AP Physics 1 Assignment - Forces
Reading: Chapter 4, sections 5.1 & 5.2, Open Stax College Physics; Chapters 3 & 4, Etkina
Objectives/HW
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The student will be able to: |
HW: |
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1 |
State Newton’s 1st and 2nd Laws of Motion and apply these laws to physical situations in order to determine what forces act on an object and to explain the object’s resulting behavior. |
1 – 5 |
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2 |
Recognize and state the proper SI unit of force and give its equivalence in fundamental units and use the relation Fnet = ma to solve problems. |
6 – 10 |
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3 |
Recognize the difference between weight and mass and convert from one to the other. |
11 – 18 |
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4 |
State and utilize Newton’s 3rd Law to solve related problems. |
19 – 21 |
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5 |
Understand and utilize the concept of the normal force to solve related problems. |
22 – 25 |
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6 |
Understand and utilize the relation between friction force, normal force, and coefficient of friction for both cases: static and kinetic. |
26 – 32 |
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7 |
State the factors that influence air resistance and describe qualitatively the effect of each factor on the magnitude of the frictional force. And explain what is meant by “terminal velocity”. |
33 – 35 |
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8 |
Resolve forces into components using trigonometry and use the results to solve related force problems. |
36 – 40 |
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9 |
Apply the concept of force components to objects on an incline and solve related problems. |
41 – 47 |
Homework Problems
1. Using Newton’s Laws explain why you must push harder on the pedals of a single-speed bicycle to start it moving than to keep it moving with a constant velocity.
2. Suppose you have a nearly empty jar of salsa that you want to pour into a bowl. Of course you will turn the jar upside down – but sometimes this is not enough to get the salsa out of the jar. Usually you will end up not only turning the jar over but also shaking it up and down. Using Newton’s Laws explain what factors cause the salsa to come out of the jar.
3. The Pioneer 10 spacecraft has left our Solar System and is traveling at a speed of 29,000 mph (and has been doing so for years). Explain why this object is moving so fast although it ran out of fuel long ago.
4. If you are in a car that is struck from behind, you can receive a serious neck injury called whiplash. (a) Using Newton’s Laws explain what happens to the person’s head. (b) Using Newton’s Laws explain how a headrest helps to reduce whiplash injuries.
5. When a rocket is launched, the thrust of its engines is a constant force as it burns fuel and moves away from Earth. However, as the flight progresses, its rate of acceleration is not constant, but actually increases. Explain using Newton’s Laws.
6. A net force of 150 N causes a certain person to accelerate 1.20 m/s2. Determine the person’s mass.
7. A certain car (Mazda Miata) has a mass of 1080 kg and can go from zero to 26.8 m/s (0 to 60 mph) in 7.9 seconds. What magnitude net force must act on the car to cause this?
8. The Deep Space 1 spacecraft’s ion engine produced an average thrust of 37 mN and was fired for a total of 16000 hours. The mass of the spacecraft was 450 kg. (a) Assuming this thrust was the only force acting on it what was the spacecraft’s rate of acceleration? (b) By how much was its velocity changed over this time period?
9. Two forces act on a falling skydiver with mass 100 kg: a downward gravity force and an upward air resistance (friction) force. Suppose the net force on the skydiver is 670 N, 270.0° – this means the gravity force is 670 N greater than the friction force. (a) Determine the resulting acceleration. After the parachute opens the acceleration is 5.0 m/s2, 90.0°. (b) Determine the net force at this point. (c) Which force is larger now and by how much?
10. Starting and ending at rest, an object of mass m is caused to move a certain distance d in an amount of time t. To make this happen, what minimum amount of force, F, must act – first accelerating and then decelerating the object? Derive an expression for F.
11. (a) Compare the amount of force needed to lift a 10 kg rock on the Earth and on the Moon – which is greater and why? (b) Now compare the amount of force needed to throw the same rock horizontally at the same speed in the two locations. Explain.
12. A 95.0 kg (209 lb) boxer has matches in the Canal Zone (g = 9.782 m/s2) and in the Arctic Circle (g = 9.832 m/s2). (a) What is his mass in the Canal Zone? (b) What is his weight in the Canal Zone? (c) What is his mass in the Arctic Circle? (c) What is his weight in the Arctic Circle? (e) Based on this, should a scale or a balance be used for the “weigh-in”?
13. Suppose a certain motorcycle weighs 2450 N. What is its mass in kilograms?
14. A 4500 kg helicopter accelerates upward at 2.0 m/s2. What lift force is exerted on the propellers by the air?
15. Safety engineers estimate that an elevator “car” can hold 20 persons of 75 kg average mass. The car itself has a mass of 500 kg. Tensile strength tests show that the cable supporting the car can tolerate a maximum force of 29.6 kN. What is the greatest acceleration that the elevator’s motor can produce in the fully loaded car without breaking the cable?
16. An elevator car that weighs 3.0 kN is accelerated upward at 1.3 m/s2. What force does the cable exert to give it this acceleration?
17. A rocket with weight W is sitting vertically on a launch pad. The rocket’s engine fires to produce a thrust T, producing liftoff. Derive expressions for the following in terms of W, T, and any appropriate constants. (a) What magnitude net force acts on the rocket just as it leaves the ground? (b) What is the acceleration of the rocket?
18. A person throws a ball with mass 175 g. If the person’s hand exerts a force of 5.00 N, 50.0°, what will be the resulting acceleration of the ball? (You must include the effect of gravity.)
19. Mules are smart but stubborn. Once upon a time a particularly smart and particularly stubborn mule refused to pull its owner’s cart and gave the following argument: “I refuse to pull the cart because it is impossible to do so according to Newton’s laws of motion. According to the 2nd Law it is necessary to have a net force in order for the cart to accelerate. According to the 3rd Law no matter how hard I pull the cart forward, the cart will pull an equal amount backward and therefore the net force will be zero and the cart will not move. Even if I could pull a million Newtons forward, the cart would pull a million Newtons backward and so I refuse to even try!” What is the flaw in the mule’s argument?
20. When you drop a 0.40 kg apple, Earth exerts a force on it that accelerates it toward the Earth’s surface. Assuming Newton’s Laws are true (and they are!) the Earth must also accelerate toward the apple. (a) Given its mass is 5.974 x 1024 kg, determine the rate at which the Earth accelerates upward toward the falling apple. (b) Determine how far the Earth moves up during the time that the apple moves down 1.0 m.
21. A 115 kg astronaut on a space walk pushes against her space capsule that has mass 2250 kg. The astronaut accelerates 1.50 m/s2, 0°. (a) Find the force exerted on the astronaut. (b) Find the force exerted on the capsule. (c) Find the acceleration of the capsule.
22. Suppose a 200 g ball is in contact with the floor. (a) Determine the normal force the floor exerts on the ball when it is at rest. (b) Determine the normal force the floor exerts on the ball when it is bouncing and accelerating upward 100 m/s2. (c) Determine the force that the ball exerts on the floor as it is bounces. (d) Find the amount of normal force if the ball bounces off the ceiling with downward acceleration 100 m/s2.
23. A person stands on a bathroom scale in an elevator at rest on the ground floor of a building. The scale then reads 836 N. As the elevator begins to move upward, the scale reading briefly increases to 935 N but then returns to 836 N. As the elevator reaches the 20th floor, the scale reading briefly drops to 782 N and then once again returns to 836 N once it has stopped. (a) Determine the elevator’s acceleration as its speed increases. (b) Determine the elevator’s acceleration as its speed decreases. (c) Explain why the scale reads 836 N for most of the elevator’s trip.
24. A person lifts a
stack of two boxes by exerting a force of 60.0N upward on the bottom of the
lower box. Both boxes accelerate upward at the same rate. The upper box is
2.00 kg and the lower box is 3.00 kg. (a) Draw a free-body diagram of the
stack of boxes (treat as one object) and solve for the acceleration of the
system's center of mass. (b) Draw
a free-body diagram of the upper box and solve for the normal force pushing up
on it. (c) Draw a free-body diagram of the lower box and solve for the normal
force pushing down on it. (d) Explain how these results illustrate
Newton’s 3rd Law of motion and the effects of internal vs. external forces.
25. Masses of 30.0 kg and
10.0 kg are connected by a cord that passes over a frictionless pulley of negligible
mass. The 10.0 kg object is pulled downward by an applied force F, causing it
to accelerate down at 2.00 m/s2 while the other object accelerates up at
2.00 m/s2. (a) Treat the two objects as a system and determine the amount
of force applied. (b) Determine the tension in the cord.
26. A sled of mass 50 kg is pulled horizontally over flat ground. The static friction coefficient is 0.30, and the sliding friction coefficient is 0.10. (a) What does the sled weigh? (b) What minimum amount of force must be applied to the sled in order to start it moving? (c) What amount of applied force will keep it moving at a constant velocity of 3.0 m/s? (d) What amount of applied force will accelerate the sled at 3.0 m/s2?
27. A force of 40 N, 180° accelerates a 5.0 kg block at 6.0 m/s2, 180° along a horizontal surface. (a) Determine the force of friction acting on the block. (b) Determine the coefficient of friction.
28. A 20 kg wagon is rolling to the right across a floor. A person attempts to catch and stop the crate and applies a force of 70 N, 180.0° on it. If the coefficient of friction is 0.18, calculate the deceleration rate of the wagon as it is caught.
29. Two brothers are goofing around on the surface of a frozen lake where μ = 0.050. The older brother weighs 825 N and the younger weighs 765 N. The older brother shoves the younger with a force of 85.0 N, 0.0° (a) Find the acceleration of the younger brother. (b) Find the acceleration of the older brother. (c) Find the acceleration of the center of mass of the two-brother system – treat the two brothers as “one object”.
30. In the bed of the truck is a 15 kg crate for which μs = 0.20 and μk = 0.15. (a) What is the maximum acceleration rate of the truck at which the crate will not slide across the bed? (b) If the truck exceeds this by accelerating at 4.0 m/s2 0.0, what will be the crate’s acceleration – both relative to earth and relative to the truck?
31. A truck with mass 2000 kg tows a boat and trailer of total mass 500 kg. The frictional coefficient for the truck is 0.080 and for the trailer is 0.050 (this is due to “rolling resistance” of the tires). The force of the truck’s drive wheels pushing backward on the pavement is 3.0 kN. (a) Determine the acceleration rate of the truck and trailer moving forward together. (b) Determine the amount of force the truck’s hitch exerts forward on the trailer.
32. A 275 kg mule pushes backward with its feet 1.50 kN, 180.0° on the ground as it pulls a cart forward. The mule and the cart both accelerate forward 0.500 m/s2, 0.0°. (a) What force does the mule exert on the cart? (b) Assuming the coefficient of friction for the cart is 0.25, what is its mass?
33. The terminal velocity of a baseball falling through air is 43 m/s. However a baseball batted through air can go well over 50 m/s. Explain.
34. A ball is thrown straight up and falls back down and is caught. Make a careful graph of velocity vs. time that shows the ball rising and falling and that illustrates the effect of air resistance. With zero air resistance (and only then), the time rising and the time falling are equal and the speed at which it is caught is equal to the speed at which it was thrown. But, when air resistance is significant, which time is greater, rising or falling? and which speed is greater, throwing or catching? Refer to your graph to help explain your answer.
35. A certain ping-pong ball has mass of 2.4 g and a terminal speed of 10.0 m/s as it falls through air. Suppose the same type of ping-pong ball is then filled with water such that it has a new mass of 21.6 g and it is dropped through the air. (a) Determine the acceleration of the water-filled ball as it falls at 10.0 m/s through the air. (b) Determine the terminal speed of the water-filled ball assuming that the air resistance is proportional to the square of the speed.
36. A 40 kg crate is pulled across the ice with a rope. A force of 100 N, 30° is applied by the rope. Assume friction is negligible. (a) Determine the acceleration of the crate. (b) Determine the normal force that the crate exerts on the ice.
37. A suitcase with mass 18 kg is pulled at a constant speed by a handle that makes an angle θ with the horizontal. The frictional force on the suitcase is 27 N and the force applied on the handle is 43 N. (a) Determine the value of the angle, θ. (b) Determine the normal force exerted on the suitcase.
38. A traffic signal
weighs 150 N and hangs above an intersection. It is supported equally by wires
on either side that form an angle of 120.0°
with each other. (a) What is the tension in each of these wires? (b) If the
angle between the wires is increased to 140.0°, what is the new tension? (c) Now suppose the left
wire is tilted 20.0° from horizontal and the right is tilted 30.0° from
horizontal. Again determine the tension in each wire.
39. Joe suspends a
sign with mass m between two cables. Cable A is directed at angle θ
above horizontal and cable B is horizontal. Nothing but these two cables
supports the sign. Derive expressions for the tension in each cable in terms
of m, θ, and appropriate physical constants.
40. A person exerts a
force of 175 N, 210.0° on a 20.0 kg
crate which slides to the left across a level floor where μ = 0.400. (a) Find the normal
force on the crate. (b) Find the force of friction on the crate. (c) Find the
acceleration of the crate.
41. A 475 gram box is given a push and it then slides up and back down a ramp with a 35.0° incline. The coefficient of friction is 0.30. (a) Determine the rate of deceleration as the box slides up the ramp. (b) Determine the rate of acceleration as the box slides back down the ramp. (c) Determine the amount of applied force necessary to push the box up the ramp at a steady speed.
42. A block initially at rest slides down a ramp of length L that makes an angle of θ with the horizontal. (a) Derive an equation that predicts the time required for the block to reach the bottom of the ramp in terms of L, θ, g, and μ, the coefficient of friction. (b) This derived equation has no real solutions for angles θ ≤ tan–1 (μ). Show algebraically this is the case and explain the physical significance of this – i.e. what does this mean about an actual block on an actual ramp with actual friction?
43. A snow skier of mass 85.0 kg slides with constant velocity down a slope that makes an angle of 10.0° with the horizontal. (a) What is the coefficient of sliding friction? (b) If the slope increases to 15.0° what will be the skier’s rate of acceleration?
44. A daredevil motorcyclist of mass 70.0 kg is going to ride his 450.0 kg motorcycle up a ramp 15.0 m long tilted at an angle of 27.0°. The daredevil reaches the cycle’s top speed, 145 km/h, before starting up the ramp. You are hired as a consultant to analyze the jump. Based on this information, what do you estimate his velocity will be just as he leaves the ramp?
45. Suppose a 2.00 kg object is placed on a ramp of inclination 30.0° and the coefficients of friction are 0.40 and 0.60. A force of 18.0 N acting parallel to the ramp is not enough to start the object moving up the ramp if it is at rest, but it is enough to accelerate it up the ramp once it is in motion. (a) Explain and show mathematically why this is true. (b) Determine the acceleration up the ramp that the 18.0 N force can sustain. (c) Determine the minimum force parallel to the surface that would start the object moving down the ramp if it is initially at rest.
46. Choose and solve one
of these problems from either text:
Open Stax College Physics Problems & Exercises found at end of sections 4.5
– 4.7, 5.1
Etkina, pp. 82 – 83, Chapter 3: 35; pp. 111 - 117, Chapter 4: 17, 24, 27, 29, 30, 33, 45, 47, 54, 75, 82
47. Choose and solve another one of the following problems listed above
Selected Answers: