Download AP Physics-1 Forces HW-2 Read Textbook Chapter 5, sections 5.1

AP Physics-1
Forces HW-2
Read Textbook Chapter 5, sections 5.1 – 5.4: “Applying Newton’s Laws”
Conceptual Questions
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Suppose you jump from a low bridge and perform a perfect swan dive into the water. As you fall, you exert an
upward force on the Earth equal in magnitude to the downward force the Earth exerts on you. Why, then, does it
seem that you are the one doing all the accelerating? Since the forces are the same, why aren’t the accelerations?
Is it possible for an object at rest to have only a single force acting on it? If your answer is yes, provide an
example. If your answer is no, explain why not.
A friend tells you that since his car is at rest, there are no forces acting on it. How would you reply?
You drop two objects from the same height at the same time. Object 1 has a greater mass than object 2. If the
upward force due to air resistance is the same for both objects, which one reaches the ground first? You may
either use free-body diagrams (labeled) or equations to demonstrate the object with the larger acceleration.
Riding in an elevator moving upward with constant speed, you begin a game of darts. Do you have to adjust
your aim, compared to the way you play darts normally? Explain.
Riding in an elevator moving with a constant upward acceleration, you begin a game of darts. Do you have to
adjust your aim, compared to the way you play darts normally? Explain.
Since all objects are “weightless” for an astronaut in orbit, is it possible for astronauts to tell whether an object is
heavy or light? Explain.
A bird cage, with a parrot inside, hangs from a spring scale. The parrot decides to hop (without flapping) from
one perch to another. What can you say about the reading on the scale (a) when the parrot jumps (lunging
upward and pushing down on the perch), (b) when the parrot is in the air, and (c) when the parrot lands on the
second perch? Assume that the scale responds rapidly so that it gives an accurate reading at all times.
If you step off a high board and drop to the water below, you plunge into the water without injury. On the other
hand, if you were to drop the same distance onto solid ground, you might break a leg. Use Newton’s laws and
one of the big three kinematic equations to explain how stopping-distance affects stopping-force.
To clean a rug, you can hang it from a clothesline and beat it with a tennis racket. Use Newton’s laws to explain
why beating the rug should have a cleaning effect.
Is it possible for an object to be moving in one direction while the net force acting on it is in another direction?
If your answer is yes, provide an example. If your answer is no, explain why not.
You hold your hands out in front of you and catch a bowling ball dropped from a foot above your hands… no
problem. If, instead, you were to hold your hands about half an inch above the floor, and try the same catch, you
would have a painful experience. Why? (Don’t try this at home!)
Give the direction of the net force acting on each of the following objects. If the net force is zero, state “zero.”
(a) A car accelerating northward from a stop light. (b) A car traveling southward and slowing down. (c) A car
traveling westward with constant speed. (d) A skydiver parachuting downward with constant speed. (e) A
baseball during its flight from pitcher to catcher (ignoring air resistance).
Give an example of an object that moves in a direction that is at right angles to the net force acting on it.
On a trip to Hawaii, you notice that your plane is flying with constant speed in a straight line. What can you
conclude about the net force acting on the plane? Explain and draw a free-body diagram of the plane.
Since a bucket of water is “weightless” in space, would it hurt to kick the bucket? Explain.
Problems
Draw
free-body diagrams for every problem, ya hear?

The Vector Nature of Forces
9. • A farm tractor tows a 4300-kg trailer up a 26° incline at a steady (constant) speed of 3.0 m/s. What force does
the tractor exert on the trailer? (Ignore friction on the trailer.)
10. •
A shopper pushes a 7.5-kg shopping cart up a 13° incline, as shown in Figure 3. Find the magnitude of the
horizontal force, F, needed to give the cart an acceleration of 1.41 m / s2 .
Figure 3
11. ••
Figure 4
To give a 19-kg child a ride, two teenagers pull on a 3.7-kg sled with ropes, as indicated in Figure 4. Both
teenagers pull with a force of 55 N at an angle of 35° relative to the forward direction, which is the direction of
motion. In addition, the snow exerts a retarding force on the sled that points opposite to the direction of motion,
and has a magnitude of 57 N. Find the acceleration of the sled and child.
12. •• A 65-kg skier speeds down an straight inclined trail. The surface is smooth (negligible friction) and inclined
at an angle of 22° with the horizontal. (a) Find the direction and magnitude of the net force acting on the skier.
(b) Does the net force exerted on the skier increase, decrease, or stay the same as the slope becomes steeper?
Explain.
13. •• A train is traveling up a 3.2° incline at a speed of 3.55 m/s when the last car detaches (breaks free) and
begins to coast. How long does it take for the last car to come to rest? (Neglect friction.)
Weight
14. • You pull directly upward on a stuffed suitcase with a force of 115 N, and it accelerates upward at
0.725 m / s2 . What is (a) the mass and (b) the weight of the suitcase?
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15. • Suppose a rocket launches with an acceleration of 32 m / s . What is the “apparent weight” of an 85-kg
astronaut aboard this rocket? (“Apparent weight” is the normal force of the seat on the astronaut’s underside.)
16. •• A 1.21-g leaf falls straight down toward the ground with a constant speed of 1.1 m/s. (a) What is the force of
air resistance exerted on the leaf? (b) If the constant speed of descent is greater than 1.1 m/s, is the force of air
resistance greater than, less than, or the same as in part (a)? Explain.
17. •• As part of a physics experiment, you stand on a bathroom scale in an elevator. Though your normal weight is
610 N, the scale at the moment reads 730 N. (a) Is the acceleration of the elevator upward, downward, or zero?
Explain. (b) Calculate the magnitude of the elevator’s acceleration.
Normal Forces
18. • A 23-kg suitcase is being pulled by a strap that is at an angle of 25° above the horizontal. If the normal force
exerted on the suitcase by the floor is 180 N, what is the magnitude of the force Fstrap (@ 25°) applied to the
handle-strap?
19. • A 9.3-kg child sits in a 3.7-kg high chair. (a) Draw a free-body diagram for the child, and find the normal
force exerted by the chair on the child. (b) Draw a free-body diagram for the chair, and find the normal force
exerted by the floor on the chair.
20. •• A 5.0-kg bag of potatoes sits on the bottom of a stationary shopping cart. Sketch a free-body diagram for the
bag of potatoes. Now suppose the cart moves with a constant velocity. How does this affect your free-body
diagram?
21. •• A gardener pushes an old-fashioned lawn mower to the right. The handle of the mower makes an angle of
32° with the surface of the lawn. (a) If a 209-N force is applied along the handle (in the 328° direction) of the
18-kg mower, what is the normal force exerted by the lawn on the mower? (b) If the angle between the surface
of the lawn and the handle of the mower is increased, does the normal force exerted by the lawn increase,
decrease, or stay the same? Explain.
Answers available online as an extension of this file.
Answers
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Ftractor on trailer = 18,470 N @ 26°
F = 27.8 N
a = 1.46 m/s2 @ 180°
(a) The net force on the skier is just the component of her weight parallel to the incline, F g. The net force
on the skier, as well as the direction of her motion, is parallel to the slope.
 FNET on skier = 239 N downhill parallel to slope.
(b) As the slope becomes steeper, the net force increases. This is because as the incline increases, sin 
approaches 1. In this case, the skier is falling. As the incline decreases, sin  approaches zero and the
skier no longer accelerates. In this case, the force of gravity is balanced by the normal force of the
ground on the skier.
After the last car breaks free, it will continue in the direction of the train until the parallel component of its
weight, Fg, brings it to rest (and then pulls it downhill).
The acceleration due to gravity is 0.547 m/s2, so from kinematics you’ll get t = 6.49 s s
(a) 10.9 kg
(b) 107 N
FN = 3.55 kN
(a) The leaf is falling with constant speed, therefore the net force on it is zero. Fair on leaf = 11.9 milli-N
(b) The force of air resistance is the same. Motion with constant velocity implies no net force.
(a) The direction of acceleration is upward. An upward acceleration results in an apparent weight greater
than the actual weight.
(b) a = 1.93 m/s2
Fstrap = 107 N
(a) FN (chair on child) = 91.1 N @ 90°
(b) FN (floor on chair) = 127 N @ 90°
FBD should include two equal and opposite vertical forces: Fg (earth on taters)  and FN (cart on taters)  If the cart
moves at constant velocity…The free-body diagram does not change. A constant velocity implies zero
acceleration (zero net force).
(a) FN = 287 N @ 90°
(b) The normal force increases because…as  increases, sin increases, so the vertical component of the
applied force down along the handle increases. To balance this downward force the lawn must exert a
bigger normal force upward.