Chapter Problems
4–4 to 4–6 Newton’s
Laws, Gravitational Force, Normal Force
1.
(I) What force is needed to
accelerate a child on a sled (total mass = 60.0 kg) at 1.25 m/s2?
2.
(I) A net force of 265
N accelerates a bike and rider at 2.3 m/s2. What is the mass of
the bike and rider together?
3. (I) How much tension must a rope withstand if it is used to accelerate a 960-kg car horizontally along a frictionless surface
4. (I) What is the weight of a 76-kg astronaut (a) on Earth, (b) on the Moon (g = 1.7m/s2), (c) on Mars (g = 3.7 m/s2), (d) in
outer
space traveling with constant velocity?
5.
(II) A 20.0-kg box
rests on a table. (a) What is the
weight of the box and the normal force acting on it? (b)
A 10.0-kg box is placed on top of the 20.0-kg box, as shown in the figure
below. Determine the normal force that the table exerts on the 20.0-kg box
and the normal force that the 20.0-kg box exerts on the 10.0-kg box.
6.
(II) What average
force is required to stop an 1100-kg car in 8.0 s if the car is traveling at
95 km/h?
7.
(II) What average
force is needed to accelerate a 7.00-gram pellet from rest to 125 m/s over a
distance of 0.800 m along the barrel of a rifle?
8. (II) A fisherman yanks a fish vertically out of the water with an acceleration of 2.5 m/s2 using very light fishing line that has a breaking strength of 22 N.
The fisherman unfortunately loses the
fish as the line snaps. What can you say about the mass of the fish?
9. (II) A 0.140-kg baseball traveling 35.0 m/s strikes the catcher’s mitt, which, in bringing the ball to rest, recoils backward
11.0 cm. What was the average force
applied by the ball on the glove?
10.
(II) How much tension
must a rope withstand if it is used to accelerate a 1200-kg car vertically
upward at 0l80 m/s2 ?
11. (II) A particular race car can cover a quarter-mile track (402 m) in 6.40 s starting from a standstill.
Assuming the acceleration is constant, how many “g’s” does the driver experience? If the combined mass of the driver
and race car
is 485 kg, what horizontal force must the road exert on the tires?
12. (II) A 12.0-kg bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?
13. (II) An elevator (mass 4850 kg) is to be designed so that the maximum acceleration is 0.0680g. What are the maximum
and minimum forces the motor should exert on the
supporting cable?
14. (II) A 75-kg petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets
tied together can support a mass of only 58
kg. How might the thief use this “rope” to escape? Give a quantitative
answer.
15. (II) A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly
reads only 0.75 of the person’s regular weight.
Calculate the acceleration of the elevator, and find the direction of
acceleration.
16. (II) The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration
can it give the elevator without breaking?
17. (II) (a) What is the acceleration of two falling sky divers (mass 132 kg including parachute) when the upward force of
air resistance is equal to one-fourth of their weight? (b) After popping open the parachute, the divers descend leisurely to
the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?
18. (III) A person jumps from the roof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that
his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and
(b)
the average force exerted on his torso by his legs during deceleration.
19.
(I) A box weighing 77.0 N rests on
a table. A rope tied to the box runs vertically upward over a pulley and a
weight is hung from the other end (figure below). Determine the force that
the table exerts on the box if the weight hanging on the other side of the
pulley weighs (a) 30.0 N, (b)
60.0 N, and (c) 90.0 N.
20.
(I) Draw the free-body
diagram for a basketball player (a)
just before leaving the ground on a jump, and (b)
while in the air.
21. (I) Sketch the free-body diagram of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and
is flying toward the outfield.
22. (I) A 650-N force acts in a northwesterly direction. A second 650-N force must be exerted in what direction so that
the resultant of the two forces points westward?
Illustrate your answer with a vector diagram.
23. (II) Arlene is to walk across a “high wire” strung horizontally between two buildings 10.0 m apart. The sag in the rope when
she is at the midpoint is 10.0º as shown in
the figure below.
If her mass is 50.0 kg, what is the tension in the rope at this point?
24. (II) The two forces F1 and F2 shown in (a) below and b (looking down) act on a 27.0-kg object on a frictionless tabletop.
If F1 = 10.2 N and F2
= 16.0 N find the net force on the object and its acceleration for (a)
and (b).
25.
(II) One 3.2-kg paint bucket is
hanging by a massless cord from another 3.2-kg paint bucket, also hanging by
a massless cord, as shown in the figure below. (a)
If the buckets are at rest, what is the tension in each cord? (b)
If the two buckets are pulled upward with an acceleration of
1.60 m/s2 by the upper
cord, calculate the tension in each cord.
26.
(II) A person pushes a 14.0-kg lawn
mower at constant speed with a force of F = 88.0 N directed along the
handle, which is at an angle of 45.0º to the horizontal (Fig. 4–45). (a)
Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force
on the mower, then (c) the normal
force exerted vertically upward on the mower by the ground. (d)
What force must the person exert on the lawn mower to accelerate it from
rest to 1.5 m/s in 2.5 seconds, assuming the same friction force?
27.
(II) Two snowcats tow a housing
unit to a new location at McMurdo Base, Antarctica, as shown in the figure
below. The sum of the forces FA and FB exerted on the
unit by the horizontal cables is parallel to the line L, and FA = 4500 N.
Determine FB and the magnitude of FA + FB.
28.
(II) A train
locomotive is pulling two cars of the same mass behind it, (see figure
belos). Determine the ratio of the tension in the coupling between the
locomotive and the first car
to that between the
first car and the second car
for any nonzero
acceleration of the train.
29.
(II) A window washer pulls herself
upward using the bucket–pulley apparatus shown in the figure below. (a)
How hard must she pull downward to raise herself slowly at constant speed? (b)
If she increases this force by 15%, what will her acceleration be? The mass
of the person plus the bucket is 65 kg.
30.
(II) At the instant a race began, a
65-kg sprinter exerted a force of 720 N on the starting block at a 22º angle
with respect to the ground. (a)
What was the horizontal acceleration of the sprinter? (b)
If the force was exerted for 0.32 s, with what speed did the sprinter leave
the starting block?
31.
(II) Figure 4–49 shows
a block (mass m1) on a smooth horizontal surface, connected by a
thin cord that passes over a pulley to a second block (m2) which
hangs vertically. (a) Draw a
free-body diagram for each block, showing the force of gravity on each, the
force (tension) exerted by the cord, and any normal force. (b)
Apply Newton’s second law to find formulas for the acceleration of the
system and for the tension in the cord. Ignore friction and the masses of
the pulley and cord.
32.
(II) A pair of fuzzy
dice is hanging by a string from your rearview mirror. While you are
accelerating from a stoplight to 28 m/s in 6.0 s, what angle
does the string make
with the vertical? See the figure below.
33.
(III) Three blocks on
a frictionless horizontal surface are in contact with each other, as shown
in Fig. 4–51. A force
is applied to block 1
(mass m1) (a) Draw a
free-body diagram for each block. Determine (b)
the acceleration of the system (in terms of
and
), (c) the net
force on each block, and (d) the
force of contact that each block exerts on its neighbor. (e)
If
and
give numerical answers
to (b), (c),
and (d). Do your answers make
sense intuitively?
34.
(III) The two masses
shown in Fig. 4–52 are each initially 1.80 m above the ground, and the
massless frictionless pulley is 4.8 m above the ground. What maximum height
does the lighter object reach after the system is released? [Hint:
First determine the acceleration of the lighter mass and then its velocity
at the moment the heavier one hits the ground. This is its “launch” speed.
Assume it doesn’t hit the pulley.]
35.
(III) Suppose two
boxes on a frictionless table are connected by a heavy cord of mass 1.0 kg.
Calculate the acceleration of each box and the tension at each end of the
cord, using the free-body diagrams shown in Fig. 4–53. Assume
and ignore sagging of
the cord. Compare your results to Example 4–12 and Fig. 4–22.
4–8 Newton’s
Laws with Friction; Inclines
36.
(I) If the coefficient of kinetic
friction between a 35-kg crate and the floor is 0.30, what horizontal force
is required to move the crate at a steady speed across the floor? What
horizontal force is required if µk is zero?
37.
(I) A force of 48.0 N is required
to start a 5.0-kg box moving across a horizontal concrete floor. (a)
What is the coefficient of static friction between the box and the floor? (b)
If the 48.0-N force continues, the box accelerates at 0.70 m/s2 .
What is the coefficient of kinetic
friction?
38.
(I) Suppose that you are standing
on a train accelerating at 0.20g.
What minimum coefficient of static friction must exist between your feet and
the floor if you are not to slide?
39.
(I) What is the maximum
acceleration a car can undergo if the coefficient of static friction between
the tires and the ground is 0.80?
40.
(II) The coefficient of static
friction between hard rubber and normal street pavement is about 0.8. On how
steep a hill (maximum angle) can you leave a car parked?
41.
(II) A 15.0-kg box is released on a
32º incline and accelerates down the incline at 0.30 m/s2. Find
the friction force impeding its motion. What is the coefficient of kinetic
friction?
42.
(II) A car can decelerate at -4.80
m/s without skidding when coming to rest on a level road. What would its
deceleration be if the road were inclined at 13º uphill? Assume the same
static friction coefficient.
43.
(II) (a)
A box sits at rest on a rough 30º inclined plane. Draw the free-body
diagram, showing all the forces acting on the box. (b)
How would the diagram change if the box were sliding down the plane? (c)
How would it change if the box were sliding up the plane after an initial
shove?
44.
(II) Drag-race tires in contact
with an asphalt surface have a very high coefficient of static friction.
Assuming a constant acceleration and no slipping of tires, estimate the
coefficient of static friction needed for a drag racer to cover 1.0 km in 12
s, starting from rest.
45.
(II) The coefficient of kinetic
friction for a 22-kg bobsled on a track is 0.10. What force is required to
push it down a 6.0º incline and achieve a speed of 60 km/h at the end of 75
m?
46.
(II) For the system of Fig. 4–32
(Example 4–20) how large a mass would box A have to have to prevent any
motion from occurring? Assume µs = -0.30.
47.
(II) A box is given a push so that
it slides across the floor. How far will it go, given that the coefficient
of kinetic friction is 0.20 and the push imparts an initial speed of 4.0
m/s?
48.
(II) Two crates, of
mass 75 kg and 110 kg, are in contact and at rest on a horizontal surface
(Fig. 4–54). A 620-N force is exerted on the 75-kg crate. If the coefficient
of kinetic friction is 0.15, calculate (a)
the acceleration of the system, and (b)
the force that each crate exerts on the other. (c)
Repeat with the crates reversed.
49.
(II) A flatbed truck
is carrying a heavy crate. The coefficient of static friction between the
crate and the bed of the truck is 0.75. What is the maximum rate at which
the driver can decelerate and still avoid having the crate slide against the
cab of the truck?
50.
(II) On an icy day, you worry about
parking your car in your driveway, which has an incline of 12º. Your
neighbor’s driveway has an incline of 9.0º, and the driveway across the
street is at 6.0º. The coefficient of static friction between tire rubber
and ice is 0.15. Which driveway(s) will be safe to park in?
51.
(II) A child slides down a slide
with a 28º incline, and at the bottom her speed is precisely half what it
would have been if the slide had been frictionless. Calculate the
coefficient of kinetic friction between the slide and the child.
52.
(II) The carton shown in the figure
below lies on a plane tilted at an angle
q=
22.0 degrees to
the horizontal, with µk = 0.12. (a)
Determine the acceleration of the carton as it slides down the plane. (b)
If the carton starts from rest 9.30 m up the plane from its base, what will
be the carton’s speed when it reaches the bottom of the incline?
53.
(II) A carton is given
an initial speed of 3.0 m/s up the 22.0º plane shown in the figure below. (a)
How far up the plane will it go? (b)
How much time elapses before it returns to its starting point? Ignore
friction.
54.
(II) A roller coaster
reaches the top of the steepest hill with a speed of 6.0 km/h It then
descends the hill, which is at an average angle of 45º and is 45.0 m long.
What will its speed be when it reaches the bottom? Assume µk =
0.18.
55.
(II) An 18.0-kg box is
released on a 37.0º incline and accelerates down the incline at 0.27 m/s2,
Find the friction force impeding its motion. How large is the coefficient of
kinetic friction?
56.
(II) A small box is
held in place against a rough wall by someone pushing on it with a force
directed upward at 28º above the horizontal. The coefficients of static and
kinetic friction between the box and wall are 0.40 and 0.30, respectively.
The box slides down unless the applied force has magnitude 13 N. What is the
mass of the box?
57.
(II) Piles of snow on
slippery roofs can become dangerous projectiles as they melt. Consider a
chunk of snow at the ridge of a roof with a pitch of 30º. (a)
What is the minimum value of the coefficient of static friction that will
keep the snow from sliding down? (b)
As the snow begins to melt, the coefficient of static friction decreases and
the snow eventually slips. Assuming that the distance from the chunk to the
edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20,
calculate the speed of the snow chunk when it slides off the roof. (c)
If the edge of the roof is 10.0 m above ground, what is the speed of the
snow when it hits the ground?
58.
(III) (a)
Show that the minimum stopping distance for an automobile traveling at speed
v is equal to v2/2µsg where µs
is the coefficient of static friction between the tires and the road,
and g is the acceleration of
gravity. (b) What is this
distance for a 1200-kg car traveling 95 km/h if µs = 0.75?
59.
(III) A coffee cup on
the dashboard of a car slides forward on the dash when the driver
decelerates from 45 km/h to rest in
3.5 s or less, but not if he decelerates in a longer time. What is the
coefficient of static friction between the cup and the dash?
60.
(III) A small block of
mass m is given an initial speed
V0 up a ramp inclined at angle
q
to the horizontal. It travels a distance
d up the ramp and comes to rest.
Determine a formula for the coefficient of kinetic friction between block
and ramp.
61.
(III) The 75-kg
climber in Fig. 4–56 is supported in the “chimney” by the friction forces
exerted on his shoes and back. The static coefficients of friction between
his shoes and the wall, and between his back and the wall, are 0.80 and
0.60, respectively. What is the minimum normal force he must exert? Assume
the walls are vertical and that friction forces are both at a maximum.
Ignore his grip on the rope.
62.
(III) Boxes are moved on a conveyor
belt from where they are filled to the packing station 11.0 m away. The belt
is initially stationary and must finish with zero speed. The most rapid
transit is accomplished if the belt accelerates for half the distance, then
decelerates for the final half of the trip. If the coefficient of static
friction between a box and the belt is 0.60, what is the minimum transit
time for each box?