Question 1

The momentum of an object at a given instant is in the same direction as its:

Accepted Answer

By definition, momentum is defined as mass times velocity. Therefore, the direction of momentum will always be in the same direction as the velocity of the object.

Question 2

The velocity of the center of mass of a system of particles changes as v = 4.5 t + 2.4 t² + 1.1 t³, where v is in meters per second.If the system starts from rest at t = 0, what is its position at t = 3.0 s?

Accepted Answer

To find the position, integrate the velocity function with respect to time. The integral of v = 4.5t + 2.4t^2 + 1.1t^3 is s(t) = (4.5/2)t^2 + (2.4/3)t^3 + (1.1/4)t^4 + C. Since the system starts from rest, C = 0. Evaluating at t = 3.0 s gives s(3) = (4.5/2)(3)^2 + (2.4/3)(3)^3 + (1.1/4)(3)^4 = 64 m.

Question 3

A 1.0 kg-ball moving at 2.0 m/s perpendicular to a wall rebounds from the wall at 1.5 m/s.The change in the momentum of the ball is:

Accepted Answer

The answer of A 1.0 kg-ball moving at 2.0 m/s...

Question 4

For a two-body collision, involving objects with different masses, a frame of reference which has the same velocity relative to the laboratory as does the center of mass of the two objects is:

Accepted Answer

In a two-body collision, the total momentum of the two objects is conserved. Therefore, in a frame of reference where the total momentum of the two objects is zero, the momentum before and after the collision is also zero. This frame of reference is called the center of mass frame, and it has the same velocity relative to the laboratory as the center of mass of the two objects. Therefore, the best choice is D.

Question 5

Two objects, P and Q, have the same momentum.Q can have more kinetic energy than P if it:

Accepted Answer

Kinetic energy is directly proportional to the square of velocity. Therefore, if two objects have the same momentum but different kinetic energy, the one with the higher kinetic energy must have a higher velocity.

Question 6

Force:

Accepted Answer

Force is defined as the time rate of change of momentum, according to Newton's second law of motion, which states that the force acting on an object is equal to the rate of change of its momentum. This principle is fundamental in classical mechanics.

Question 7

A ball hits a wall and rebounds with the same speed, as diagrammed below.The changes in the components of the momentum of the ball are:

Accepted Answer

The answer of A ball hits a wall and rebounds...

Question 8

The velocity of the center of mass of a system of particles changes as v = 4.5 t + 2.4 t² + 1.1 t³, where v is in meters per second.If the system starts from rest at t = 0, what is its acceleration at t = 3.0 s?

Accepted Answer

The answer of The velocity of the center of mass...

Question 9

When you step on the accelerator to increase the speed of your car, the force that accelerates the car is:

Accepted Answer

The force that actually accelerates the car is the force of friction of the road on the tires. This frictional force pushes the car forward as the tires rotate and push against the road surface.

Question 10

Two bodies, A and B, have equal kinetic energies.The mass of A is nine times that of B.The ratio of the momentum of A to that of B is:

Accepted Answer

Since kinetic energy is equal, and mass of A is nine times that of B, the velocity of B is three times that of A. Therefore, the momentum of A is three times that of B.

Question 11

A 2.0-kg mass is attached to one end of a spring with a spring constant of 100 N/m and a 4.0-kg mass is attached to the other end.The masses are placed on a horizontal surface and the spring is compressed 10 cm.The spring is then released with the masses at rest and the masses oscillate.When the spring has its equilibrium length for the first time the 2.0-kg mass has a speed of 0.36 m/s.The mechanical energy that has been lost to this instant is:

Accepted Answer

The mechanical energy lost is equal to the work done by friction, which is equal to the force of friction times the distance moved. The force of friction is equal to the coefficient of friction times the normal force, which is equal to the weight of the masses. The distance moved is equal to the amplitude of the oscillation, which is equal to the initial compression of the spring. Therefore, the mechanical energy lost is equal to:$$W_f=\mu mgd=(0.1)(6)(0.1)=0.06J$$

Question 12

Momentum may be expressed in:

Accepted Answer

Momentum is defined as the product of mass and velocity, which can be expressed in units of kg·m/s. Since 1 N = 1 kg·m/s^2, multiplying by seconds (s) gives N·s, which is a correct unit for momentum.

Question 13

A large wedge with a mass of 10 kg rests on a horizontal frictionless surface, as shown.A block with a mass of 5.0 kg starts from rest and slides down the inclined surface of the wedge, which is rough.At one instant the vertical component of the block's velocity is 3.0 m/s and the horizontal component is 6.0 m/s.At that instant the velocity of the wedge is:

Accepted Answer

Since the block is sliding down the rough surface of the wedge, there must be a frictional force acting on it. This frictional force must be parallel to the incline and points opposite to the direction of motion. The force of friction will produce a torque about the center of mass of the wedge, causing it to rotate counterclockwise. Therefore, the velocity of the wedge must be in the same direction as the force of friction, which is opposite to the direction of motion of the block at that instant. Since the horizontal component of the block's velocity is to the right, the velocity of the wedge must be to the left. Therefore, the answer is B) 3.0 m/s, right.

Question 14

A particle moves along the x axis.Its momentum is graphed below as a function of time.Rank the numbered regions according to the magnitude of the force acting on the particle, least to greatest.

Accepted Answer

The answer of A particle moves along the x axis.Its...

Question 15

The position of the center of mass of a system of particles moves as x = 4.5 t + 2.4 t² + 1.1 t³, where x is in meters.If the system starts from rest at t = 0, what is its velocity at t = 3.0 s?

Accepted Answer

The answer of The position of the center of mass...

Question 16

The acceleration of the center of mass of a system of particles changes as a = 4.5t + 2.4t² + 1.1t³, where a is in m/s².If the system starts from rest at t = 0, what is its velocity at t = 2.0 s?

Accepted Answer

The answer of The acceleration of the center of mass...

Question 17

If the total momentum of a system is changing:

Accepted Answer

According to Newton's Second Law, the rate of change of momentum of a system is equal to the net external force acting on the system. Therefore, if the total momentum of a system is changing, there must be a net external force acting on the system.

Question 18

A 2.5-kg stone is released from rest and falls toward Earth.After 4.0 s, the magnitude of its momentum is:

Accepted Answer

The momentum of an object is given by the product of its mass and velocity (p = mv). When the stone is released, it accelerates due to gravity (g = 9.8 m/s^2). After 4.0 seconds, its velocity (v) can be calculated using the equation v = gt, where t is the time. Thus, v = 9.8 m/s^2 * 4.0 s = 39.2 m/s. The momentum of the stone is then p = mv = 2.5 kg * 39.2 m/s = 98 kg∙m/s.

Question 19

Block A, with a mass of 4.0 kg, is moving with a speed of 2.0 m/s while block B, with a mass of 8.0 kg, is moving in the opposite direction with a speed of 3.0 m/s.The momentum of the center of mass of the two-block system is:

Accepted Answer

The momentum of the center of mass of the system can be calculated by adding the momentum of each block. The momentum of block A is $p_A = m_A \cdot v_A = 4.0 \, \text{kg} \cdot 2.0 \, \text{m/s} = 8.0 \, \text{kg} \cdot \text{m/s}$. The momentum of block B, moving in the opposite direction, is $p_B = m_B \cdot v_B = 8.0 \, \text{kg} \cdot (-3.0) \, \text{m/s} = -24.0 \, \text{kg} \cdot \text{m/s}$. Adding these momenta gives $8.0 - 24.0 = -16.0 \, \text{kg} \cdot \text{m/s}$, indicating a momentum of 16 m/s in the direction opposite to A, which is the same direction as B.

Question 20

The momentum of an object at a given instant is independent of its:

Accepted Answer

Momentum is defined as the product of an object's mass and its velocity at a given instant. Therefore, it directly depends on the object's mass (B), speed (C), and velocity (D), as these factors determine its momentum. Inertia (A) is a property that describes an object's resistance to changes in its motion, which indirectly affects momentum but is not a direct factor in its calculation. Acceleration (E), however, is the rate of change of velocity over time and does not directly influence the momentum at a specific instant; instead, it affects how the momentum changes over time.

Quiz 9: Center of Mass and Linear Momentum