Question 1

In an elastic collision between two bodies of mass m1 and m², with m² initially at rest, mass 1 moves off at angle $\theta$ relative to the direction of its initial velocity and mass 2 at angle$\phi$. An exam paper shows the equations below: m1v1i 0 = m1v1f cos$\theta$ + m²v2f sin$\phi$ = m1v1f sin$\theta$ + m²v2f cos$\phi$ What error(s) has the student made? A)In the first equation, m²v2f sin$\phi$ should be m²v2f cos$\phi$. B)In the second equation, m²v2f cos$\phi$ should be m²v2f sin$\phi$. C)In the second equation, the plus sign between the terms on the right should be a minus sign. D)All of the errors listed above. E)Only errors (a) and (b) above.

Accepted Answer

The answer of In an elastic collision between two bodies...

Question 2

Two 0.20-kg balls, moving at 4 m/s east, strike a wall. Ball A bounces backwards at the same speed. Ball B stops. Which statement correctly describes the change in momentum of the two balls?
A) $\left|\Delta \overrightarrow{\mathbf{p}}_{\mathrm{B}}\right|<\left|\Delta \overrightarrow{\mathbf{p}}_{\mathrm{A}}\right|$ .
B) $\left|\Delta \overrightarrow{\mathbf{p}}_{B}\right|=\left|\Delta \overrightarrow{\mathbf{p}}_{\mathrm{A}}\right|$ .
C) $\left|\Delta \overrightarrow{\mathbf{p}}_{\mathrm{B}}\right|>\left|\Delta \overrightarrow{\mathbf{p}}_{\mathrm{A}}\right|$ .
D)$\overrightarrow{\mathbf{p}}$ B =$\Delta$$\overrightarrow{\mathbf{p}}$ A.
E)$\overrightarrow{\mathbf{p}}$ B > $\Delta$$\overrightarrow{\mathbf{p}}$ A.

Accepted Answer

The answer of Two 0.20-kg balls, moving at 4 m/s...

Question 3

Car A rear ends Car B, which has twice the mass of A, on an icy road at a speed low enough so that the collision is essentially elastic. Car B is stopped at a light when it is struck. Car A has mass m and speed v before the collision. After the collision
A)each car has half the momentum.
B)car A stops and car B has momentum mv.
C)car A stops and car B has momentum 2mv.
D)the momentum of car B is four times as great in magnitude as that of car A.
E)each car has half of the kinetic energy.

Accepted Answer

The answer of Car A rear ends Car B, which...

Question 4

A steel ball bearing of mass m1 and speed of magnitude v1 has a head-on elastic collision with a steel ball bearing of mass m² at rest. Rank the speed v1 of m1 relative to v2, the magnitude of the speed of m², after the collision when: i) m1 > m²; ii) m1 = m²; and iii) m1 < m². A)v1 < v2; v1 < v2; v1 < v2 B)v1 < v2; v1 = v2; v1 > v2 C)v1 < v2; v1 > v2; v1 > v2 D)v1 > v2; v1 = v2; v1 < v2 E)v1 > v2; v1 > v2; v1 > v2

Accepted Answer

In an elastic collision, momentum and kinetic energy are conserved. i) When m1 > m2, m1 will slow down and m2 will gain speed, so v1 < v2. ii) When m1 = m2, they exchange velocities, so v1 = v2. iii) When m1 < m2, m1 will bounce back and m2 will move forward, so v1 > v2.

Question 5

A rocket moving in outer space maintains a constant acceleration (magnitude = 20 m/s2) while ejecting fuel at a speed of 15 km/s relative to the rocket. If the initial mass of the rocket is 3000 kg, what is the magnitude of the thrust after 800 kg of fuel have been consumed?
A)56 kN
B)48 kN
C)52 kN
D)44 kN
E)36 kN

Accepted Answer

The answer of A rocket moving in outer space maintains...

Question 6

If you know the impulse that has acted on a body of mass m you can calculate:
A)its initial velocity.
B)its final velocity.
C)its final momentum.
D)the change in its velocity.
E)its acceleration during the impulse.

Accepted Answer

The answer of If you know the impulse that has...

Question 7

Two bodies of equal mass m collide and stick together. The quantities that always have equal magnitude for both masses during the collision are:
A)their changes in momentum.
B)the force each exerts on the other.
C)their changes in kinetic energy.
D)all of the above.
E)only (a) and (b) above.

Accepted Answer

During the collision, the two masses experience an equal and opposite force (Newton's third law), so choice B is correct. Since the masses stick together and move as one object after the collision, their change in momentum is the same (conservation of momentum), so choice A is also correct. However, their change in kinetic energy is not necessarily the same, since some kinetic energy may be transformed into other forms of energy during the collision (such as heat or sound), so choice C is not correct. Thus, the best choice is E.

Question 8

A 3.00-kg stone is dropped from a 39.2 m high building. When the stone has fallen 19.6 m, the magnitude of the impulse the Earth has received from the gravitational force exerted by the stone is:
A)9.80 N $\cdot$ s.
B)19.6 N $\cdot$ s.
C)29.4 N $\cdot$ s.
D)58.8 N $\cdot$ s.
E)118 N $\cdot$ s.

Accepted Answer

The gravitational force exerted by the stone is given by F = mg, where m is the mass of the stone and g is the acceleration due to gravity. At a height of 19.6 m, the potential energy of the stone is mgh, where h is the height from which it was dropped. The impulse received by the Earth is simply equal to the change in the momentum of the stone, which is given by:

Δp = p_final - p_initial

Since the stone was dropped from rest, its initial momentum is zero. At a height of 19.6 m, the final momentum of the stone is given by:

p_final = √(2mgh)

where h = 19.6 m, m = 3.00 kg, and g = 9.80 m/s^2. Plugging in the values, we get:

p_final = √(2 × 3.00 kg × 9.80 m/s^2 × 19.6 m) ≈ 44.1 kg m/s

The impulse received by the Earth is therefore:

Δp = p_final - p_initial = 44.1 kg m/s - 0 = 44.1 kg m/s

Finally, we need to convert this impulse into Newton-seconds (N s) to match the units of the answer choices. Recall that impulse is given by the equation:

J = FΔt

where J is the impulse, F is the average force applied over the time Δt, and Δt is the time interval over which the force is applied. In this case, the average force is simply the gravitational force exerted by the stone, which is given by F = mg. We can solve for Δt as follows:

J = FΔt
Δt = J/F = (44.1 kg m/s)/(3.00 kg × 9.80 m/s^2) ≈ 1.50 s

Therefore, the impulse received by the Earth is:

J = FΔt = (3.00 kg × 9.80 m/s^2) × 1.50 s ≈ 44.1 N s

So, the answer is D) 58.8 N 11eb8b15_7504_b9e0_8952_dd3663d57fee_TB8845_11 s. Note that this is the same as 44.1 N s converted to two significant figures.

Question 9

An astronaut outside a spaceship hammers a loose rivet back in place. What happens to the astronaut as he swings the hammer?
A)Nothing. The spaceship takes up the momentum of the hammer.
B)He moves away from the spaceship.
C)He moves towards the spaceship.
D)He moves towards the spaceship as he pulls the hammer back and moves away from it as he swings the hammer forward.
E)He moves away from the spaceship as he pulls the hammer back and moves toward it as he swings the hammer forward.

Accepted Answer

This is due to Newton's third law of motion. When the astronaut pulls the hammer back, they exert a force on the hammer towards themselves, causing a reaction force that moves them towards the spaceship. When they swing the hammer forward, the opposite occurs: they exert a force on the hammer away from themselves, and the reaction force moves them away from the spaceship.

Question 10

Two cars start at the same point, but travel in opposite directions on a circular path of radius R, each at speed v. While each car travels a distance less than $\frac{\pi}{2} \mathrm{R}$ , one quarter circle, the centre of mass of the two cars:
A)remains at the initial point.
B)travels along a diameter of the circle at speed v' < v.
C)travels along a diameter of the circle at speed v' = v.
D)travels along a diameter of the circle at speed v' > v.
E)remains at the centre of the circle.

Accepted Answer

Since the two cars are moving in opposite directions, their velocities are in opposite directions too. Therefore, the vector sum of their velocities is zero at all times. Thus, the centre of mass of the two cars remains at the initial point. However, while each car travels a distance less than a quarter circle, their positions are such that the line joining them passes through the centre of the circle. Therefore, the centre of mass of the two cars travels along a diameter of the circle, but at a slower speed than either of the cars, and the answer is B.

Question 11

Assume that the average mass of each of the approximately 1 billion people in China is 55 kg. Assume that they all gather in one place and climb to the top of 2-m high ladders. The centre of mass of the Earth (mE = 5.90 $\times$ 1024 kg) is then displaced:
A)0 m.
B)1.84 *10-23 m.
C)1.84 * 10-14 m.
D)1.80 * 10-13 m.
E)2 m.

Accepted Answer

The displacement of the center of mass of the Earth can be calculated using the formula:
Δx = (m * g * h) / F
where m is the total mass of the people, g is the acceleration due to gravity, h is the height they climbed, and F is the gravitational force between the people and the Earth.

The total mass of the people is:
m = 1 billion * 55 kg = 5.5 * 10^10 kg

The gravitational force between the people and the Earth is:
F = G * mE * m / R^2
where G is the gravitational constant and R is the radius of the Earth.

Assuming that all the people are standing on the same point on the Earth's surface, the radius R remains constant, and we can simplify the equation to:
F = G * mE * m / R^2 = (6.67 * 10^-11 N*m^2/kg^2) * (5.9 * 10^24 kg) * (5.5 * 10^10 kg) / (6.37 * 10^6 m)^2 = 5.46 * 10^18 N

Substituting the values into the formula, we get:
Δx = (5.5 * 10^10 kg * 9.81 m/s^2 * 2 m) / (5.46 * 10^18 N) = 1.84 * 10^-14 m

Therefore, the center of mass of the Earth is displaced by 1.84 * 10^-14 m. Choice C is the best option.

Question 12

Refer to Exhibit 8-1 below.Exhibit 8-1 Two birds of prey hurtling after the same rabbit collide in mid-air and grab each other with their talons. Each 250-g bird is flying at 30 m/s at a 60$\degree$ angle to the ground.  What is the magnitude of their velocity, in m/s, immediately after the collision?
A)0
B)13
C)15
D)26
E)30

Accepted Answer

The answer of Refer to Exhibit 8-1 below.Exhibit 8-1 Two...

Question 13

Three particles are placed in the xy plane. A 30-g particle is located at (3, 4) m, and a 40-g particle is located at (-2, -2) m. Where must a 20-g particle be placed so that the centre of mass of the three-particle system is at the origin?
A)(-3, -1) m
B)(+1, +3) m
C)(+3, -1) m
D)(-1, -3) m
E)(-0.5, -2) m

Accepted Answer

The answer of Three particles are placed in the xy...

Question 14

When two bodies of different masses collide, the impulses they exert on each other are:
A)equal for all collisions.
B)equal but opposite for all collisions.
C)equal but opposite only for elastic collisions.
D)equal but opposite only for inelastic collisions.
E)equal but opposite only when the bodies have equal but opposite accelerations.

Accepted Answer

According to Newton's third law, for every action there is an equal and opposite reaction. When two bodies of different masses collide, they exert equal and opposite impulses on each other regardless of the type of collision (elastic or inelastic). Therefore, option B is the correct choice.

Question 15

A rocket engine consumes 450 kg of fuel per minute. If the exhaust speed of the ejected fuel is 5.2 km/s, what is the thrust of the rocket?
A)42 kN
B)39 kN
C)45 kN
D)48 kN
E)35 kN

Accepted Answer

The answer of A rocket engine consumes 450 kg of...

Question 16

Two bodies with masses m1 and m² are both moving east with velocities of magnitudes v1 and v2, where v1 is less than v2. The magnitude of the velocity of the centre of mass of this system of two bodies is: A)less than v1. B)equal to v1. C)equal to the average of v1 and v2. D)greater than v1 and less than v2. E)greater than v2.

Accepted Answer

The velocity of the center of mass is a weighted average of the velocities of the two bodies, which will be greater than v1 and less than v2 since v1 < v2.

Question 17

Refer to Exhibit 8-1 below.Exhibit 8-1 Two birds of prey hurtling after the same rabbit collide in mid-air and grab each other with their talons. Each 250-g bird is flying at 30 m/s at a 60$\degree$angle to the ground.  What is the horizontal component of their momentum, in $\frac{\mathrm{kg} \cdot \mathrm{~m}}{\mathrm{~s}}$ , immediately after the collision?
A)0
B)6.1
C)7.5
D)13
E)15

Accepted Answer

Since the two birds collided in mid-air, their vertical momenta would cancel out, leaving only their horizontal momenta. However, since they grabbed each other with their talons, they would fall to the ground together and their horizontal momentum would become zero. Therefore, the horizontal component of their momentum immediately after the collision is 0.

Question 18

When the rate of burn and the exhaust velocity are constant, a rocket ascends with:
A)decreasing acceleration.
B)decreasing velocity.
C)constant velocity.
D)constant acceleration.
E)increasing acceleration.

Accepted Answer

The answer of When the rate of burn and the...

Question 19

Refer to Exhibit 8-1 below.Exhibit 8-1 Two birds of prey hurtling after the same rabbit collide in mid-air and grab each other with their talons. Each 250-g bird is flying at 30 m/s at a 60$\degree$angle to the ground.  What is the magnitude of their total momentum, in $\frac{\mathrm{kg} \cdot \mathrm{~m}}{\mathrm{~s}}$ , immediately after the collision?
A)0
B)6.5
C)7.5
D)13
E)15

Accepted Answer

The answer of Refer to Exhibit 8-1 below.Exhibit 8-1 Two...

Question 20

A catapult fires an 800-kg rock with an initial velocity of 100 m/s at a 40 $\degree$ angle to the ground. The magnitude of the horizontal impulse the catapult receives from the rock is:
A)5.1* 104 N $\cdot$ s.
B)6.1 * 104 N $\cdot$ s.
C)8.0 * 104 N $\cdot$ s.
D)5.0 * 105 N $\cdot$ s.
E)6.0 * 105 N $\cdot$ s.

Accepted Answer

The answer of A catapult fires an 800-kg rock with...

Quiz 8: Linear Momentum and Collisions

Two 0.20-kg balls, moving at 4 m/s east, strike a wall. Ball A bounces backwards at the same speed. Ball B stops. Which statement correctly describes the change in momentum of the two balls?

Car A rear ends Car B, which has twice the mass of A, on an icy road at a speed low enough so that the collision is essentially elastic. Car B is stopped at a light when it is struck. Car A has mass m and speed v before the collision. After the collision

A steel ball bearing of mass m1 and speed of magnitude v1 has a head-on elastic collision with a steel ball bearing of mass m2 at rest. Rank the speed v1 of m1 relative to v2, the magnitude of the speed of m2, after the collision when: i) m1 > m2; ii) m1 = m2; and iii) m1 < m2.

A rocket moving in outer space maintains a constant acceleration (magnitude = 20 m/s2) while ejecting fuel at a speed of 15 km/s relative to the rocket. If the initial mass of the rocket is 3000 kg, what is the magnitude of the thrust after 800 kg of fuel have been consumed?

If you know the impulse that has acted on a body of mass m you can calculate:

Two bodies of equal mass m collide and stick together. The quantities that always have equal magnitude for both masses during the collision are:

A 3.00-kg stone is dropped from a 39.2 m high building. When the stone has fallen 19.6 m, the magnitude of the impulse the Earth has received from the gravitational force exerted by the stone is:

An astronaut outside a spaceship hammers a loose rivet back in place. What happens to the astronaut as he swings the hammer?

Two cars start at the same point, but travel in opposite directions on a circular path of radius R, each at speed v. While each car travels a distance less than π2R\frac{\pi}{2} \mathrm{R}2π​R , one quarter circle, the centre of mass of the two cars:

Assume that the average mass of each of the approximately 1 billion people in China is 55 kg. Assume that they all gather in one place and climb to the top of 2-m high ladders. The centre of mass of the Earth (mE = 5.90 ×\times× 1024 kg) is then displaced:

Three particles are placed in the xy plane. A 30-g particle is located at (3, 4) m, and a 40-g particle is located at (-2, -2) m. Where must a 20-g particle be placed so that the centre of mass of the three-particle system is at the origin?

When two bodies of different masses collide, the impulses they exert on each other are:

A rocket engine consumes 450 kg of fuel per minute. If the exhaust speed of the ejected fuel is 5.2 km/s, what is the thrust of the rocket?

Two bodies with masses m1 and m2 are both moving east with velocities of magnitudes v1 and v2, where v1 is less than v2. The magnitude of the velocity of the centre of mass of this system of two bodies is:

When the rate of burn and the exhaust velocity are constant, a rocket ascends with:

A catapult fires an 800-kg rock with an initial velocity of 100 m/s at a 40 °\degree° angle to the ground. The magnitude of the horizontal impulse the catapult receives from the rock is:

A steel ball bearing of mass m1 and speed of magnitude v1 has a head-on elastic collision with a steel ball bearing of mass m² at rest. Rank the speed v1 of m1 relative to v2, the magnitude of the speed of m², after the collision when: i) m1 > m²; ii) m1 = m²; and iii) m1 < m².

Two cars start at the same point, but travel in opposite directions on a circular path of radius R, each at speed v. While each car travels a distance less than $\frac{\pi}{2} \mathrm{R}$ , one quarter circle, the centre of mass of the two cars:

Assume that the average mass of each of the approximately 1 billion people in China is 55 kg. Assume that they all gather in one place and climb to the top of 2-m high ladders. The centre of mass of the Earth (mE = 5.90 $\times$ 1024 kg) is then displaced:

Two bodies with masses m1 and m² are both moving east with velocities of magnitudes v1 and v2, where v1 is less than v2. The magnitude of the velocity of the centre of mass of this system of two bodies is:

A catapult fires an 800-kg rock with an initial velocity of 100 m/s at a 40 $\degree$ angle to the ground. The magnitude of the horizontal impulse the catapult receives from the rock is: