushes the broom with a 5.0 N force. a. Sum the forces in the y-direction. What is the value of the normal force? b. Sum of the forces in the x-direction. What is the value of the frictional force opposing the motion? c. If the frictional force were suddenly reduced to zero, what would happen to the broom? Unit II-A: Balanced Forces Worksheet 9 1. A diver dives off of a raft - what happens to the diver? The raft? How does this relate to Newton's Third Law? 2. A tennis racquet hits a tennis ball. Why doesn't the racquet swing backwards when the ball hits it? (Shouldn't it swing back because of action-reaction forces?) 3. What action-reaction forces are involved when a rocket engine fires? Why doesn't a rocket need air to push on? Free Particle M Inter 1. Explain what a normal force is and give an ex 4. What forces are acting on a book sitting on a table? Are action-reaction forces involved in this situation? 2. Can an inanimate object (such as a table) exe by an inanimate object change? Explain and giv 5. If two people each standing on a scooter board push off of each other what happens (relate to Newton's Third Law)? 3. If the acceleration of an object is zero, are no 6. In #5 how would the distance moved by the scooter boards compare if one person had a lot more mass than the other person? 7. If a person standing on a scooter pushes off of a wall, what happens? Can this situation be explained in terms of Newton's Third Law (action-reaction)? 4. How does the force block A exerts on block Draw and label a quantitative force diagram for 8. How does the force block A exerts on block B compare to the force block B exerts on block A? Draw and label a quantitative force diagram for each block, using equality marks on the vectors. 5. How does the force block A exerts on block B compare to the Draw and label a force diagram for each block, using equality ma 9. How does the force block A exerts on block B compare to the force block B exerts on block A? Draw and label a force diagram for each block, using equality marks on the vectors. 6. How does the force block A exerts on block B compar Draw and label a force diagram for each block, using equ 10. How does the force block A exerts on block B compare to the force block B exerts on block A? Draw and label a force diagram for each block, using equality marks on the vectors. 6. How does the force block A exerts on block B compare to the Draw and label a force diagram for each block, using equality ma 11. Draw and label all of the action-reaction paired forces for the person pulling the sled. 6. cord is 25˚ above the horizontal. mass of kids and sled = 100 kg Tension in cord isInstruction 120 N. Program ©2009 Modeling Friction force is 15 N. 12. TRUE or FALSE: As you sit in your seat in the physics classroom, the Earth pulls Find the acceleration of the sled.down 2 upon your body with a gravitational force; the reaction force is the chair pushing upwards on your body with an equal magnitude. If False, correct the answer. ©2009 Modeling Instruction Program 2 Unit II-A: Balanced Forces Review Worksheet EQUATION Fg = (10 N/kg) m 1. State Newton’s 1st Law. (remember 3 things about it…) 2. State Newton’s 3rd Law. 3. What is the difference between mass and weight? What are the units of each? 4. A piece of dry ice is kicked across the floor. If it has little to no friction, what will it do? What would happen if you exerted a constant force on it? 5. What quantity describes how much inertia an object possesses? 6. When an object is in equilibrium, what must Fnet equal? 7. A) You are in the front of a bus, standing in the isle wearing roller-blades. The bus suddenly starts to accelerate forward. What happens to you? Why? B) Now the bus is moving at a constant velocity. What is your motion relative to the bus? Explain. 8. When you fire a rifle, why do you feel the kick-back? (Explain using Newton’s 3rd Law). 9. When you push on a book, the book pushes back on you with the same force. So why does the book move, and not you? 10. A 1000-N crate is dragged across a factory floor at a constant velocity by pulling on a rope with a force of 400 N, as shown in the picture. 30 A) Draw a force diagram of the forces acting on the crate and label them. B) Write equations for the vertical and horizontal components of the forces. C) Find the force of friction on the crate. D) Find the normal force on the crate. 8. A 90 kg skier takes to the slopes and re E) With what force does the block pull on the rope? a. D coo sur 12. A 90 kg skier takes to the slopes and reaches a constant velocity. A) Draw a force diagram for the skier. (Hint: use a coordinate axis parallel and perpendicular to the hill's surface) B) Determine the skier's weight. C) Determine the Normal Force. b. Determine the skier's weight. D) Determine the Frictional Force. c. Determine the component of the d. Determine the component of the