Question 1

What is the physical significance of the area under the curve shown in the figure?
A) work
B) impulse
C) velocity
D) acceleration
E) mass

Accepted Answer

The area under the curve of a velocity-time graph represents the impulse, which is the product of force and time.

Question 2

A 4.0-kg block, initially at rest, experiences a force that varies with time as shown in the figure. When t = 6.0 ms, the speed of the block is
A) 3.0 m/s
B) 5.0 m/s
C) 6.0 m/s
D) 12 m/s
E) 6.0 km/s

Accepted Answer

The answer of  A 4.0-kg block, initially at rest,...

Question 3

While in horizontal flight at a speed of 20 m/s, a baseball of mass 0.11 kg is struck by a bat. After leaving the bat, the baseball has a speed of 29 m/s in a direction opposite to its original direction. The magnitude of the impulse given the ball is
A) 0.99 kg · m/s
B) 5.4 kg · m/s
C) 2.2 kg · m/s
D) 3.2 kg · m/s
E) 0.55 kg · m/s

Accepted Answer

We can use the impulse-momentum theorem which states that the impulse given to an object is equal to its change in momentum. Mathematically:

I = Δp

Where I is the impulse and Δp is the change in momentum.

The initial momentum of the ball is:

p1 = m*v1

Where m is the mass of the ball, and v1 is its initial velocity.

p1 = (0.11 kg)(20 m/s) = 2.2 kg·m/s

The final momentum of the ball is:

p2 = m*v2

Where v2 is the final velocity of the ball after being struck by the bat. Note that the direction of the velocity is opposite to the initial direction.

p2 = (0.11 kg)(−29 m/s) = −3.19 kg·m/s

The change in momentum is:

Δp = p2 − p1 = −5.39 kg·m/s

The magnitude of the impulse is the absolute value of the change in momentum:

|I| = |Δp| = 5.39 kg·m/s

Therefore, the answer is B) 5.4 kg·m/s.

Question 4

Two balls of equal mass are thrown against a massive wall with equal velocities. The first rebounds with a speed equal to its striking speed, and the second sticks to the wall. The impulse that the first ball transmits to the wall, relative to the second, is
A) twice as great.
B) half as great.
C) the same.
D) four times as great.
E) one-fourth as great.

Accepted Answer

The first ball experiences a change in velocity that is twice its initial velocity (since it reverses direction at the same speed), while the second ball comes to a stop, experiencing a change in velocity equal to its initial velocity. Therefore, the impulse (which depends on the change in momentum, and thus velocity, for a given mass) transmitted by the first ball is twice as great as that transmitted by the second ball.

Question 5

A ball with a mass of 50 g is dropped from a point 5.41 m above a sidewalk. The ball is in contact with the sidewalk for 8.1 $\times$ 10^-3 s. What is the magnitude of the average force exerted on the ball? A) 0.12 kN B) 89 N C) 9.2 N D) 0.49 N E) It cannot be determined without knowing how high the ball bounces.

Accepted Answer

The answer of A ball with a mass of 50...

Question 6

A helium atom (mass = 4m) moving with speed V collides elastically with a tritium (hydrogen 3 ) atom (mass = 3m) at rest. Calculate the speed of the tritium atom after the collision.
A) 0.86 V
B) 1.33 V
C) 1.14 V
D) 1.25 V
E) 1.00 V

Accepted Answer

The answer of A helium atom (mass = 4m) moving...

Question 7

A pitcher throws a baseball with a velocity of 27 m/s. After being struck by a bat the ball travels in the opposite direction with a velocity of 40 m/s. If the ball has a mass of 0.11 kg and is in contact with the bat for 3.0 ms, the average force exerted by the bat on the ball is
A) 0.99 kN
B) 4.8 kN
C) 1.5 kN
D) 7.4 kN
E) 2.5 kN

Accepted Answer

The answer of A pitcher throws a baseball with a...

Question 8

The force exerted on a 10-kg mass is given by
F = 10 + 2t
Where the units are SI. If the mass starts from rest, its velocity after 2 s is
A) 14 m/s
B) 2.0 m/s
C) 2.4 m/s
D) 0.20 m/s
E) 0.24 km/s

Accepted Answer

Using Newton's second law, F = ma, we can find the acceleration of the mass at any time t by dividing both sides of the equation by the mass:

a = F/m = (10 + 2t)/10

To find the velocity after 2 seconds, we need to integrate the acceleration function over the time interval [0, 2]:

v = ∫ a dt = ∫ (10 + 2t)/10 dt

v = [10t/10 + t^2/10] from 0 to 2

v = (20/10 + 4/10) - (0 + 0)/10

v = 2.4 m/s

Therefore, the best choice is (C).

Question 9

The force exerted on a body of mass 10 kg varies with time according to
F = 20t + 10
Where the units are SI. If the velocity of the body was zero at t = 0, its velocity at t = 5 s is
A) 11 m/s
B) 16 m/s
C) 23 m/s
D) 30 m/s
E) 0.11 km/s

Accepted Answer

The answer of The force exerted on a body of...

Question 10

A ball of mass m strikes a wall that is perpendicular to its path at speed +v and rebounds in the opposite direction with a speed -v. The impulse imparted to the ball by the wall is
A) 2mv
B) mv
C) zero
D) -mv
E) -2mv

Accepted Answer

The impulse imparted to the ball by the wall can be calculated using the equation:

impulse = change in momentum

Since the momentum of the ball changes from mv (in the positive direction) before the collision to -mv (in the negative direction) after the collision, the change in momentum is:

Δp = (-mv) - (mv) = -2mv

Therefore, the impulse imparted to the ball by the wall is equal to:

impulse = Δp = -2mv

which corresponds to choice E.

Question 11

A ball of mass m and velocity ₁ collides with and sticks to a ball of mass M and velocity ₂. If the pair moves on with velocity , the impulse given the ball of mass m during the collision must have been A) m( - ₁) B) m( + ₁) C) (m + M) D) (m + M)( - ₂) E) zero

Accepted Answer

The answer of  A ball of mass m and...

Question 12

A body is acted on by an impulsive force from time t = 0 to time t = 10 ms. During this time, the force decreases uniformly from 10³ N to zero as shown in the graph. The change in momentum of the body during this interval is A) 10 kg · m/s B) 5.0 kg · m/s C) 0.16 kg · m/s D) 10⁵ kg · m/s E) a value that cannot be determined from this graph.

Accepted Answer

The change in momentum of an object can be calculated by the formula Δp = FΔt, where Δp is the change in momentum, F is the average force applied over the time interval, and Δt is the time interval. In this case, the force decreases uniformly from 10 N to 0 N over a time interval of 10 ms (0.01 s), so the average force can be calculated as follows:

average force = (10 N + 0 N)/2 = 5 N

The time interval is 0.01 s. Therefore, the change in momentum is:

Δp = FΔt = 5 N x 0.01 s = 0.05 kg · m/s

Therefore, the best choice is B, with a change in momentum of 5.0 kg · m/s.

Question 13

The graph shows the momentum of a body as a function of time. The time at which the force acting on the body is greatest is
A) 0.5 s
B) 2.5 s
C) 4.0 s
D) 1.5 s
E) 5.0 s

Accepted Answer

The answer of  The graph shows the momentum of...

Question 14

Two balls are dropped from a height of 6 m. Ball A bounces up to a height of 4 m whereas ball B bounces up to 2 m. Which ball experiences the larger impulse during its collision with the floor?
A) ball A
B) ball B
C) They both experience the same impulse.
D) It is impossible to tell without knowing the masses of the balls.
E) It is impossible to tell without knowing the durations of the collisions.

Accepted Answer

The answer of Two balls are dropped from a height...

Question 15

A 20-g bullet with an initial velocity of 3.0 $\times$ 10⁴ cm/s penetrates 6.0 cm into a stationary wall. The average force exerted on the bullet by the wall in bringing it to rest is approximately A) 1.5 $\times$ 10⁴ N B) 2.3 $\times$ 10³ N C) 9.8 $\times$ 10^-3 N D) 2.0 $\times$ 10² N E) 4.7 $\times$ 10^-2 N

Accepted Answer

The average force exerted on the bullet can be calculated using the work-energy principle. The work done by the force is equal to the change in kinetic energy of the bullet. The initial kinetic energy of the bullet is given by $ \frac{1}{2}mv^2 $, where $ m = 0.02 $ kg (converting 20 g to kg) and $ v = 300 $ m/s (converting 30000 cm/s to m/s). The final kinetic energy is 0 (since the bullet comes to rest). The work done by the force is also equal to the force times the distance over which it acts ( $ F \times d $ ), where $ d = 0.06 $ m (converting 6 cm to m). Solving for $ F $ gives us the average force.

Question 16

A helium atom (mass = 4m) moving with speed  collides elastically with a deuterium (hydrogen 2 ) atom (mass = 2m) at rest. Calculate the percentage change in the kinetic energy of the helium atom after the collision.
A) 11%
B) 36%
C) 50%
D) 64%
E) 89%

Accepted Answer

The answer of A helium atom (mass = 4m) moving...

Question 17

An automatic rifle fires 0.040-kg projectiles at a speed of 800 m/s. If the gunner holding the rifle in her hands can exert an average force of 160 N against the gun, the maximum number of projectiles she can fire in one minute is
A) 15
B) 300
C) 800
D) 4000
E) 48,000

Accepted Answer

The maximum number of projectiles she can fire in one minute is equal to the number of times she can exert the force to fire the rifle in one minute. The force required to fire one projectile is: 
$$F= \Delta p/\Delta t$$
where $\Delta p$ is the momentum of the projectile and $\Delta t$ is the time required to fire one projectile. Solving for $\Delta t$, we get:
$$\Delta t = \Delta p/F$$
The momentum of each projectile is:
$$p = mv = (0.040 	ext{ kg})(800 	ext{ m/s}) = 32 	ext{ Ns}$$
Therefore, the time required to fire one projectile is:
$$\Delta t = (32 	ext{ Ns})/(160 	ext{ N}) = 0.2 	ext{ s}$$
The number of projectiles that can be fired in one minute is:
$$	ext{Number of projectiles} = (60 	ext{ s})/(0.2 	ext{ s}) = 300$$
Therefore, the correct answer is choice B: 300.

Question 18

A particle of unknown mass has a momentum of 73 kg · m/s. At a time 7.3 s later, the momentum of the particle is 38 kg · m/s. What is the magnitude of the force acting on the particle during the interval, assuming the motion is in a straight line?
A) It cannot be determined because the mass of the particle is not given.
B) 4.8 N
C) 10 N
D) 5.3 N
E) 9.4 N

Accepted Answer

The force acting on the particle can be calculated using the change in momentum (impulse) and the time interval. The change in momentum is the final momentum minus the initial momentum, which is 38 kg·m/s - 73 kg·m/s = -35 kg·m/s. The time interval is 7.3 s. The force is then calculated using the formula F = Δp/Δt, where Δp is the change in momentum and Δt is the time interval. So, F = -35 kg·m/s / 7.3 s = -4.79 N, which is approximately 4.8 N in magnitude. The negative sign indicates the direction of the force, but the question asks for the magnitude, so we take the absolute value.

Question 19

Using a mallet, you strike a ball of mass 0.50 kg that is initially at rest. The force F on the ball as a function of time is plotted in the figure. At t = 2.0 ms, the speed of the ball is
A) 10 m/s
B) 8.0 m/s
C) 6.0 m/s
D) 4.0 m/s
E) 2.0 m/s

Accepted Answer

From the force-time graph, we can see that the time interval during which the force is being applied is from 0 ms to 2 ms. During this time, the impulse (change in momentum) of the ball is given by the area under the force-time graph:

Impulse = force x time = (0.20 N) x (2.0 × 10^-3 s) = 4.0 × 10^-4 Ns

By the impulse-momentum theorem, this impulse is equal to the change in the ball's momentum:

p = mv

Δp = p - p0 = mv - 0

Δp = mv

Δp = 4.0 × 10^-4 Ns

Therefore, the final velocity of the ball is:

v = Δp/m

v = (4.0 × 10^-4 Ns)/(0.50 kg)

v = 0.8 m/s

Thus, the speed of the ball at t = 2.0 ms is 0.8 m/s, which is closest to 4.0 m/s (choice D).

Question 20

A car having a total mass of 2250 kg and traveling at 72 km/h smashes into a tree. The car is stopped in 0.25 s. The driver of the car is not held in place by a seat belt or any other restraining device. Just after the impact but before the driver hits any part of the car, the acceleration of the driver is A) 80 m/s² toward the tree. B) zero with respect to the tree. C) 80 m/s² away from the tree. D) 1.8 $\times$10²m/s² with respect to the car. E) 37 m/s² away from the tree.

Accepted Answer

The answer of A car having a total mass of...

Quiz 8: Systems of Particles and Conservation of Linear Momentum

What is the physical significance of the area under the curve shown in the figure?

A 4.0-kg block, initially at rest, experiences a force that varies with time as shown in the figure. When t = 6.0 ms, the speed of the block is

While in horizontal flight at a speed of 20 m/s, a baseball of mass 0.11 kg is struck by a bat. After leaving the bat, the baseball has a speed of 29 m/s in a direction opposite to its original direction. The magnitude of the impulse given the ball is

Two balls of equal mass are thrown against a massive wall with equal velocities. The first rebounds with a speed equal to its striking speed, and the second sticks to the wall. The impulse that the first ball transmits to the wall, relative to the second, is

A ball with a mass of 50 g is dropped from a point 5.41 m above a sidewalk. The ball is in contact with the sidewalk for 8.1 ×\times× 10-3 s. What is the magnitude of the average force exerted on the ball?

A helium atom (mass = 4m) moving with speed V collides elastically with a tritium (hydrogen 3 ) atom (mass = 3m) at rest. Calculate the speed of the tritium atom after the collision.

A pitcher throws a baseball with a velocity of 27 m/s. After being struck by a bat the ball travels in the opposite direction with a velocity of 40 m/s. If the ball has a mass of 0.11 kg and is in contact with the bat for 3.0 ms, the average force exerted by the bat on the ball is

The force exerted on a 10-kg mass is given by F = 10 + 2t Where the units are SI. If the mass starts from rest, its velocity after 2 s is

The force exerted on a body of mass 10 kg varies with time according to F = 20t + 10 Where the units are SI. If the velocity of the body was zero at t = 0, its velocity at t = 5 s is

A ball of mass m strikes a wall that is perpendicular to its path at speed +v and rebounds in the opposite direction with a speed -v. The impulse imparted to the ball by the wall is

A ball of mass m and velocity 1 collides with and sticks to a ball of mass M and velocity 2. If the pair moves on with velocity , the impulse given the ball of mass m during the collision must have been

A body is acted on by an impulsive force from time t = 0 to time t = 10 ms. During this time, the force decreases uniformly from 103 N to zero as shown in the graph. The change in momentum of the body during this interval is

The graph shows the momentum of a body as a function of time. The time at which the force acting on the body is greatest is

Two balls are dropped from a height of 6 m. Ball A bounces up to a height of 4 m whereas ball B bounces up to 2 m. Which ball experiences the larger impulse during its collision with the floor?

A 20-g bullet with an initial velocity of 3.0 ×\times× 104 cm/s penetrates 6.0 cm into a stationary wall. The average force exerted on the bullet by the wall in bringing it to rest is approximately

A helium atom (mass = 4m) moving with speed collides elastically with a deuterium (hydrogen 2 ) atom (mass = 2m) at rest. Calculate the percentage change in the kinetic energy of the helium atom after the collision.

An automatic rifle fires 0.040-kg projectiles at a speed of 800 m/s. If the gunner holding the rifle in her hands can exert an average force of 160 N against the gun, the maximum number of projectiles she can fire in one minute is

A particle of unknown mass has a momentum of 73 kg · m/s. At a time 7.3 s later, the momentum of the particle is 38 kg · m/s. What is the magnitude of the force acting on the particle during the interval, assuming the motion is in a straight line?

Using a mallet, you strike a ball of mass 0.50 kg that is initially at rest. The force F on the ball as a function of time is plotted in the figure. At t = 2.0 ms, the speed of the ball is

A ball with a mass of 50 g is dropped from a point 5.41 m above a sidewalk. The ball is in contact with the sidewalk for 8.1 $\times$ 10^-3 s. What is the magnitude of the average force exerted on the ball?

A ball of mass m and velocity ₁ collides with and sticks to a ball of mass M and velocity ₂. If the pair moves on with velocity , the impulse given the ball of mass m during the collision must have been

A body is acted on by an impulsive force from time t = 0 to time t = 10 ms. During this time, the force decreases uniformly from 10³ N to zero as shown in the graph. The change in momentum of the body during this interval is

A 20-g bullet with an initial velocity of 3.0 $\times$ 10⁴ cm/s penetrates 6.0 cm into a stationary wall. The average force exerted on the bullet by the wall in bringing it to rest is approximately