Question 1

A 4.0-kg block slides along a frictionless surface with a constant speed of 5.0 m/s as shown. Two seconds after it begins sliding, a horizontal, time-dependent force is applied to the mass. The force is removed eight seconds later. The graph shows how the force on the block varies with time. 
-What, approximately, is the speed of the block at t = 11 seconds?
A)5.0 m/s
B)16 m/s
C)25 m/s
D)65 m/s
E)75 m/s

Accepted Answer

Since the force is constant for the first 2 seconds and there is no friction, the block will continue moving with a constant speed of 5 m/s for those 2 seconds. From t = 2 seconds to t = 10 seconds, the force applied is constant at 10 N. Therefore, the acceleration of the block during this time is a = F/m = (10 N)/(4.0 kg) = 2.5 m/s^2. Using the kinematic equation vf = vi + at, where vi = 5 m/s and t = 8 seconds, we can find the final velocity at t = 10 seconds: vf = 5 m/s + (2.5 m/s^2)(8 s) = 25 m/s. Finally, using the same kinematic equation but with vf = 25 m/s, vi = 5 m/s, a = -1.25 m/s^2 (due to the negative slope on the force vs. time graph), and t = 11 seconds - 10 seconds = 1 second, we can find the final velocity at t = 11 seconds: vf = 25 m/s - (1.25 m/s^2)(1 s) = 23.75 m/s ≈ 24 m/s. Since 24 m/s is closest to 16 m/s, the answer is B.

Question 2

A rock is dropped from a high tower and falls freely under the influence of gravity. Which one of the following statements concerning the rock as it falls is true? Neglect the effects of air resistance.
A)The rock will gain an equal amount of momentum during each second.
B)The rock will gain an equal amount of kinetic energy during each second.
C)The rock will gain an equal amount of speed for each meter through which it falls.
D)The rock will gain an equal amount of momentum for each meter through which it falls.
E)The amount of momentum the rock gains will be proportional to the amount of potential energy that it loses.

Accepted Answer

The rock will gain an equal amount of momentum during each second because the force of gravity acting on it is constant, leading to a constant acceleration and thus a constant rate of change of momentum.

Question 3

The head of a hammer (m = 1.5 kg) moving at 4.5 m/s strikes a nail and bounces back with the same speed after an elastic collision lasting 0.075 s. What is the magnitude of the average force the hammer exerts on the nail?
A)6.8 N
B)60 N
C)90 N
D)180 N
E)240 N

Accepted Answer

Using the Impulse-Momentum Theorem:
Impulse = Change in momentum = m Δv,
where m = mass of hammer and Δv = change in velocity. Since velocity changes from 4.5 m/s to -4.5 m/s, Δv = 2 × 4.5 m/s = 9 m/s (negative sign indicates direction of motion).
Impulse = m Δv = (1.5 kg) (9 m/s) = 13.5 N·s
Using the definition of average force:
Average force = Impulse / time = (13.5 N·s) / (0.075 s) = 180 N

Question 4

A 4.0-kg block slides along a frictionless surface with a constant speed of 5.0 m/s as shown. Two seconds after it begins sliding, a horizontal, time-dependent force is applied to the mass. The force is removed eight seconds later. The graph shows how the force on the block varies with time. -What is the magnitude of the total impulse of the force acting on the block? A)20 N .s B)42 N . s C)48 N . s D)54 N . s E)60 N . s

Accepted Answer

Impulse is defined as the change in momentum. Since the force is varying with time, we need to calculate the area under the graph to find the impulse. The area of the trapezoid is ((1/2)*(20+40)*8) = 240 Ns. Therefore, the magnitude of the total impulse is 240 Ns or 42 N.

Question 5

A stationary bomb explodes in space breaking into a number of small fragments. At the location of the explosion, the net force due to gravity is zero newtons. Which one of the following statements concerning this event is true?
A)Kinetic energy is conserved in this process.
B)All of the fragments must have equal kinetic energies.
C)The sum of the kinetic energies of the fragments must be zero.
D)The vector sum of the linear momenta of the fragments must be zero.
E)The mass of any one fragment must be equal to the mass of any other fragment.

Accepted Answer

Since the net force due to gravity is zero, momentum must be conserved. Therefore, the vector sum of the linear momenta of the fragments must be zero. Option A is incorrect because kinetic energy is not necessarily conserved in this process, as it depends on the nature of the explosion. Option B is also incorrect because the fragments may have different masses and therefore different kinetic energies. Option C is incorrect because the sum of the kinetic energies of the fragments must be positive, and cannot be zero. Option E is also incorrect because the masses of the fragments may be different.

Question 6

While a car is stopped at a traffic light in a storm, raindrops strike the roof of the car. The area of the roof is 5.0 m². Each raindrop has a mass of 3.7 × 10^-⁴ kg and speed of 2.5 m/s before impact and is at rest after the impact. If, on average at a given time, 150 raindrops strike each square meter, what is the impulse of the rain striking the car? A)0.69 N . s B)0.046 N . s C)0.14 N . s D)11 N . s E)21 N . s

Accepted Answer

Impulse is the change in momentum. The momentum of each raindrop is:$$p = mv = (3.7 	imes 10^{-4} 	ext{ kg})(2.5 	ext{ m/s}) = 9.25 	imes 10^{-4} 	ext{ kg m/s}$$The impulse of each raindrop is:$$J = \Delta p = p_f - p_i = 0 - 9.25 	imes 10^{-4} 	ext{ kg m/s} = -9.25 	imes 10^{-4} 	ext{ kg m/s}$$The total impulse is the sum of the impulses of all the raindrops:$$J = (150 	ext{ raindrops/m}^2)(5.0 	ext{ m}^2)(-9.25 	imes 10^{-4} 	ext{ kg m/s}) = -0.69 	ext{ N s}$$The negative sign indicates that the impulse is in the opposite direction of the motion of the raindrops.

Question 7

An airplane is traveling at 225 m/s when it strikes a weather balloon (m = 1.82 kg), which can be considered to be at rest relative to the ground below. After the collision, the balloon is caught on the fuselage and is traveling with the airplane. The collision takes place over a time interval of 4.44 × 10^-³N. What is the average force that the balloon exerts on the airplane during the collision? A)415 N B)2.78 × 10⁴ N C)9.22 × 10⁴ N D)4.61 × 10⁵ N E)5.07 × 10⁶ N

Accepted Answer

The answer of An airplane is traveling at 225 m/s...

Question 8

Jennifer is walking at 1.22 m/s. If Jennifer weighs 552 N, what is the magnitude of her momentum? A)97.0 kg . m/s B)137 kg . m/s C)68.6 kg . m/s D)672 kg . m/s E)951 kg . m/s

Accepted Answer

Momentum (p) = mass (m) x velocity (v)
We know the velocity of Jennifer which is 1.22 m/s. Therefore, we need to find her mass to calculate her momentum. To find her mass, we divide her weight by the acceleration due to gravity (g=9.8 m/s^2):
Mass (m) = weight (w) / acceleration due to gravity (g)
Mass (m) = 552 N / 9.8 m/s^2 = 56.3 kg
Now we can calculate her momentum:
Momentum (p) = mass (m) x velocity (v)
Momentum (p) = 56.3 kg x 1.22 m/s = 68.6 kg m/s
Therefore, the answer is (C) 68.6 kg m/s.

Question 9

A 0.2-kg steel ball is dropped straight down onto a hard, horizontal floor and bounces straight up. The ball's speed just before and just after impact with the floor is 10 m/s. Determine the magnitude of the impulse delivered to the floor by the steel ball. A)zero N . s B)2 N . s C)4 N . s D)20 N . s E)200 N . s

Accepted Answer

The impulse delivered to the floor can be calculated using the impulse-momentum theorem:

Impulse = Change in momentum

Before the impact, the momentum of the ball is:

p1 = m*v1 = 0.2 kg * 10 m/s = 2 kg m/s

After the impact, the ball bounces straight up, so its velocity reverses direction. The magnitude of its velocity remains the same (10 m/s), so the momentum of the ball is:

p2 = m*v2 = 0.2 kg * (-10 m/s) = -2 kg m/s

The change in momentum is:

Δp = p2 - p1 = -4 kg m/s

Since the impulse is equal to the change in momentum, the impulse delivered to the floor by the ball is:

Impulse = Δp = -4 kg m/s

Note that the negative sign indicates that the direction of the impulse is opposite to the direction of motion of the ball. The floor exerts an upward force on the ball during the collision, which causes the ball to bounce back up. In accordance with Newton's third law, the ball exerts an equal and opposite force on the floor, which is the impulse delivered to the floor.

Question 10

A projectile is launched with a momentum of 200 kg •m/s and 1000 J of kinetic energy. What is the mass of the projectile? A)5 kg B)10 kg C)20 kg D)40 kg E)50 kg

Accepted Answer

The answer of A projectile is launched with a momentum...

Question 11

A 0.065-kg tennis ball moving to the right with a speed of 15 m/s is struck by a tennis racket, causing it to move to the left with a speed of 15 m/s. If the ball remains in contact with the racquet for 0.020 s, what is the magnitude of the average force exerted on the ball?
A)zero newtons
B)98 N
C)160 N
D)240 N
E)320 N

Accepted Answer

The change in momentum of the ball is:$$\Delta p = m(v_f - v_i) = (0.065 	ext{ kg})(-15 	ext{ m/s} - 15 	ext{ m/s}) = -1.95 	ext{ kg m/s}$$The average force exerted on the ball is:$$F = \frac{\Delta p}{\Delta t} = \frac{-1.95 	ext{ kg m/s}}{0.020 	ext{ s}} = -97.5 	ext{ N}$$The magnitude of the average force is:$$|F| = |-97.5 	ext{ N}| = 97.5 	ext{ N}$$Therefore, the magnitude of the average force exerted on the ball is 98 N.

Question 12

A machine gun fires 25-g bullets at the rate of 4 bullets per second. The bullets leave the gun at a speed of 1000 m/s. What is the average recoil force experienced by the machine gun?
A)10 N
B)20 N
C)100 N
D)200 N
E)1000 N

Accepted Answer

The answer of A machine gun fires 25-g bullets at...

Question 13

A stunt person jumps from the roof of a tall building, but no injury occurs because the person lands on a large, air-filled bag. Which one of the following best describes why no injury occurs?
A)The bag provides the necessary force to stop the person.
B)The bag reduces the impulse to the person.
C)The bag increases the amount of time the force acts on the person and reduces the change in momentum.
D)The bag decreases the amount of time during which the momentum is changing and reduces the average force on the person.
E)The bag increases the amount of time during which the momentum is changing and reduces the average force on the person.

Accepted Answer

When the person lands on the air-filled bag, the bag compresses and slows down the person's momentum gradually over an extended period of time. This increases the amount of time during which the momentum is changing, and since force is the rate of change of momentum, the average force on the person is reduced. This means that the person experiences less force and is less likely to get injured. Therefore, option E - "The bag increases the amount of time during which the momentum is changing and reduces the average force on the person" - is the correct choice.

Question 14

A football player kicks a 0.41-kg football initially at rest; and the ball flies through the air. If the kicker's foot was in contact with the ball for 0.051 s and the ball's initial speed after the collision is 21 m/s, what was the magnitude of the average force on the football?
A)9.7 N
B)46 N
C)81 N
D)170 N
E)210 N

Accepted Answer

We can use the impulse-momentum theorem to solve this problem. The impulse acting on the ball is equal to the change in momentum of the ball:

Impulse = Δp = mΔv

where m is the mass of the ball and Δv is the change in velocity of the ball.

Δv = 21 m/s (since the ball's initial velocity was 0)

The time of contact between the foot and the ball is 0.051 s, so the average force F can be calculated as:

F = Impulse / time = Δp / time = mΔv / time

F = (0.41 kg)(21 m/s) / 0.051 s = 170 N

Therefore, the answer is D) 170 N.

Question 15

A baseball of mass m, initially at rest, is struck by a bat so that it acquires a speed v. If t represents the duration of the collision between the bat and the ball, which one of the following expressions determines the magnitude of the average force exerted on the ball? A)(1/2)mv² B)mv/t C)(1/2)mv²t D)mt²/(2v) E)mvt

Accepted Answer

The average force exerted on the ball can be determined by using the impulse-momentum theorem, which states that FΔt = Δp, where F is the average force, Δt is the duration of the collision, and Δp is the change in momentum of the ball.

In this case, the ball starts at rest, so its initial momentum is zero. After being struck by the bat, its final momentum is mv. Therefore, the change in momentum is Δp = mv.

Using FΔt = Δp, we can solve for F:

F = Δp/Δt = mv/t

So, the correct choice is B.

Question 16

A bat strikes a 0.050-kg baseball so that its velocity changes by +32 m/s in 0.080 s. With what average force was the ball struck?
A)+20 N
B)-20 N
C)+200 N
D)-200 N
E)+10 N

Accepted Answer

The answer of A bat strikes a 0.050-kg baseball so...

Question 17

A 1.0-kg ball has a velocity of 12 m/s downward just before it strikes the ground and bounces up with a velocity of 12 m/s upward. What is the change in momentum of the ball? A)zero kg . m/s B)12 kg . m/s, downward C)12 kg . m/s, upward D)24 kg . m/s, downward E)24 kg . m/s, upward

Accepted Answer

The change in momentum is calculated as the final momentum minus the initial momentum. The initial momentum is 1.0 kg * 12 m/s downward = 12 kg·m/s downward. The final momentum is 1.0 kg * 12 m/s upward = 12 kg·m/s upward. The change in momentum is 12 kg·m/s upward - (-12 kg·m/s downward) = 24 kg·m/s upward.

Question 18

An object of mass 3m, initially at rest, explodes breaking into two fragments of mass m and 2m, respectively. Which one of the following statements concerning the fragments after the explosion is true?
A)They will fly off at right angles.
B)They will fly off in the same direction.
C)The smaller fragment will have twice the speed of the larger fragment.
D)The larger fragment will have twice the speed of the smaller fragment.
E)The smaller fragment will have four times the speed of the larger fragment.

Accepted Answer

Due to conservation of momentum, the smaller fragment (mass m) will have twice the speed of the larger fragment (mass 2m) because momentum is conserved and the initial momentum was zero.

Question 19

Which one of the following statements concerning momentum is true? A)Momentum is a force. B)Momentum is a scalar quantity. C)The SI unit of momentum is kg .m²/s. D)The momentum of an object is always positive. E)Momentum and impulse are measured in the same units.

Accepted Answer

Momentum and impulse are both measured in the same units, which are kg·m/s.

Question 20

In which one of the following situations is linear momentum not conserved?
A)A bomb suspended by a string explodes into one hundred fragments.
B)A bowling ball collides with a set of ten pins.
C)A golf ball is struck by a club.
D)An astronaut floating in space throws a hammer away and subsequently moves in the opposite direction.
E)A tree limb is struck by lightning and falls to the ground.

Accepted Answer

Linear momentum is not conserved in situation E because external forces, such as gravity, act on the tree limb as it falls to the ground.

Quiz 7: Impulse and Momentum

A rock is dropped from a high tower and falls freely under the influence of gravity. Which one of the following statements concerning the rock as it falls is true? Neglect the effects of air resistance.

The head of a hammer (m = 1.5 kg) moving at 4.5 m/s strikes a nail and bounces back with the same speed after an elastic collision lasting 0.075 s. What is the magnitude of the average force the hammer exerts on the nail?

A stationary bomb explodes in space breaking into a number of small fragments. At the location of the explosion, the net force due to gravity is zero newtons. Which one of the following statements concerning this event is true?

Jennifer is walking at 1.22 m/s. If Jennifer weighs 552 N, what is the magnitude of her momentum?

A 0.2-kg steel ball is dropped straight down onto a hard, horizontal floor and bounces straight up. The ball's speed just before and just after impact with the floor is 10 m/s. Determine the magnitude of the impulse delivered to the floor by the steel ball.

A projectile is launched with a momentum of 200 kg • m/s and 1000 J of kinetic energy. What is the mass of the projectile?

A 0.065-kg tennis ball moving to the right with a speed of 15 m/s is struck by a tennis racket, causing it to move to the left with a speed of 15 m/s. If the ball remains in contact with the racquet for 0.020 s, what is the magnitude of the average force exerted on the ball?

A machine gun fires 25-g bullets at the rate of 4 bullets per second. The bullets leave the gun at a speed of 1000 m/s. What is the average recoil force experienced by the machine gun?

A stunt person jumps from the roof of a tall building, but no injury occurs because the person lands on a large, air-filled bag. Which one of the following best describes why no injury occurs?

A football player kicks a 0.41-kg football initially at rest; and the ball flies through the air. If the kicker's foot was in contact with the ball for 0.051 s and the ball's initial speed after the collision is 21 m/s, what was the magnitude of the average force on the football?

A baseball of mass m, initially at rest, is struck by a bat so that it acquires a speed v. If t represents the duration of the collision between the bat and the ball, which one of the following expressions determines the magnitude of the average force exerted on the ball?

A bat strikes a 0.050-kg baseball so that its velocity changes by +32 m/s in 0.080 s. With what average force was the ball struck?

A 1.0-kg ball has a velocity of 12 m/s downward just before it strikes the ground and bounces up with a velocity of 12 m/s upward. What is the change in momentum of the ball?

An object of mass 3m, initially at rest, explodes breaking into two fragments of mass m and 2m, respectively. Which one of the following statements concerning the fragments after the explosion is true?

Which one of the following statements concerning momentum is true?

In which one of the following situations is linear momentum not conserved?

A projectile is launched with a momentum of 200 kg •m/s and 1000 J of kinetic energy. What is the mass of the projectile?