Question 1

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 2

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 an egg drops on the grass, the time interval for stopping is greater. The grass provides a cushion effect which increases the time interval for stopping. This means that the force exerted on the egg is spread out over a longer period of time, reducing the impact force and decreasing the likelihood of the egg breaking.

Question 3

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 4

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 change in momentum is directly proportional to the magnitude of the force and the time interval during which the force acts. The clay is malleable and will deform when it hits the wall, which will increase the time interval and reduce the force exerted on the wall. On the other hand, the rubber ball will bounce off the wall with a shorter time interval and a greater force, resulting in a greater change in momentum compared to the clay.

Question 5

A 15.0-g bullet is fired into a 1,500-g block of wood which is suspended as a ballistic pendulum.The combined mass swings up to a height of 8.50 cm.What was the kinetic energy of the combined mass immediately after the collision?

Accepted Answer

To solve this problem, we can use the conservation of momentum and conservation of energy equations. First, we can use conservation of momentum to find the velocity of the combined mass immediately after the collision:
m_bullet * v_bullet = (m_bullet + m_block) * v_combined
15g * v_bullet = (15g + 1500g) * v_combined
v_combined = 15g * v_bullet / 1515g

Next, we can use conservation of energy to find the kinetic energy of the combined mass at this velocity:
KE_combined = (1/2) * (m_bullet + m_block) * v_combined^2
KE_combined = (1/2) * 1515g * ((15g * v_bullet / 1515g)^2)
KE_combined = 1.262 J (to three significant figures)

Question 6

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 7

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 8

A 5.00-g bullet is fired into a 800-g block of wood suspended as a ballistic pendulum.The combined mass swings up to a height of 8.00 cm.What was the kinetic energy of the bullet immediately before the collision?

Accepted Answer

The correct answer is A.The kinetic energy of the bullet immediately before the collision is equal to the potential energy of the combined mass at the maximum height. The potential energy is given by:$$PE = mgh$$where:* m is the combined mass of the bullet and the block of wood* g is the acceleration due to gravity* h is the maximum height reached by the combined massSubstituting the given values into the equation, we get:$$PE = (5.00 g + 800 g)(9.81 m/s^2)(0.08 m) = 102 J$$Therefore, the kinetic energy of the bullet immediately before the collision was 102 J.

Question 9

A 24-g bullet moving at 900 m/s is fired through a one-kg block of wood emerging at a speed of 200 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 can use conservation of momentum to find the velocity of the block after the collision:
p = mv
Total momentum before collision = (24 g)(900 m/s) = 21600 g*m/s
Total momentum after collision = (1024 g)(v block) where v block is the velocity of the block after the collision
21600 g*m/s = (1024 g)(v block)
v block = 21.09375 m/s

Now we can use the kinetic energy equation to find the kinetic energy of the block:
KE = 1/2 * m * v^2
KE = 1/2 * (1000 g) * (21.09375 m/s)^2
KE = 14,062.5 J or 0.14 kJ

Question 10

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 11

A man standing on frictionless ice throws a 1.00-kg mass at 29.0 m/s at an angle of elevation of 50.0°.What was the magnitude of the man's momentum immediately after throwing the mass?

Accepted Answer

The answer of A man standing on frictionless ice throws...

Question 12

A billiard ball is moving in the x-direction at 25.0 cm/s and strikes another billiard ball moving in the y-direction at 45.0 cm/s.As a result of the collision,the first ball moves at 55.0 cm/s,and the second ball stops.In what final direction does the first ball move?

Accepted Answer

The answer of A billiard ball is moving in the...

Question 13

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 answer of A billiard ball is moving in the...

Question 14

A 29-g bullet moving at 1,100 m/s is fired through a one-kg block of wood emerging at a speed of 150 m/s.If the block had been originally at rest and is free to move,what is its resulting speed?

Accepted Answer

Using the conservation of momentum: initial momentum = final momentum. (0.029 kg * 1100 m/s) = (0.029 kg * 150 m/s) + (1 kg * v). Solving for v gives v = 27.6 m/s.

Question 15

A high-diver of mass 73 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 73 kg jumps...

Question 16

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 17

A 7.00-g bullet is fired into a 545-g block of wood suspended as a ballistic pendulum.The combined mass swings up to a height of 9 cm.What was the magnitude of the momentum of the combined mass immediately after the collision?

Accepted Answer

The potential energy at the highest point is equal to the kinetic energy just after the collision. Using mgh = 0.5 * (m+M) * v^2, solve for v, then use p = (m+M) * v to find the momentum.

Question 18

A 71-kg man is standing in a 25-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

The man and the boat will move in opposite directions due to conservation of momentum. Since the boat is lighter, it will move a larger distance to the left compared to the man's movement to the right.

Question 19

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 6.5 × 10⁵ m/s,what is the speed of the thorium nucleus?

Accepted Answer

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

Question 20

A 22-g bullet moving at 1,200 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)(0.022 kg)(1200 m/s)^2 = 396 J. 
The final kinetic energy of the bullet is (1/2)(0.022 kg)(100 m/s)^2 = 11 J. 
The change in kinetic energy of the bullet is therefore -385 J. 
The block is free to move, so its final velocity can be found using conservation of momentum: 
(0.022 kg)(1200 m/s) = (1 kg + 0.022 kg)(v) 
v = 22.08 m/s 
The initial kinetic energy of the block is zero, and its final kinetic energy is (1/2)(1 kg)(22.08 m/s)^2 = 256.9 J. 
The change in kinetic energy of the block is therefore 256.9 J. 
The total change in kinetic energy of the system is the sum of the changes in kinetic energy of the bullet and the block: 
-385 J + 256.9 J = -128.1 J, which is approximately -15.4 kJ.

Quiz 6: Momentum and Collisions

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

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:

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 15.0-g bullet is fired into a 1,500-g block of wood which is suspended as a ballistic pendulum.The combined mass swings up to a height of 8.50 cm.What was the kinetic energy of the combined mass immediately after the collision?

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?

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

A 5.00-g bullet is fired into a 800-g block of wood suspended as a ballistic pendulum.The combined mass swings up to a height of 8.00 cm.What was the kinetic energy of the bullet immediately before the collision?

A 24-g bullet moving at 900 m/s is fired through a one-kg block of wood emerging at a speed of 200 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?

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

A man standing on frictionless ice throws a 1.00-kg mass at 29.0 m/s at an angle of elevation of 50.0°.What was the magnitude of the man's momentum immediately after throwing the mass?

A billiard ball is moving in the x-direction at 25.0 cm/s and strikes another billiard ball moving in the y-direction at 45.0 cm/s.As a result of the collision,the first ball moves at 55.0 cm/s,and the second ball stops.In what final direction does the first ball move?

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?

A 29-g bullet moving at 1,100 m/s is fired through a one-kg block of wood emerging at a speed of 150 m/s.If the block had been originally at rest and is free to move,what is its resulting speed?

A high-diver of mass 73 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?

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 7.00-g bullet is fired into a 545-g block of wood suspended as a ballistic pendulum.The combined mass swings up to a height of 9 cm.What was the magnitude of the momentum of the combined mass immediately after the collision?

A 71-kg man is standing in a 25-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) :

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 6.5 × 10⁵ m/s,what is the speed of the thorium nucleus?

A 22-g bullet moving at 1,200 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?

Quiz 6: Momentum and Collisions

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

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:

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 15.0-g bullet is fired into a 1,500-g block of wood which is suspended as a ballistic pendulum.The combined mass swings up to a height of 8.50 cm.What was the kinetic energy of the combined mass immediately after the collision?

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?

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

A 5.00-g bullet is fired into a 800-g block of wood suspended as a ballistic pendulum.The combined mass swings up to a height of 8.00 cm.What was the kinetic energy of the bullet immediately before the collision?

A 24-g bullet moving at 900 m/s is fired through a one-kg block of wood emerging at a speed of 200 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?

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

A man standing on frictionless ice throws a 1.00-kg mass at 29.0 m/s at an angle of elevation of 50.0°.What was the magnitude of the man's momentum immediately after throwing the mass?

A billiard ball is moving in the x-direction at 25.0 cm/s and strikes another billiard ball moving in the y-direction at 45.0 cm/s.As a result of the collision,the first ball moves at 55.0 cm/s,and the second ball stops.In what final direction does the first ball move?

A 29-g bullet moving at 1,100 m/s is fired through a one-kg block of wood emerging at a speed of 150 m/s.If the block had been originally at rest and is free to move,what is its resulting speed?

A high-diver of mass 73 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?

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 7.00-g bullet is fired into a 545-g block of wood suspended as a ballistic pendulum.The combined mass swings up to a height of 9 cm.What was the magnitude of the momentum of the combined mass immediately after the collision?

A 71-kg man is standing in a 25-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) :

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 6.5 × 105 m/s,what is the speed of the thorium nucleus?

A 22-g bullet moving at 1,200 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?

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?

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?

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 6.5 × 10⁵ m/s,what is the speed of the thorium nucleus?