What do I need to know before solving these questions? 1. A 40 kg girl is on a swing. The length of the chain that the swing is attached to is 2.40 m.
If the girl is swinging and her speed at the lowest point is 2.0 m/s, what is the tension in
the chain at this point?
2. The braking force on a 15,680N car is 6.4 x 10

2 N. The car initially is moving at 20 m/s.

The car finally stops. What is the car’s mass?
3. The braking force on a 15,680N car is 6.4 x 10

2 N. The car initially is moving at 20m/s.

The car finally stops. What is its initial momentum?
4. The braking force on a 15,680N car is 6.4 x 10

2 N. The car initially is moving at 20m/s.

The car finally stops. What is the change in the car’s momentum?
5. A car of mass m1 stopped at a traffic light is rear-ended by a car with mass m2
. The cars
become entangled. The second car was moving at v2 = 30.0 m/s before the collision.
What is the velocity of the entangled cars after the collision in terms of masses m1 and
m2
, and the initial velocity of the second car?
6. A 9.00x10

2 kg car travelling east at 15.0 m/s collides with a 7.50x10

2 kg car travelling
north at 20.0 m/s. The cars stick together. Ignore unbalanced forces. What is the speed
of the wreckage just after the collision? In what direction does the wreckage move after
the collision?
7. A 0.240 kg glider moving with a velocity of 0.600 m/s collides head-on with a 0.260 kg
glider moving along the same line in the opposite direction with a velocity of 0.200 m/s.
The collision is perfectly inelastic. What is the final velocity of the combined gliders?
8. A 2.50 kg rock is dropped from rest at a height of 3.75 m. What impulse does gravity
impart to the rock from the instant that it is dropped until it hits the ground, assuming
negligible air resistance?
9. Blocks A and B are moving toward each other along the x axis. A has a mass of 2.0 kg
and a velocity of 50 m/s, while B has a mass of 4.0 kg and a velocity of -25 m/s. They
collide head-on in an elastic collision. After the collision, what are the velocities of A and
B?
10. A large platform is initially at rest on a smooth frictionless surface. A dog on the platform
starts running toward the east. The mass of the dog is one-half the mass of the platform.
When the dog moves toward the east with speed vo

, the platform moves ...

11. A very light ideal spring of spring constant (force constant) 2.5 N/cm is 15 cm long when
nothing is attached to it. It is now used to pull horizontally on a 12.5-kg box on a perfectly
smooth horizontal floor. You observe that the box starts from rest and moves 96 cm
during the first 1.6 s of its motion with constant acceleration. How long is the spring
during this motion?
12. A 2.00-kg object is lifted vertically through 3.00 m by a 150-N force. How much work is
done on the object by gravity during this process?
13. How fast must a 6.0-kg cat run to have a kinetic energy of 150 J?
14. You want to store 1,000 J of energy in an ideal spring when it is compressed by only 2.5
cm. What should be the force constant (spring constant) of this spring?
15. An 80-kg man is skating northward and happens to suddenly collide with a 20-kg boy
who is ice skating toward the east. Immediately after the collision, the man and boy are

seen to be moving together at 2.5 m/s in a direction 60° north of east. How fast was the
boy moving just before the collision?
16. A 0.32-kg ball is moving horizontally at 30 m/s just before suddenly bouncing off a wall
Just after the bounce, it is moving horizontally at 25 m/s but in the opposite direction.
a. What is the magnitude of the change in momentum of the ball during the
bounce?
b. What percentage of the ball's original kinetic energy was lost in the collision?
17. As shown in the figure, a bullet of mass 0.010 kg moving horizontally suddenly strikes a
block of wood of mass 1.5 kg that is suspended as a pendulum. The bullet lodges in the
wood, and together they swing upward an angle of 36.87
o
. The length of the string is 2.0

m. What was the speed of the bullet just before it struck the wooden block? 1. A race car circles 10 times around a circular 8.0-km track in 20 min. Using SI units
a. What is its average speed for the ten laps?
b. What is its average velocity for the ten laps?

2. Human reaction times are worsened by alcohol. How much further (in feet) would a
drunk driver's car travel before he hits the brakes than a sober driver's car? Assume that
both are initially traveling at 50.0 mi/h and their cars have the same acceleration while
slowing down, and that the sober driver takes 0.33 s to hit the brakes in a crisis, while the
drunk driver takes 1.0 s to do so. (5280 ft = 1 mi)

3. The velocity v(t) of a particle as a function of time is given by v(t) = (2.3 m/s) + (4.1
m/s2
)t - (6.2 m/s3
)t2
. What is the average acceleration of the particle between t = 1.0 s and

t = 2.0 s?

4. A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m
to the water below. How far does the rock travel horizontally before striking the water,
assuming negligible air resistance?

5. A marble moving 1.48 m/s rolls off the top edge of a 125-cm high table in a room where
there is no appreciable air resistance and the acceleration due to gravity is 9.80 m/s2
.

a. How far from the base of the table will it strike the floor?
b. How long will it be in the air?

6. An athlete competing in the long jump leaves the ground with a speed of 9.14 m/s at an
angle of 55° with the vertical. What is the length of the athlete's jump if air resistance is
of no significance?

7. A projectile is fired from ground level with an initial speed of 55.6 m/s at an angle of
41.2° above the horizontal. Neglect air resistance, take upward as the positive direction,
and use g = 9.80 m/s2
.

a. Determine the time necessary for the projectile to reach its maximum height.
b. Determine the maximum height reached by the projectile.
c. Determine the horizontal and vertical components of the velocity vector at the
maximum height.
d. Determine the horizontal and vertical components of the acceleration vector at the
maximum height.

8. In the figure, block A has a mass of 3.00 kg. It rests on a smooth horizontal table and is
connected by a very light horizontal string over an ideal pulley to block B, which has a
mass of 2.00 kg. When block B is gently released from rest, how long does it take block
B to travel 80.0 cm?

9. A crate with a total mass of 50 kg is initially at rest on a level floor. A horizontal force of
150 N pushes the crate across the floor at a constant acceleration of 1.20 m/s2

. What is the
magnitude of the frictional force acting on the crate? What is the coefficient of kinetic
friction, μk?

10. Three blocks, light connecting ropes, and a light frictionless pulley comprise a system, as
shown in the figure. An external force of magnitude P is applied downward on block A,
causing block A to accelerate downward at a constant 2.5 m/s2. The tension in the rope
connecting block B and block C is equal to 60 N.
a. What is the magnitude of the force P?
b. What is the mass of block C?

11. A spring-loaded dart gun is used to shoot a dart straight up into the air, and the dart
reaches a maximum height of 24 meters above its point of release. The same dart is shot
up a second time from the same gun, but this time the spring is compressed only half as
far (compared to the first shot). How far up does the dart go this time? (Neglect friction
and assume the spring is ideal and massless.)

12. A 0.500-kg ball traveling horizontally on a frictionless surface approaches a very massive
stone at 20.0 m/s perpendicular to wall and rebounds with 70.0% of its initial kinetic
energy. What is the magnitude of the change in momentum of the stone?

13. A 620-g object traveling at 2.1 m/s collides head-on with a 320-g object traveling in the
opposite direction at 3.8 m/s. If the collision is perfectly elastic, what is the change in the
kinetic energy of the 620-g object?

14. A 2.3-kg object traveling at 6.1 m/s collides head-on with a 3.5-kg object traveling in the
opposite direction at 4.8 m/s. If the collision is perfectly elastic, what is the final speed of
the 2.3-kg object?

15. A 900-kg car traveling east at 15.0 m/s collides with a 750-kg car traveling north at 20.0
m/s. The cars stick together. Assume that any other unbalanced forces are negligible.
(a) What is the speed of the wreckage just after the collision?
(b) In what direction does the wreckage move just after the collision?

16. Two ice skaters push off against one another starting from a stationary position. The
45.0-kg skater acquires a speed of 0.375 m/s. What speed does the 60.0-kg skater
acquire? Assume that any other unbalanced forces during the collision are negligible.

17. What is the magnitude of the cross product of a vector of magnitude 2.00 m pointing east
and a vector of magnitude 4.00 m pointing 30.0° west of north?

18. A 2.00-m rod of negligible mass connects two very small objects at its ends. The mass of
one object is 1.00 kg and the mass of the other is unknown. The center of mass of this
system is on the rod a distance 1.60 m from the 1.00-kg mass object. What is the mass of
the other object?

19. At any angular speed, a certain uniform solid sphere of diameter D has half as much
rotational kinetic energy as a certain uniform thin-walled hollow sphere of the same
diameter when both are spinning about an axis through their centers. If the mass of the
solid sphere is M, the mass of the hollow sphere is?

20. In the figure, two blocks, of masses 2.00 kg and 3.00 kg, are connected by a light string
that passes over a frictionless pulley of moment of inertia 0.00400 kg · m2 and radius
5.00 cm. The coefficient of friction for the tabletop is 0.300. The blocks are released from
rest. Using energy methods, find the speed of the upper block just as it has moved 0.600
m.

21. A 72.0-kg person pushes on a small doorknob with a force of 5.00 N perpendicular to the
surface of the door. The doorknob is located 0.800 m from the axis of the frictionless
hinges of the door. The door begins to rotate with an angular acceleration of 2.00 rad/s2
.

What is the moment of inertia of the door about the hinges?

22. A solid uniform sphere of mass 1.85 kg and diameter 45.0 cm spins about an axle through
its center. Starting with an angular velocity of 2.40 rev/s, it stops after turning through
18.2 rev with uniform acceleration. The net torque acting on this sphere as it is slowing
down is closest to what value?

23. In the figure, a very light rope is wrapped around a wheel of radius R = 2.0 meters and
does not slip. The wheel is mounted with frictionless bearings on an axle through its
center. A block of mass 14 kg is suspended from the end of the rope. When the system is
released from rest it is observed that the block descends 10 meters in 2.0 seconds. What is
the moment of inertia of the wheel?

24.1. An airplane increases its speed at the average rate of 15 m/s 2 . How much time
does it take to increase its speed from 100 m/s to 160 m/s?
2. The position x(t) of a particle as a function of time t is given by the equation x(t) =
(3.5 m/s)t - (5.0 m/s 2 )t 2 . What is the average velocity of the particle between t =
0.30 s and t = 0.40 s?
3. A car that is initially moving at 7.50 m/s begins to accelerate forward uniformly at
0.550 m/s 2 .
a. How long after beginning to accelerate does it take the car to move 3.50
km?
b. How fast is the car moving just as it has traveled 3.50 km?
4. At the instant a traffic light turns green, a car that has been waiting at the
intersection starts ahead with a constant acceleration of 2.00 m/s 2 . At that
moment a truck traveling with a constant velocity of 15.0 m/s overtakes and
passes the car.
a. Calculate the time necessary for the car to reach the truck.
b. Calculate the distance beyond the traffic light that the car will pass the
truck.
c. Determine the speed of the car when it passes the truck.
5. A car is moving with a constant acceleration. At time t = 5.0 s its velocity is 8.0
m/s in the forward direction, and at time t = 8.0 s its velocity is 12.0 m/s forward.
What is the distance traveled in that interval of time?
6. A car is traveling at 26.0 m/s when the driver suddenly applies the brakes,
causing the car to slow down with constant acceleration. The car comes to a stop
in a distance of 120 m. How fast was the car moving when it was 60.0 m past the
point where the brakes were applied?
7. A player hits a tennis ball into the air with an initial velocity of 32 m/s at 35° from
the vertical. How fast is the ball moving at the highest point in its trajectory if air
resistance is negligible?
8. A stone is thrown horizontally with an initial speed of 10 m/s from the edge of a
cliff. A stopwatch measures the stone&#39;s trajectory time from the top of the cliff to
the bottom to be 4.3 s. What is the height of the cliff if air resistance is negligibly
small?
9. At target practice, a rifle bullet is fired at an angle of 30° below the horizontal with
an initial velocity of 800 m/s from the top of a cliff 80 m high. How far from the
base of the cliff does it strike the level ground below if air resistance is negligible?
10. A batter hits a home run in which the ball travels 110 m horizontally with no
appreciable air resistance. If the ball left the bat at 50° above the horizontal just
above ground level, how fast was it hit?
11. A hunter points a rifle horizontally and holds it 3.30 m above the ground. The
bullet leaves the barrel at 325 m/s and experiences no significant air resistance.
The acceleration due to gravity at this location is 9.80 m/s 2 .

a. How long does it take for the bullet to strike the ground?
b. How far horizontally does it travel?
12. A projectile leaves the ground at 150 m/s and reaches a maximum height of 0.57
km. If there was no air resistance, at what angle above the horizontal did it leave
the ground?
13. A boy kicks a football from ground level with an initial velocity of 20 m/s at an
angle of 30° above the horizontal. What is the horizontal distance to the point
where the football hits the ground if we neglect air resistance?
14. A projectile is fired from ground level at an angle above the horizontal on an
airless planet where g = 10.0 m/s 2 . The initial x and y components of its velocity
are 86.6 m/s and 50.0 m/s respectively. How long after firing does it take before
the projectile hits the level ground?
15. A projectile is fired at an angle above the horizontal at a location where g = 9.8
m/s 2 . The initial x and y components of its velocity are 86.6 m/s and 50 m/s
respectively. At what angle was the projectile fired above the horizontal?
16. As shown in the figure, a 10-kg block on a perfectly smooth horizontal table is
connected by a horizontal string to a 63-kg block that is hanging over the edge of
the table. What is the magnitude of the acceleration of the 10-kg block when the
other block is gently released?

17. A 50-kg box is being pushed along a horizontal surface. The coefficient of static
friction between the box and the ground is 0.65, and the coefficient of kinetic
friction is 0.35. What horizontal force must be exerted on the box for it to
accelerate at 1.2 m/s 2 ?
18. A 50-kg box is resting on a horizontal floor. A force of 250 N directed at an angle
of 30.0° below the horizontal is applied to the box. The coefficient of static friction
between the box and the surface is 0.40, and the coefficient of kinetic friction is
0.30. What is the force of friction on the box?
19. The figure shows a 100-kg block being released from rest from a height of 1.0 m.
It then takes 0.53 s for it to reach the floor. What is the mass m of the block on
the left? There is no friction or mass in the pulley, and the connecting rope is very
light.

20. A 10-kg sign is held by two ropes as shown in the figure. What is the tension on

rope A?

21. A 3.0-kg and a 5.0-kg box rest side-by-side on a perfectly smooth, level floor. A
horizontal force of 32 N is applied to the 3.0-kg box pushing it against the 5.0-kg
box, and, as a result, both boxes slide along the floor. How hard do the two
boxes push against each other?
22. An object slides on a level floor. It slows and comes to a stop with a constant
acceleration of magnitude 2.4 m/s 2 . What is the coefficient of kinetic friction
between the object and the floor?
23. A 50-kg box is being pushed along a horizontal surface. The coefficient of static
friction between the box and the ground is 0.65, and the coefficient of kinetic
friction is 0.35. What horizontal force must be exerted on the box for it to
accelerate at 1.2 m/s 2 ?
24. A 50-kg box is resting on a horizontal floor. A force of 250 N directed at an angle
of 30.0° below the horizontal is applied to the box. The coefficient of static friction
between the box and the surface is 0.40, and the coefficient of kinetic friction is
0.30. What is the force of friction on the box?
25. A baseball player is running to second base at 5.03 m/s. When he is 4.80 m from
the plate he goes into a slide. The coefficient of kinetic friction between the player
and the ground is 0.180, and the coefficient of static friction is 3.14. What is his
speed when he reaches the plate? 1. An airplane increases its speed at the average rate of 15 m/s2

. How much time does it

take to increase its speed from 100 m/s to 160 m/s?
2. A car that is initially moving at 7.50 m/s begins to accelerate forward uniformly at 0.550
m/s2
.
a. How long after beginning to accelerate does it take the car to move 3.50 km?
b. How fast is the car moving just as it has traveled 3.50 km?
3. At the instant a traffic light turns green, a car that has been waiting at the intersection
starts ahead with a constant acceleration of 2.00 m/s2

. At that moment a truck traveling

with a constant velocity of 15.0 m/s overtakes and passes the car.
a. Calculate the time necessary for the car to reach the truck.
b. Calculate the distance beyond the traffic light that the car will pass the truck.
c. Determine the speed of the car when it passes the truck.
4. A car is moving with a constant acceleration. At time t = 5.0 s its velocity is 8.0 m/s in
the forward direction, and at time t = 8.0 s its velocity is 12.0 m/s forward. What is the
distance traveled in that interval of time?
5. A car is traveling at 26.0 m/s when the driver suddenly applies the brakes, causing the car
to slow down with constant acceleration. The car comes to a stop in a distance of 120 m.
How fast was the car moving when it was 60.0 m past the point where the brakes were
applied?
6. A player hits a tennis ball into the air with an initial velocity of 32 m/s at 35° from the
vertical. How fast is the ball moving at the highest point in its trajectory if air resistance
is negligible?
7. A stone is thrown horizontally with an initial speed of 10 m/s from the edge of a cliff. A
stopwatch measures the stone's trajectory time from the top of the cliff to the bottom to be
4.3 s. What is the height of the cliff if air resistance is negligibly small?
8. At target practice, a rifle bullet is fired at an angle of 30° below the horizontal with an
initial velocity of 800 m/s from the top of a cliff 80 m high. How far from the base of the
cliff does it strike the level ground below if air resistance is negligible?
9. A batter hits a home run in which the ball travels 110 m horizontally with no appreciable
air resistance. If the ball left the bat at 50° above the horizontal just above ground level,
how fast was it hit?
10. A hunter points a rifle horizontally and holds it 3.30 m above the ground. The bullet
leaves the barrel at 325 m/s and experiences no significant air resistance. The acceleration
due to gravity at this location is 9.80 m/s2
.

a. How long does it take for the bullet to strike the ground?
b. How far horizontally does it travel?
11. A projectile leaves the ground at 150 m/s and reaches a maximum height of 0.57 km. If
there was no air resistance, at what angle above the horizontal did it leave the ground?
12. A boy kicks a football from ground level with an initial velocity of 20 m/s at an angle of
30° above the horizontal. What is the horizontal distance to the point where the football
hits the ground if we neglect air resistance?
13. A projectile is fired from ground level at an angle above the horizontal on an airless
planet where g = 10.0 m/s2

. The initial x and y components of its velocity are 86.6 m/s
and 50.0 m/s respectively. How long after firing does it take before the projectile hits the
level ground?

14. A projectile is fired at an angle above the horizontal at a location where g = 9.8 m/s2
. The
initial x and y components of its velocity are 86.6 m/s and 50 m/s respectively. At what
angle was the projectile fired above the horizontal?