Assignment
 Forces

The student will be able to: 
HW: 
1 
State 
1
– 5 
2 
Recognize and state the proper SI unit of
force and give its equivalence in fundamental units and use the relation F_{net}
= ma to solve problems. 
6
– 10 
3 
Recognize the difference between weight and
mass and convert from one to the other. 
11
– 18 
4 
State and utilize 
19
– 21 
5 
Understand and utilize the concept of the
normal force to solve related problems. 
22
– 25 
6 
Understand and utilize the relation between
friction force, normal force, and coefficient of friction for both
cases: static and kinetic. 
26
– 32 
7 
Resolve forces into components using
trigonometry and use the results to solve related force problems. 
33
– 37 
8 
Apply the concept of force components to
objects on an incline and solve related problems. 
38
– 42 
1.
Using
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 not only turn the jar over but also shake it up and
down. Use
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.
A person in a car that is struck from
behind can receive a serious neck injury called whiplash due to his head
“whipping backward”. (a) Use
5.
When the space shuttle is launched from
Earth, a constant force is applied and the shuttle accelerates upward. As the flight progresses, its rate of
acceleration increases. Explain using
6.
A net force of 150 N causes a
certain person to accelerate 1.20 m/s^{2}. 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. Just after the parachute
opens, the acceleration is 5.0 m/s^{2}, 90.0°. (b) Determine the net force at this
point. (c) Which force is larger now and
by how much?
10. Suppose
you hook a 1.5 kg fish while using line that is rated at 38 N (it can only
sustain that much force before breaking – about “9lb test”). If the fish fights back with 40 N of
force, what is the minimum acceleration rate you must play out the line in
order to keep it from breaking?
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
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/s^{2}. 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/s^{2}.
What force does the cable exert to give it this acceleration?
17. A
rocket with a mass of 23.0 Mg is sitting vertically on a launch pad. The rocket’s engine fires to produce a thrust
of 680 kN. (a)
What is the net force acting 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
20. When
you drop a 0.40 kg apple, Earth exerts a force on it that accelerates it toward
the Earth’s surface. Assuming
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/s^{2}, 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/s^{2}. (c) Determine the force that the ball
exerts on the floor as it is bouncing with acceleration 100 m/s^{2},
90.0°.
23. The
maximum force a grocery sack can withstand and not rip is 250 N. If 20 kg of groceries are lifted from
the floor to the table with an acceleration of 5.0 m/s^{2}, will the
sack hold? Assume the person’s hand is
not underneath the sack. Hint: draw a free body diagram of the sack’s
contents (treat as a single object).
24. 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 20^{th}
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.
25. 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 freebody diagram of the stack of
boxes (treat as one object) and solve for the acceleration. (b) Draw a freebody diagram of the upper box
and solve for the normal force pushing up on it. (c) Draw a freebody diagram of the lower box
and solve for the normal force pushing down on it. (d) Explain how these results are consistent
with
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/s^{2}?
27. A
force of 40 N, 180°
accelerates a 5.0 kg block at 6.0 m/s^{2}, 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 wagon
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 m=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.
30. A
truck accelerates from rest toward 0.0°. In the bed of the truck is a 15 kg crate for
which m_{static}
= 0.20 and m_{sliding}
= 0.15. (a) What is the maximum acceleration
rate at which the crate will not slide across the bed? (b) If the truck exceeds this, what will be
the acceleration of the crate?
31. A
truck with mass 2000 kg tows a boat and trailer of total mass 500
kg. The rolling coefficient of friction
for the truck is 0.080 and for the trailer is 0.050. 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/s^{2}, 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. 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.
34. A
suitcase with mass 18 kg is pulled at a constant speed by a handle that makes
an angle q
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, q. (b) Determine the normal force exerted on the
suitcase.
35. 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) As the
wires get closer to horizontal what happens to the tension?
36. Joe
hangs a sign weighing 750 N with two cables.
Cable A is directed toward 120.0°. Cable B is directed toward 0.0°. Nothing but these two cables supports the
sign. Calculate the tension in cable
B.
37. 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 m = 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.
38. You
slide a 325 N trunk up a 20.0°
inclined plane with a constant velocity by exerting a force of 211 N parallel
to the inclined plane. (a) Determine the
component of the trunk’s weight parallel to the plane. (b) What would be the sum of your applied
force, friction, and the parallel component of the trunk’s weight and why? (c) Determine the friction acting on the
trunk. (d) Determine the coefficient of
friction.
39. 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.
40. 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?
41. Choose
and solve one of the following problems from your book, pp. 104 –
111:
19, 20, 34, 36, 46, 57, 60, 64, 67, 77
42. Choose
and solve another one of the following problems from your book, pp. 104
– 111:
19, 20, 34, 36, 46, 57, 60, 64, 67, 77
Answers
to Selected Homework Problems:
1.
2.
3.
4.a.
b.
5.
6. 125 kg
7. 3700 N
8. a. 8.2 ´ 10^{}^{5} m/s^{2}
b. 4700 m/s
9. a. 6.70 m/s^{2}, 270.0°
b. 500 N, 90.0°
c.
10. 1.3 m/s^{2}
11.
12. a.
b. 929 N
c.
d. 934 N
e.
13. 250 kg
14. 53 kN, 90°
15. 5.0 m/s^{2}, 90°
16. 3400 N, 90°
17. a. 455 kN, 90.0°
b. 19.8 m/s^{2}, 90.0°
18. 22.0 m/s^{2}, 33.4°
19.
20. a. 6.6 ´ 10^{}^{25} m/s^{2}
b. 6.7 ´ 10^{}^{26} m
(~ 1/10billion the width of a
single proton!)
21. a. 173 N, 0.0°
b. 173 N, 180.0°
c. 76.6 mm/s^{2}, 180.0°
22. a. 1.96 N, 90.0°
b. 22.0 N, 90.0°
c.
23. No, the sack will rip – would need to
withstand 300 N or not exceed 2.7 m/s^{2}
24. a. 1.2 m/s^{2}, 90°
b. 0.63 m/s^{2}, 270°
c.
25. a. 2.2 m/s^{2}, 90.0°
b. 24.0 N, 90.0°
c. 24.0 N, 270.0°
d.
26. a. 490 N
b. 150 N
c. 49 N
d. 200 N
27. a. 10 N
b. 0.20
28. 5.3 m/s^{2}
29. a. 0.599 m/s^{2}, 0.0°
b. 0.520 m/s^{2}, 180.0°
30. a. 2.0 m/s^{2}
b. 1.5 m/s^{2}
31. a. 0.47 m/s^{2}
b. 480 N
32. a. 1360 N, 0.0°
b. 462 kg
33. a. 2.2 m/s^{2}, 0.0°
b. 340 N, 270°
34. a. 51°
b. 140 N
35. a. 150 N
b. 220 N
c.
36. 430 N
37. a. 284 N, 90.0°
b. 113 N, 0.0°
c. 1.9 m/s^{2}, 180.0°
38. a. 111 N
b.
c. 100 N
d. 0.327
39. a. 8.0 m/s^{2}
b. 3.2 m/s^{2}
c. 3.8 N
40. a. 0.176
b. 0.867 m/s^{2}
41.
42.