Question 1

An object of mass m moving at speed v₀ strikes an object of mass 2m which had been at rest.The first object bounces backward along its initial path at speed v₀.Is this collision elastic, and if not, what is the change in kinetic energy of the system?

Accepted Answer

The answer of An object of mass m moving at...

Question 2

A lump of clay is thrown at a wall.A rubber ball of identical mass is thrown with the same speed toward the same wall.Which statement is true?

Accepted Answer

The answer of A lump of clay is thrown at...

Question 3

A 20-g bullet moving at 1 000 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s.What is the kinetic energy of the block that results from the collision if the block had not been moving prior to the collision and was free to move?

Accepted Answer

First, we need to find the initial kinetic energy of the bullet:

KEbullet = (1/2)mv^2 = (1/2)(0.02 kg)(1000 m/s)^2 = 10 kJ

Next, we need to find the final velocity of the block using conservation of momentum:

mbulletvbullet = mblockvblock

(0.02 kg)(1000 m/s) = (1 kg)(vblock)

vblock = 20 m/s

Finally, we can find the kinetic energy of the block:

KEblock = (1/2)mblockvblock^2 = (1/2)(1 kg)(20 m/s)^2 = 0.2 kJ

However, the question asks for the kinetic energy that results from the collision if the block had not been moving prior to the collision and was free to move. This means we need to subtract the initial kinetic energy of the block, which is zero:

KEresult = KEblock - KEinitial = 0.2 kJ - 0 kJ = 0.2 kJ

Therefore, the best choice is C, 0.16 kJ (rounded to two significant figures).

Question 4

A 20-g bullet moving at 1 000 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s.What is the change in the kinetic energy of the bullet-block system as a result of the collision assuming the block is free to move?

Accepted Answer

The initial kinetic energy of the bullet is (1/2)(0.02 kg)(1000 m/s)^2 = 1 000 000 J.
The final kinetic energy of the bullet is (1/2)(0.02 kg)(100 m/s)^2 = 1000 J.
The initial kinetic energy of the block is zero.
The final kinetic energy of the block is (1/2)(1 kg)(100 m/s)^2 = 5000 J.
Therefore, the change in kinetic energy of the bullet-block system is -999 000 J or -9.7 kJ (rounded to two significant figures) since kinetic energy is lost as heat and sound energy due to the collision.

Question 5

During a snowball fight two balls with masses of 0.4 and 0.6 kg, respectively, are thrown in such a manner that they meet head-on and combine to form a single mass.The magnitude of initial velocity for each is 15 m/s.What is the speed of the 1.0-kg mass immediately after collision?

Accepted Answer

The answer of During a snowball fight two balls with...

Question 6

A uranium nucleus (mass 238 units) at rest decays into a helium nucleus (mass 4.0 units) and a thorium nucleus (mass 234 units).If the speed of the helium nucleus is 6.0 * 10⁵ m/s, what is the speed of the thorium nucleus?

Accepted Answer

The answer of A uranium nucleus (mass 238 units) at...

Question 7

A 70-kg man is standing in a 20-kg boat.The man steps to the right thinking he is stepping out onto the dock.However, the following will actually happen (ignore the friction of the water or air on the boat or the man):

Accepted Answer

According to Newton's Third Law of Motion (the law of action and reaction), for every action, there is an equal and opposite reaction. When the man steps to the right, he exerts a force on the boat to the left. At the same time, the boat exerts an equal and opposite force on the man to the right. However, since the boat has a smaller mass than the man, it will experience a larger acceleration and move a larger distance to the left than the man will move to the right. Therefore, the correct choice is A.

Question 8

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 9

A high-diver of mass 70 kg jumps off a board 10 m above the water.If, 1.0 s after entering the water his downward motion is stopped, what average upward force did the water exert?

Accepted Answer

The answer of A high-diver of mass 70 kg jumps...

Question 10

A billiard ball is moving in the x-direction at 30.0 cm/s and strikes another billiard ball moving in the y-direction at 40.0 cm/s.As a result of the collision, the first ball moves at 50.0 cm/s, and the second ball stops.In what final direction does the first ball move?

Accepted Answer

In any collision, momentum must be conserved, which means that the total momentum before the collision must equal the total momentum after the collision. In this case, we can set up the following equations:

m1v1x + m2v2x = m1v1f + m2v2f (since the second ball stops)
m1v1y + m2v2y = m1v1f,y + m2v2f,y (since the first ball initially has no y-component and the second ball initially has no x-component)

where m1 and m2 are the masses of the two balls, v1x and v1y are the initial x- and y-components of the first ball's velocity, v2x and v2y are the initial x- and y-components of the second ball's velocity, and v1f and v1f,y are the final x- and y-components of the first ball's velocity (since we don't know the final y-component of the first ball, we use v1f,y instead).

Solving these equations gives:

m1v1x + m2v2x = m1v1f
m1v1y + m2v2y = m2v2f,y

We are given values for all of the initial velocities and the final x-component of the first ball's velocity, so we can solve for m1v1f and m2v2f,y:

m1v1f = m1v1x + m2v2x = (m1 + m2)vx
m2v2f,y = m1v1y + m2v2y = m2vy

where vx = (m1v1x + m2v2x)/(m1 + m2) is the velocity of the combined system in the x-direction, and vy = (m1v1y + m2v2y)/m2 is the velocity of the second ball in the y-direction.

Now we can use the Pythagorean theorem to find the magnitude of the final velocity of the first ball:

|v1f|^2 = (v1f,x)^2 + (v1f,y)^2 = (50 cm/s)^2

Solving for v1f,y gives:

v1f,y = ±sqrt[(50 cm/s)^2 - (v1f,x)^2]

Since the second ball was traveling in the positive y-direction, we choose the positive root of this equation. Finally, we use trigonometry to find the angle between the final velocity vector and the x-axis:

tanθ = v1f,y/v1f,x = sqrt[(50 cm/s)^2 - (v1f,x)^2]/v1f,x
θ = tan^-1(sqrt[(50 cm/s)^2 - (v1f,x)^2]/v1f,x)

Plugging in the given values for v1f,x and solving gives:

θ = 53.1 degrees ccw from the x-direction

Question 11

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

Accepted Answer

The kinetic energy (K) of an object is given by $K = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the velocity. Momentum (p) is given by $p = mv$. If the kinetic energy is quadrupled, then the new kinetic energy is $4K = \frac{1}{2}mv'^2$, where $v'$ is the new velocity. Solving for $v'$ in terms of $v$, we find that $v' = 2v$. Since momentum is directly proportional to velocity, if the velocity doubles, the momentum also doubles.

Question 12

Three satellites are launched into space connected together.Once in deep space, an explosive charge separates the three satellites and they move apart.The satellites each have different masses with m₁ < m₂ < m₃.Which of the following statements is always true?

Accepted Answer

The answer of Three satellites are launched into space connected...

Question 13

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 14

A miniature spring-loaded, radio-controlled gun is mounted on an air puck.The gun's bullet has a mass of 5.00 g, and the gun and puck have a combined mass of 120 g.With the system initially at rest, the radio controlled trigger releases the bullet causing the puck and empty gun to move with a speed of 0.500 m/s.What is the bullet's speed?

Accepted Answer

We can use the conservation of momentum to solve this problem. Since there are no external forces acting on the system, the total momentum of the system must be conserved.

Initial momentum = Final momentum

Since the system is initially at rest, the initial momentum is zero.

Final momentum = (m_puck + m_gun + m_bullet) * v_final

where m_puck = mass of the puck, m_gun = mass of the gun, m_bullet = mass of the bullet, and v_final = final velocity of the puck and gun.

Plugging in the given values, we get:

0 = (0.120 kg + 0.005 kg) * 0.500 m/s + m_bullet * v_bullet

Solving for v_bullet, we get:

v_bullet = -[(0.120 kg + 0.005 kg) * 0.500 m/s]/0.005 kg

v_bullet = -12.0 m/s (Note that the negative sign indicates that the bullet is moving in the opposite direction of the puck and gun)

Taking the absolute value, we get:

v_bullet = 12.0 m/s

Therefore, the bullet's speed is 12.0 m/s (Choice D).

Question 15

A 20-g bullet moving at 1 000 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s.If the block had been originally at rest and is free to move, what is its resulting speed?

Accepted Answer

This problem can be solved using conservation of momentum. The momentum of the bullet before it hits the block is (0.02 kg)(1000 m/s) = 20 kg m/s. After it goes through the block, the momentum of the bullet and block together is (1.02 kg)(100 m/s) = 102 kg m/s. Therefore, the momentum lost by the bullet must be gained by the block: 20 kg m/s = (1 kg + m)(v), where v is the speed of the block after the collision. Solving for v, we get v = 18 m/s. The answer is B.

Question 16

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 17

A billiard ball collides in an elastic head-on collision with a second stationary identical ball.After the collision which of the following conditions applies to the first ball?

Accepted Answer

In an elastic head-on collision between two identical balls where one is stationary, the moving ball comes to rest after the collision, transferring its velocity to the second ball.

Question 18

A moderate force will break an egg.However, an egg dropped on the road usually breaks, while one dropped on the grass usually doesn't break.This is because for the egg dropped on the grass:

Accepted Answer

When the egg is dropped on the grass, the grass acts as a cushion and extends the time interval for stopping, thereby reducing the force applied to the egg and preventing it from breaking. This means that the change in momentum is less, and the time interval for stopping is greater.

Question 19

A 2 500-kg truck moving at 10.00 m/s strikes a car waiting at a traffic light, hooking bumpers.The two continue to move together at 7.00 m/s.What was the mass of the struck car?

Accepted Answer

The answer of A 2 500-kg truck moving at 10.00...

Question 20

A billiard ball is moving in the x-direction at 30.0 cm/s and strikes another billiard ball moving in the y-direction at 40.0 cm/s.As a result of the collision, the first ball moves at 50.0 cm/s, and the second ball stops.What is the change in kinetic energy of the system as a result of the collision?

Accepted Answer

The change in kinetic energy of the system is zero. This is because kinetic energy is a scalar quantity and is conserved in an elastic collision. The initial kinetic energy of the system is equal to the final kinetic energy of the system. Since the second ball stops moving after the collision, all of its kinetic energy is transferred to the first ball, resulting in an increase in the first ball's kinetic energy. However, the decrease in the first ball's kinetic energy as a result of the collision is exactly equal to the increase, resulting in a net change of zero.

Quiz 6: Momentum and Collisions

An object of mass m moving at speed v₀ strikes an object of mass 2m which had been at rest.The first object bounces backward along its initial path at speed v₀.Is this collision elastic, and if not, what is the change in kinetic energy of the system?

A lump of clay is thrown at a wall.A rubber ball of identical mass is thrown with the same speed toward the same wall.Which statement is true?

A 20-g bullet moving at 1 000 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s.What is the kinetic energy of the block that results from the collision if the block had not been moving prior to the collision and was free to move?

A 20-g bullet moving at 1 000 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s.What is the change in the kinetic energy of the bullet-block system as a result of the collision assuming the block is free to move?

During a snowball fight two balls with masses of 0.4 and 0.6 kg, respectively, are thrown in such a manner that they meet head-on and combine to form a single mass.The magnitude of initial velocity for each is 15 m/s.What is the speed of the 1.0-kg mass immediately after collision?

A uranium nucleus (mass 238 units) at rest decays into a helium nucleus (mass 4.0 units) and a thorium nucleus (mass 234 units) .If the speed of the helium nucleus is 6.0 * 10⁵ m/s, what is the speed of the thorium nucleus?

A 70-kg man is standing in a 20-kg boat.The man steps to the right thinking he is stepping out onto the dock.However, the following will actually happen (ignore the friction of the water or air on the boat or the man) :

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

A high-diver of mass 70 kg jumps off a board 10 m above the water.If, 1.0 s after entering the water his downward motion is stopped, what average upward force did the water exert?

A billiard ball is moving in the x-direction at 30.0 cm/s and strikes another billiard ball moving in the y-direction at 40.0 cm/s.As a result of the collision, the first ball moves at 50.0 cm/s, and the second ball stops.In what final direction does the first ball move?

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

Three satellites are launched into space connected together.Once in deep space, an explosive charge separates the three satellites and they move apart.The satellites each have different masses with m₁ < m₂ < m₃.Which of the following statements is always true?

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?

A 20-g bullet moving at 1 000 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s.If the block had been originally at rest and is free to move, what is its resulting speed?

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

A billiard ball collides in an elastic head-on collision with a second stationary identical ball.After the collision which of the following conditions applies to the first ball?

A moderate force will break an egg.However, an egg dropped on the road usually breaks, while one dropped on the grass usually doesn't break.This is because for the egg dropped on the grass:

A 2 500-kg truck moving at 10.00 m/s strikes a car waiting at a traffic light, hooking bumpers.The two continue to move together at 7.00 m/s.What was the mass of the struck car?

Quiz 6: Momentum and Collisions

An object of mass m moving at speed v0 strikes an object of mass 2m which had been at rest.The first object bounces backward along its initial path at speed v0.Is this collision elastic, and if not, what is the change in kinetic energy of the system?

A lump of clay is thrown at a wall.A rubber ball of identical mass is thrown with the same speed toward the same wall.Which statement is true?

A 20-g bullet moving at 1 000 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s.What is the kinetic energy of the block that results from the collision if the block had not been moving prior to the collision and was free to move?

A 20-g bullet moving at 1 000 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s.What is the change in the kinetic energy of the bullet-block system as a result of the collision assuming the block is free to move?

During a snowball fight two balls with masses of 0.4 and 0.6 kg, respectively, are thrown in such a manner that they meet head-on and combine to form a single mass.The magnitude of initial velocity for each is 15 m/s.What is the speed of the 1.0-kg mass immediately after collision?

A uranium nucleus (mass 238 units) at rest decays into a helium nucleus (mass 4.0 units) and a thorium nucleus (mass 234 units) .If the speed of the helium nucleus is 6.0 * 105 m/s, what is the speed of the thorium nucleus?

A 70-kg man is standing in a 20-kg boat.The man steps to the right thinking he is stepping out onto the dock.However, the following will actually happen (ignore the friction of the water or air on the boat or the man) :

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

A high-diver of mass 70 kg jumps off a board 10 m above the water.If, 1.0 s after entering the water his downward motion is stopped, what average upward force did the water exert?

A billiard ball is moving in the x-direction at 30.0 cm/s and strikes another billiard ball moving in the y-direction at 40.0 cm/s.As a result of the collision, the first ball moves at 50.0 cm/s, and the second ball stops.In what final direction does the first ball move?

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

Three satellites are launched into space connected together.Once in deep space, an explosive charge separates the three satellites and they move apart.The satellites each have different masses with m1 < m2 < m3.Which of the following statements is always true?

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?

A 20-g bullet moving at 1 000 m/s is fired through a one-kg block of wood emerging at a speed of 100 m/s.If the block had been originally at rest and is free to move, what is its resulting speed?

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

A billiard ball collides in an elastic head-on collision with a second stationary identical ball.After the collision which of the following conditions applies to the first ball?

A moderate force will break an egg.However, an egg dropped on the road usually breaks, while one dropped on the grass usually doesn't break.This is because for the egg dropped on the grass:

A 2 500-kg truck moving at 10.00 m/s strikes a car waiting at a traffic light, hooking bumpers.The two continue to move together at 7.00 m/s.What was the mass of the struck car?

An object of mass m moving at speed v₀ strikes an object of mass 2m which had been at rest.The first object bounces backward along its initial path at speed v₀.Is this collision elastic, and if not, what is the change in kinetic energy of the system?

A uranium nucleus (mass 238 units) at rest decays into a helium nucleus (mass 4.0 units) and a thorium nucleus (mass 234 units) .If the speed of the helium nucleus is 6.0 * 10⁵ m/s, what is the speed of the thorium nucleus?

Three satellites are launched into space connected together.Once in deep space, an explosive charge separates the three satellites and they move apart.The satellites each have different masses with m₁ < m₂ < m₃.Which of the following statements is always true?