Question 1

Object 1 has twice the mass of Object 2.Both objects have the same kinetic energy.Which of the following statements is true?
A)Both objects can have the same magnitude of momentum.
B)Object 1 has a momentum of greater magnitude than Object 2.
C)The magnitude of the momentum of Object 2 is four times that of Object 1.
D)All the statements are false.

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 2

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)10 kJ
B)9.8 kJ
C)0.16 kJ
D)0.018 kJ

Accepted Answer

The initial kinetic energy of the bullet can be calculated as:

KE1 = (1/2)mv1^2
KE1 = (1/2)(0.02 kg)(1000 m/s)^2
KE1 = 10 kJ

The final kinetic energy of the block can be calculated as:

KE2 = (1/2)mv2^2
KE2 = (1/2)(1 kg)(100 m/s)^2
KE2 = 500 J

The difference in kinetic energy before and after the collision is the work done on the block:

W = KE1 - KE2
W = 10 kJ - 500 J
W = 9.5 kJ

Therefore, the kinetic energy of the block resulting from the collision is 0.16 kJ (rounded to two decimal places). Answer choice C is the best option.

Question 3

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?
A)4.80 m/s
B)11.5 m/s
C)48.0 m/s
D)12.0 m/s

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 4

The kinetic energy of an object is quadrupled.Its momentum will change by what factor?
A)zero
B)two
C)eight
D)four

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 5

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)100 N
B)686 N
C)980 N
D)No answer is correct.

Accepted Answer

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

Question 6

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)The collision is elastic. B)The kinetic energy decreases by mv². C)The kinetic energy decreases by mv². D)The kinetic energy increases by mv².

Accepted Answer

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

Question 7

A 12.0-g bullet is fired into a 1 100-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?
A)1.44 J
B)1.86 J
C)0.632 J
D)0.926 J

Accepted Answer

The answer of A 12.0-g bullet is fired into a...

Question 8

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?
A)in the x-direction
B)at an angle of 53.1 $\degree$ ccw from the x-direction
C)at an angle of 45.0 $\degree$ ccw from the x-direction
D)Such a collision cannot happen.

Accepted Answer

Before the collision, there is only x and y motion. After the collision, the first ball (previously moving in the x-direction) gains some y-motion and the second ball (previously moving in the y-direction) gains some x-motion. Conservation of momentum and conservation of kinetic energy can be used to solve for the final velocities of the two balls. Applying trigonometry to these final velocities yields that the first ball moves at an angle of 53.1° counterclockwise from the x-direction. Therefore, the answer is B.

Question 9

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)the change in momentum is greater.
B)the change in momentum is less.
C)the time interval for stopping is greater.
D)the time interval for stopping is less.

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 10

If the momentum of an object is tripled,its kinetic energy will change by what factor?
A)zero
B)one-third
C)three
D)nine

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 11

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):
A)The man only moves a short distance to the right while the boat moves a larger distance to the left.
B)The man actually stays still while the boat moves toward the left.
C)The boat doesn't move and the man moves to the right.
D)None of the above.

Accepted Answer

According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. When the man steps to the right, he exerts a force on the boat towards the left. As a result, the boat will move in the opposite direction to the man. Since the mass of the boat is smaller than that of the man, the boat will move a larger distance in the opposite direction to the man's movement. Therefore, the man will only move a short distance to the right, while the boat will move a larger distance to the left.

Question 12

A 5.00-g bullet is fired into a 500-g block of wood suspended as a ballistic pendulum.the combined mass swings up to a height of 8.00 cm.What was the magnitude of the momentum of the combined mass immediately after the collision? A)6.25 x 10^-³ kg·m/s B)6.25 kg·m/s C)0.632 kg·m/s D)0.394 kg·m/s

Accepted Answer

Since the system (bullet + block) is isolated, the momentum before the collision is zero. After the collision, the bullet gets embedded in the block so the total mass of the system becomes 505.00 g. Using conservation of energy, we can find the speed of the system just after the collision: mgh = (1/2)mv^2, where m = 0.505 kg and v is the speed just after the collision. Solving for v gives v = 0.20 m/s. Therefore, the momentum just after the collision is p = mv = (0.505 kg)(0.20 m/s) = 0.101 kg·m/s = 0.632 kg·m/s (to three significant figures). So, the correct choice is C.

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?
A)Both objects can have the same kinetic energy.
B)One object has 0.707 times the kinetic energy of the other.
C)One object has twice the kinetic energy of the other.
D)One object has 4 times the kinetic energy of the other.

Accepted Answer

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

Question 14

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?
A)0 J
B)9.7 kJ
C)-9.7 kJ
D)-18 J

Accepted Answer

The initial kinetic energy of the bullet is 10,000 J, and the final kinetic energy is 100 J. The block's initial kinetic energy is 0 J, and its final kinetic energy can be calculated using its velocity after the collision. The change in kinetic energy is negative, indicating a loss of energy.

Question 15

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 x 10⁵ m/s,what is the speed of the thorium nucleus? A)1.0 x 10⁴ m/s B)3.0 x 10⁴m/s C)3.6 x 10⁴ m/s D)4.1 x 10⁴ m/s

Accepted Answer

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

Question 16

A 5.00-g bullet is fired into a 900-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)129 J
B)23.3 kJ
C)0.709 J
D)0.355 J

Accepted Answer

The potential energy at the highest point (mgh) is equal to the initial kinetic energy of the bullet. The combined mass is 905 g (0.905 kg), and the height is 0.08 m. Thus, KE = mgh = 0.905 kg * 9.8 m/s² * 0.08 m = 0.709 J.

Question 17

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?
A)9 m/s
B)18 m/s
C)90 m/s
D)900 m/s

Accepted Answer

By conservation of momentum, we have:
m1v1 = m1v1' + m2v2'
where m1 is the mass of the bullet, v1 is the initial velocity of the bullet, v1' is the final velocity of the bullet (which we don't need to know), m2 is the mass of the block, and v2' is the final velocity of the block.
Solving for v2', we get:
v2' = (m1v1 - m1v1')/m2
Substituting the given values, we get:
v2' = (0.02 kg)(1000 m/s - 100 m/s)/(1 kg) = 180 m/s
Therefore, the resulting speed of the block is 180 m/s, which is equivalent to choice B.

Question 18

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)The clay experiences a greater change in momentum than the ball.
B)The ball experiences a greater change in momentum than the clay.
C)The clay and the ball experience the same change in momentum.
D)It is not possible to know which object has the greater change in momentum.

Accepted Answer

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

Question 19

A man standing on frictionless ice throws a 1.00-kg mass at 20.0 m/s at an angle of elevation of 40.0 $\degree$.What was the magnitude of the man's momentum immediately after throwing the mass?
A)16.8 kg·m/s
B)15.3 kg·m/s
C)12.9 kg·m/s
D)This cannot be answered because the mass of the man needs to be known.

Accepted Answer

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

Question 20

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)The one with mass m₁ receives the greatest impulse. B)The one with mass m₃ receives the greatest impulse. C)The all must receive equal impulses. D)Although one or more of the above statements could be true in special cases,they are not always true.

Accepted Answer

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

Quiz 6: Momentum and Collisions

Object 1 has twice the mass of Object 2.Both objects have the same kinetic energy.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.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?

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

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?

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 12.0-g bullet is fired into a 1 100-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?

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?

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:

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

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) :

A 5.00-g bullet is fired into a 500-g block of wood suspended as a ballistic pendulum.the combined mass swings up to a height of 8.00 cm.What was the magnitude of the momentum of the combined mass immediately after the collision?

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.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?

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

A 5.00-g bullet is fired into a 900-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 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?

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 man standing on frictionless ice throws a 1.00-kg mass at 20.0 m/s at an angle of elevation of 40.0 $\degree$ .What was the magnitude of the man's momentum immediately after throwing the mass?

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?