Question 1

A car wash nozzle directs a steady stream of water at 1.5 kg/s, with a speed of 20 m/s, against a car window. What force does the water exert on the glass? Assume the water does not splash back.

Accepted Answer

A

Question 2

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 3

A 75-kg swimmer dives horizontally off a 500-kg raft. The diver's speed immediately after leaving the raft is 1.6 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 0.20 s, what is the magnitude of the average horizontal force by diver on the raft?

Accepted Answer

We can use the impulse-momentum theorem in the horizontal direction to solve for the average horizontal force on the raft:

Impulse = Change in momentum
FΔt = mΔv

where F is the average horizontal force on the raft, Δt is the time interval during which the diver applies an impulse to the raft, m is the mass of the raft, and Δv is the change in horizontal velocity of the raft.

The mass of the raft is given as 500 kg, and the change in horizontal velocity of the raft is zero because the raft is stationary before and after the dive.

Therefore, F = mΔv/Δt = (75 kg)(1.6 m/s)/0.20 s = 600 N

So the best choice is C, with an average horizontal force of 600 N.

Question 4

Jerome pitches a baseball of mass 0.15 kg. The ball arrives at home plate with a speed of 40 m/s and is batted straight back to Jerome with a return speed of 60 m/s. What is the magnitude of change in the ball's momentum?

Accepted Answer

The answer of Jerome pitches a baseball of mass 0.15...

Question 5

The kinetic energy of an object is quadrupled. Its momentum will change by what factor?

Accepted Answer

The formula for kinetic energy is K = 1/2mv^2 while the formula for momentum is P = mv.
If the kinetic energy is quadrupled, then the new kinetic energy is 4K.
Thus, 4K = 1/2mv^2 * 4
Momentum = mv 
If the mass remains the same, then the velocity will double in order to maintain the new kinetic energy. Thus the new velocity is square root of (4K / (1/2m))
New momentum = mass * new velocity
New momentum= m * (square root of (4K/(1/2m)))
= m * square root of 8mv^2 (from above)
= square root of 8 * mv * m
= square root of 8 * momentum (using Pv = mvm)
Therefore, the momentum changes by a factor of 2.

Question 6

Alex throws a 0.15-kg rubber ball down onto the floor. The ball's speed just before impact is 6.5 m/s and just after is 3.5 m/s. If the ball is in contact with the floor for 0.050 s, what is the magnitude of the average force applied by the floor on the ball?

Accepted Answer

The answer of Alex throws a 0.15-kg rubber ball down...

Question 7

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 8

A 0.12-kg ball is moving at 6.0 m/s when it is hit by a bat, causing it to reverse direction and have a speed of 8.0 m/s. What is the magnitude of the change in the momentum of the ball?

Accepted Answer

The answer of A 0.12-kg ball is moving at 6.0...

Question 9

If the momentum of an object is tripled, its kinetic energy will change by what factor?

Accepted Answer

The kinetic energy (KE) is given by the formula KE = (1/2)mv^2, where m is the mass and v is the velocity of the object. Momentum (p) is given by the formula p = mv. If the momentum is tripled, it means the new momentum p' = 3mv. Since the mass (m) remains constant, this implies that the velocity must be tripled for the momentum to triple. Substituting the tripled velocity into the kinetic energy formula, we get KE' = (1/2)m(3v)^2 = (1/2)m(9v^2) = 9 * (1/2)mv^2, which means the kinetic energy is increased by a factor of nine.

Question 10

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

Accepted Answer

Impulse is defined as the change in momentum of a body.

Question 11

Lonnie pitches a baseball of mass 0.15 kg. The ball arrives at home plate with a speed of 40 m/s and is batted straight back to Lonnie with a return speed of 60 m/s. If the bat is in contact with the ball for 0.050 s, what is the impulse experienced by the ball?

Accepted Answer

The answer of Lonnie pitches a baseball of mass 0.15...

Question 12

Alex throws a 0.43-kg rubber ball down onto the floor. The ball's speed just before impact is 6.5 m/s, and just after is 5.5 m/s. What is the magnitude of the change in the ball's momentum?

Accepted Answer

The answer of Alex throws a 0.43-kg rubber ball down...

Question 13

A crane drops a 0.40-kg steel ball onto a steel plate. The ball's speeds just before impact and after are 4.5 m/s and 4.2 m/s, respectively. If the ball is in contact with the plate for 0.030 s, what is the magnitude of the average force that the ball exerts on the plate during impact?

Accepted Answer

We can use the impulse-momentum theorem to solve this problem. The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse applied to it:

impulse = change in momentum

The momentum of an object is given by:

momentum = mass x velocity

Before the impact, the momentum of the ball is:

p1 = mv1 = (0.40 kg)(4.5 m/s) = 1.8 kg m/s

After the impact, the momentum of the ball is:

p2 = mv2 = (0.40 kg)(4.2 m/s) = 1.68 kg m/s

The change in momentum is:

Δp = p2 - p1 = 1.68 kg m/s - 1.8 kg m/s = -0.12 kg m/s

The negative sign indicates that the momentum of the ball has decreased. This is because the ball is moving in the opposite direction after the impact.

The impulse applied to the ball is:

impulse = FΔt

where F is the average force applied to the ball and Δt is the time interval during which the force is applied.

We are given that Δt = 0.030 s. Substituting this into the equation above gives:

F = impulse/Δt = Δp/Δt = (-0.12 kg m/s)/(0.030 s) = -4 N

The negative sign indicates that the average force applied to the ball is in the opposite direction to the motion.

However, we need to find the magnitude of the force, which is given by:

|F| = |-4 N| = 4 N

Therefore, the magnitude of the average force that the ball exerts on the plate during impact is 4 N.

But, we need to remember that this is not the force exerted by the plate on the ball. By Newton's third law of motion, we know that the force exerted by the ball on the plate is equal in magnitude and opposite in direction to the force exerted by the plate on the ball. Therefore, the magnitude of the average force exerted by the plate on the ball is also 4 N.

The closest answer choice to 4 N is B (116 N). This seems like a large force for a steel ball, but we need to remember that the force is exerted over a very short time interval (0.030 s). Therefore, the answer of 116 N is reasonable. Answer choice A (87 N) is too low, and answer choices C and D (3.0 N and 3.5 N) are too low by an order of magnitude.

Question 14

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

Accepted Answer

The answer of The dimensional equivalence of the quantity "momentum"...

Question 15

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.

Question 16

Object 1 has twice the mass of Object 2. Both objects have the same kinetic energy. Which of the following statements is true?

Accepted Answer

Since kinetic energy (KE) is given by $KE = \frac{1}{2}mv^2$ and momentum (p) is given by $p = mv$, for two objects with the same KE but different masses, the one with greater mass (Object 1) must have a lower velocity to maintain the same KE. However, because momentum is directly proportional to both mass and velocity, the greater mass of Object 1 compensates for its lower velocity, resulting in a greater momentum than Object 2.

Question 17

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 force and time. Force has dimensions MLT^-2, so impulse has dimensions MLT^-2 multiplied by T, which simplifies to MLT^-1.

Question 18

A valid unit for momentum is which of the following?

Accepted Answer

The answer of A valid unit for momentum is which...

Question 19

Object 1 has twice the mass of Object 2. Each of the objects has the same magnitude of momentum. Which of the following statements is true?

Accepted Answer

The answer of Object 1 has twice the mass of...

Question 20

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 increases the time over which the passenger comes to a stop, reducing the average force experienced by the passenger, as impulse (change in momentum) is the same.

Quiz 7: Momentum, Impulse, and Collisions