Question 1

A 70-kg swimmer dives horizontally off a 500-kg raft.The diver's speed immediately after leaving the raft is 6.0 m/s.A micro-sensor system attached to the edge of the raft measures the time interval during which the diver applies an impulse to the raft just prior to leaving the raft surface.If the time interval is read as 0.25 s,what is the magnitude of the average horizontal force by diver on the raft?

Accepted Answer

D

Question 2

The impulse experienced by a body is equivalent to its change in:

Accepted Answer

The impulse experienced by a body is equal to the change in momentum of the body. Impulse is defined as the force applied multiplied by the time duration for which the force is applied. Therefore, impulse is a measure of the change in momentum of the body. Velocity and kinetic energy may also change due to an applied force, but impulse is directly related to the change in momentum.

Question 3

The dimensional equivalent of the quantity impulse in terms of the fundamental quantities (mass,length,time)is which of the following?

Accepted Answer

Impulse is the product of mass and velocity. Velocity is the product of length and time. Therefore, the dimensional equivalent of impulse is MLT^-1.

Question 4

In an automobile collision,how does an airbag lessen the blow to the passenger? Assume as a result of the collision,the passenger stops.

Accepted Answer

The airbag helps lessen the blow to the passenger by increasing the time for the slowing process, which decreases the average force on the passenger. Unlike the windshield or dashboard, which would provide a short stopping time and a high average force on the passenger, the airbag increases the stopping time and decreases the force on the passenger. The airbag also helps distribute the force of the collision across a larger surface area of the passenger's body, further decreasing the chance of injury.

Question 5

The dimensional equivalence of the quantity "momentum" in terms of the fundamental quantities (mass,length,time)is:

Accepted Answer

Momentum is defined as the product of mass and velocity. The dimensional formula for mass is M, and for velocity (which is length per time) is LT^-1. Therefore, the dimensional formula for momentum is MLT^-1.

Question 6

Alex throws a 0.25-kg rubber ball down onto the floor.The ball's speed just before impact is 4.5 m/s,and just after is 2.9 m/s.What is the change in the magnitude of the ball's momentum?

Accepted Answer

The change in momentum ($\Delta p$) is calculated using the formula $\Delta p = m(v_f - v_i)$, where $m$ is the mass of the ball, $v_f$ is the final velocity, and $v_i$ is the initial velocity. Given that the ball is thrown down and bounces back, the direction of the velocity changes, making the change in velocity $v_f - v_i = 2.9 - (-4.5) = 7.4$ m/s. Thus, $\Delta p = 0.25 \times 7.4 = 1.85$ kg⋅m/s, which rounds to $1.9$ kg⋅m/s.

Question 7

A 0.10-kg ball is moving at 7.0 m/s when it is hit by a bat,causing it to reverse direction and have a speed of 12.0 m/s.What is the change in the magnitude of the momentum of the ball?

Accepted Answer

The change in momentum is calculated as the final momentum minus the initial momentum. The initial momentum is (0.10 kg)(7.0 m/s) = 0.70 kg⋅m/s. The final momentum is (0.10 kg)(12.0 m/s) = 1.20 kg⋅m/s. The change in magnitude is |1.20 - (-0.70)| = 1.90 kg⋅m/s.

Question 8

A car wash nozzle directs a steady stream of water at 1.10 kg/s,with a speed of 30.0 m/s,against a car window.What force does the water exert on the glass? Assume the water does not splash back.

Accepted Answer

The force exerted by the water on the glass is calculated using the formula F = Δp/Δt = m*v, where m is the mass flow rate (1.10 kg/s) and v is the velocity (30.0 m/s). Thus, F = 1.10 kg/s * 30.0 m/s = 33.0 N.

Question 9

The units of impulse are equivalent to:

Accepted Answer

Impulse is equal to force times the change in time, and the dimensions of force are kg•m/s^2 or N. Therefore, the dimensions of impulse are (kg•m/s^2)•s or kg•m/s.

Question 10

A valid unit for momentum is which of the following?

Accepted Answer

Momentum is defined as the product of mass and velocity, and is expressed as kg⋅m/s. Option A is incorrect because it includes an extra "S" which is not a valid unit. Option B is incorrect because it is missing the "s" unit for velocity. Option D is incorrect because N⋅m is a unit of work or energy, not momentum.

Question 11

A ball with original momentum +7.0 kg⋅m/s hits a wall and bounces straight back without losing any kinetic energy.The change in momentum of the ball is:

Accepted Answer

The change in momentum is equal to the final momentum minus the initial momentum. Since the ball bounces straight back without losing any kinetic energy, the final momentum will be equal in magnitude but opposite in direction to the initial momentum. Therefore, the final momentum will be -7.0 kg⋅m/s. 
Change in momentum = final momentum - initial momentum
Change in momentum = (-7.0 kg⋅m/s) - (+7.0 kg⋅m/s) 
Change in momentum = -14 kg⋅m/s, which is choice D.

Question 12

Two masses m₁ and m₂,with m₁ < m₂,have momenta with equal magnitudes.How do their kinetic energies compare?

Accepted Answer

Since momentum (p) is the product of mass (m) and velocity (v), for two objects with equal momentum, the object with the smaller mass (m₁) must have a higher velocity to compensate. Kinetic energy (KE) is given by $ \frac{1}{2}mv^2 $. Therefore, the object with the smaller mass but higher velocity will have a greater kinetic energy because the velocity is squared in the kinetic energy formula, amplifying the effect of the higher velocity.

Question 13

A soccer ball (mass = 0.43 kg)is moving at a speed of 20 m/s when it is kicked with a force of 300 N resulting in it going in the opposite direction with the same speed as before.What is the magnitude of the impulse delivered to the ball?

Accepted Answer

The impulse delivered to an object is equal to the change in its momentum.

Initial momentum = m*v = 0.43 kg * 20 m/s = 8.6 kg*m/s (to the right)
Final momentum = -m*v = -0.43 kg * 20 m/s = -8.6 kg*m/s (to the left)

Change in momentum = Final momentum - Initial momentum
= (-8.6 kg*m/s) - (8.6 kg*m/s)
= -17 kg*m/s

Since the ball was kicked in the opposite direction, the impulse delivered to it would be in the opposite direction as well. Therefore, the magnitude of the impulse would be |-17 kg*m/s| = 17 kg*m/s.

Thus, the correct answer is C.

Question 14

A rock is moving with speed v.If the mass of the rock were tripled and the speed were reduced to v/3,which of the following statements would be true?

Accepted Answer

The kinetic energy (KE) is given by $KE = \frac{1}{2}mv^2$, and the momentum (p) is given by $p = mv$. Initially, let's denote the mass as $m$ and the velocity as $v$. In the second scenario, the mass is tripled to $3m$ and the velocity is reduced to $v/3$. The kinetic energy in the first case is $KE_1 = \frac{1}{2}mv^2$, and in the second case, it is $KE_2 = \frac{1}{2}(3m)(v/3)^2 = \frac{1}{2}mv^2/3$, showing that the kinetic energy is indeed smaller in the second case. The momentum in the first case is $p_1 = mv$, and in the second case, it is $p_2 = 3m(v/3) = mv$, showing that the momenta are the same in both cases.

Question 15

Lonnie pitches a baseball of mass 0.500 kg.The ball arrives at home plate with a speed of 35.0 m/s and is batted straight back to Lonnie with a return speed of 50.0 m/s.If the bat is in contact with the ball for 0.055 s,what is the impulse experienced by the ball?

Accepted Answer

The impulse experienced by the ball is given by the change in momentum of the ball, which can be calculated as follows:

Initial momentum of the ball = m*v1 = 0.500 kg * 35.0 m/s = 17.5 kg*m/s
Final momentum of the ball = m*v2 = 0.500 kg * (-50.0 m/s) = -25.0 kg*m/s

Change in momentum = final momentum - initial momentum = (-25.0 - 17.5) kg*m/s = -42.5 kg*m/s

The negative sign indicates that the direction of the impulse is opposite to the initial momentum of the ball.

Since the bat is in contact with the ball for 0.055 s, the average force exerted by the bat on the ball can be calculated as follows:

Average force = change in momentum / time = (-42.5 kg*m/s) / (0.055 s) = -773 N

Again, the negative sign indicates that the force is in the opposite direction to the initial momentum of the ball.

Therefore, the impulse experienced by the ball is 42.5 N*s (choice B).

Question 16

The law of conservation of momentum is applicable to systems made up of objects described by which of the following?

Accepted Answer

The law of conservation of momentum applies to all systems regardless of scale (macroscopic or microscopic) and includes objects interacting through forces such as friction. It states that the total momentum of a closed system is constant if no external forces act on it.

Question 17

Jerome pitches a baseball of mass 0.300 kg.The ball arrives at home plate with a speed of 40.0 m/s and is batted straight back to Jerome with a return speed of 52.0 m/s.What is the magnitude of change in the ball's momentum?

Accepted Answer

The answer of Jerome pitches a baseball of mass 0.300...

Question 18

A crane drops a 0.250-kg steel ball onto a steel plate.The ball's speeds just before impact and after are 4.00 m/s and 3.70 m/s,respectively.If the ball is in contact with the plate for 0.035 s,what is the magnitude of the average force that the ball exerts on the plate during impact?

Accepted Answer

The impulse on the ball is equal to the change in its momentum:$$J=mv_f-mv_i$$$$J=(0.250	ext{ kg})(3.70	ext{ m/s})-(0.250	ext{ kg})(4.00	ext{ m/s})=-0.075	ext{ kg$\cdot$m/s}$$The average force exerted by the ball on the plate is:$$F=\frac{J}{t}=\frac{-0.075	ext{ kg$\cdot$m/s}}{0.035	ext{ s}}=\boxed{2.14	ext{ N}}$$

Question 19

Alex throws a 0.250-kg rubber ball down onto the floor.The ball's speed just before impact is 5.30 m/s,and just after is 3.71 m/s.If the ball is in contact with the floor for 0.028 s,what is the magnitude of the average force applied by the floor on the ball?

Accepted Answer

The magnitude of the average force applied by the floor on the ball can be calculated using the change in momentum over time, which is given by the formula $ F_{avg} = \frac{\Delta p}{\Delta t} $, where $ \Delta p $ is the change in momentum and $ \Delta t $ is the time interval. The change in momentum $ \Delta p = m(v_f - v_i) $, where $ m $ is the mass of the ball, $ v_f $ is the final velocity (upwards, so we take it as positive 3.71 m/s), and $ v_i $ is the initial velocity (downwards, so we take it as negative -5.30 m/s). Plugging in the values, $ \Delta p = 0.250 \times (3.71 - (-5.30)) = 0.250 \times 9.01 = 2.2525 $ kg·m/s. The time interval $ \Delta t = 0.028 $ s. Therefore, $ F_{avg} = \frac{2.2525}{0.028} \approx 80.4 $ N.

Question 20

If a glass of water is on a table with a piece of paper under it,it is relatively easy to pull the paper out without disturbing the glass very much if the pull is done very quickly.This is because,with a quick pull:

Accepted Answer

The key principle here is that by pulling the paper quickly, the time during which the force is applied is reduced, minimizing the chance for the glass to be disturbed significantly. This is not directly about the force being less, the momentum of the paper, or changes in the coefficient of kinetic friction, but rather about the short duration of the applied force.

Quiz 6: Momentum, Impulse, and Collisions

The impulse experienced by a body is equivalent to its change in:

The dimensional equivalent of the quantity impulse in terms of the fundamental quantities (mass,length,time) is which of the following?

In an automobile collision,how does an airbag lessen the blow to the passenger? Assume as a result of the collision,the passenger stops.

The dimensional equivalence of the quantity "momentum" in terms of the fundamental quantities (mass,length,time) is:

Alex throws a 0.25-kg rubber ball down onto the floor.The ball's speed just before impact is 4.5 m/s,and just after is 2.9 m/s.What is the change in the magnitude of the ball's momentum?

A 0.10-kg ball is moving at 7.0 m/s when it is hit by a bat,causing it to reverse direction and have a speed of 12.0 m/s.What is the change in the magnitude of the momentum of the ball?

A car wash nozzle directs a steady stream of water at 1.10 kg/s,with a speed of 30.0 m/s,against a car window.What force does the water exert on the glass? Assume the water does not splash back.

The units of impulse are equivalent to:

A valid unit for momentum is which of the following?

A ball with original momentum +7.0 kg⋅m/s hits a wall and bounces straight back without losing any kinetic energy.The change in momentum of the ball is:

Two masses m₁ and m₂,with m₁ < m₂,have momenta with equal magnitudes.How do their kinetic energies compare?

A soccer ball (mass = 0.43 kg) is moving at a speed of 20 m/s when it is kicked with a force of 300 N resulting in it going in the opposite direction with the same speed as before.What is the magnitude of the impulse delivered to the ball?

A rock is moving with speed v.If the mass of the rock were tripled and the speed were reduced to v/3,which of the following statements would be true?

Lonnie pitches a baseball of mass 0.500 kg.The ball arrives at home plate with a speed of 35.0 m/s and is batted straight back to Lonnie with a return speed of 50.0 m/s.If the bat is in contact with the ball for 0.055 s,what is the impulse experienced by the ball?

The law of conservation of momentum is applicable to systems made up of objects described by which of the following?

Jerome pitches a baseball of mass 0.300 kg.The ball arrives at home plate with a speed of 40.0 m/s and is batted straight back to Jerome with a return speed of 52.0 m/s.What is the magnitude of change in the ball's momentum?

A crane drops a 0.250-kg steel ball onto a steel plate.The ball's speeds just before impact and after are 4.00 m/s and 3.70 m/s,respectively.If the ball is in contact with the plate for 0.035 s,what is the magnitude of the average force that the ball exerts on the plate during impact?

Alex throws a 0.250-kg rubber ball down onto the floor.The ball's speed just before impact is 5.30 m/s,and just after is 3.71 m/s.If the ball is in contact with the floor for 0.028 s,what is the magnitude of the average force applied by the floor on the ball?

If a glass of water is on a table with a piece of paper under it,it is relatively easy to pull the paper out without disturbing the glass very much if the pull is done very quickly.This is because,with a quick pull:

Quiz 6: Momentum, Impulse, and Collisions

The impulse experienced by a body is equivalent to its change in:

The dimensional equivalent of the quantity impulse in terms of the fundamental quantities (mass,length,time) is which of the following?

In an automobile collision,how does an airbag lessen the blow to the passenger? Assume as a result of the collision,the passenger stops.

The dimensional equivalence of the quantity "momentum" in terms of the fundamental quantities (mass,length,time) is:

Alex throws a 0.25-kg rubber ball down onto the floor.The ball's speed just before impact is 4.5 m/s,and just after is 2.9 m/s.What is the change in the magnitude of the ball's momentum?

A 0.10-kg ball is moving at 7.0 m/s when it is hit by a bat,causing it to reverse direction and have a speed of 12.0 m/s.What is the change in the magnitude of the momentum of the ball?

A car wash nozzle directs a steady stream of water at 1.10 kg/s,with a speed of 30.0 m/s,against a car window.What force does the water exert on the glass? Assume the water does not splash back.

The units of impulse are equivalent to:

A valid unit for momentum is which of the following?

A ball with original momentum +7.0 kg⋅m/s hits a wall and bounces straight back without losing any kinetic energy.The change in momentum of the ball is:

Two masses m1 and m2,with m1 < m2,have momenta with equal magnitudes.How do their kinetic energies compare?

A soccer ball (mass = 0.43 kg) is moving at a speed of 20 m/s when it is kicked with a force of 300 N resulting in it going in the opposite direction with the same speed as before.What is the magnitude of the impulse delivered to the ball?

A rock is moving with speed v.If the mass of the rock were tripled and the speed were reduced to v/3,which of the following statements would be true?

Lonnie pitches a baseball of mass 0.500 kg.The ball arrives at home plate with a speed of 35.0 m/s and is batted straight back to Lonnie with a return speed of 50.0 m/s.If the bat is in contact with the ball for 0.055 s,what is the impulse experienced by the ball?

The law of conservation of momentum is applicable to systems made up of objects described by which of the following?

Jerome pitches a baseball of mass 0.300 kg.The ball arrives at home plate with a speed of 40.0 m/s and is batted straight back to Jerome with a return speed of 52.0 m/s.What is the magnitude of change in the ball's momentum?

A crane drops a 0.250-kg steel ball onto a steel plate.The ball's speeds just before impact and after are 4.00 m/s and 3.70 m/s,respectively.If the ball is in contact with the plate for 0.035 s,what is the magnitude of the average force that the ball exerts on the plate during impact?

Alex throws a 0.250-kg rubber ball down onto the floor.The ball's speed just before impact is 5.30 m/s,and just after is 3.71 m/s.If the ball is in contact with the floor for 0.028 s,what is the magnitude of the average force applied by the floor on the ball?

If a glass of water is on a table with a piece of paper under it,it is relatively easy to pull the paper out without disturbing the glass very much if the pull is done very quickly.This is because,with a quick pull:

Two masses m₁ and m₂,with m₁ < m₂,have momenta with equal magnitudes.How do their kinetic energies compare?