# Test Prep

### Multiple Choice

#### 8.1 Linear Momentum, Force, and Impulse

- Scalar
- Vector

When does the net force on an object increase?

- When Δ
**p**decreases - When Δ
*t*increases - When Δ
*t*decreases

In the equation Δ**p** = *m*(**v**_{f} − **v**_{i}) , which quantity is considered to be constant?

- Initial velocity
- Final velocity
- Mass
- Momentum

- $0.24\phantom{\rule{thinmathspace}{0ex}}\text{s}$
- $4.15\phantom{\rule{thinmathspace}{0ex}}\text{s}$
- $62\phantom{\rule{thinmathspace}{0ex}}\text{s}$
- $600\phantom{\rule{thinmathspace}{0ex}}\text{s}$

#### 8.2 Conservation of Momentum

In the equation **L** = *I***ω**, what is *I*?

- Linear momentum
- Angular momentum
- Torque
- Moment of inertia

Give an example of an isolated system.

- A cyclist moving along a rough road
- A figure skater gliding in a straight line on an ice rink
- A baseball player hitting a home run
- A man drawing water from a well

#### 8.3 Elastic and Inelastic Collisions

In which type of collision is kinetic energy conserved?

- Elastic
- Inelastic

In physics, what are structureless particles that cannot rotate or spin called?

- Elastic particles
- Point masses
- Rigid masses

Two objects having equal masses and velocities collide with each other and come to a rest. What type of a collision is this and why?

- Elastic collision, because internal kinetic energy is conserved
- Inelastic collision, because internal kinetic energy is not conserved
- Elastic collision, because internal kinetic energy is not conserved
- Inelastic collision, because internal kinetic energy is conserved

- Yes
- No

### Short Answer

#### 8.1 Linear Momentum, Force, and Impulse

If an object’s velocity is constant, what is its momentum proportional to?

- Its shape
- Its mass
- Its length
- Its breadth

- Its impulse would be constant.
- Its impulse would be zero.
- Its impulse would be increasing.
- Its impulse would be decreasing.

- It is zero, because the net force is equal to the rate of change of the momentum.
- It is zero, because the net force is equal to the product of the momentum and the time interval.
- It is nonzero, because the net force is equal to the rate of change of the momentum.
- It is nonzero, because the net force is equal to the product of the momentum and the time interval.

How can you express impulse in terms of mass and velocity when neither of those are constant?

- $\Delta \text{p}=\text{\Delta}(m\text{v})$
- $\frac{\text{\Delta}\text{p}}{\text{\Delta}t}=\frac{\text{\Delta}(m\text{v})}{\text{\Delta}t}$
- $\text{\Delta}\text{p}=\text{\Delta}(\frac{m}{\text{v}})$
- $\frac{\text{\Delta}\text{p}}{\text{\Delta}t}=\frac{1}{\text{\Delta}t}\text{\xb7}\text{\Delta}(m\text{v})$

How can you express impulse in terms of mass and initial and final velocities?

- $\text{\Delta}\text{p}\text{=}m\text{(}{\text{v}}_{\text{f}}-{\text{v}}_{\text{i}}\text{)}$
- $\frac{\text{\Delta}\text{p}}{\text{\Delta}t}\text{=}\frac{m\text{(}{\text{v}}_{\text{f}}-{\text{v}}_{\text{i}}\text{)}}{\text{\Delta}t}$
- $\text{\Delta}\text{p}\text{=}\frac{\text{(}{\text{v}}_{\text{f}}-{\text{v}}_{\text{i}}\text{)}}{m}$
- $\frac{\text{\Delta}\text{p}}{\text{\Delta}t}=\frac{1}{m}\frac{({\text{v}}_{\text{f}}-{\text{v}}_{\text{i}})}{\text{\Delta}t}$

Why do we use average force while solving momentum problems? How is net force related to the momentum of the object?

- Forces are usually constant over a period of time, and net force acting on the object is equal to the rate of change of the momentum.
- Forces are usually not constant over a period of time, and net force acting on the object is equal to the product of the momentum and the time interval.
- Forces are usually constant over a period of time, and net force acting on the object is equal to the product of the momentum and the time interval.
- Forces are usually not constant over a period of time, and net force acting on the object is equal to the rate of change of the momentum.

#### 8.2 Conservation of Momentum

Under what condition(s) is the angular momentum of a system conserved?

- When net torque is zero
- When net torque is not zero
- When moment of inertia is constant
- When both moment of inertia and angular momentum are constant

- It increases.
- It decreases.
- It stays constant.
- It becomes zero.

- Force is zero.
- Force is not zero.
- Force is constant.
- Force is decreasing.

#### 8.3 Elastic and Inelastic Collisions

Two objects collide with each other and come to a rest. How can you use the equation of conservation of momentum to describe this situation?

*m*_{1}**v**_{1}+*m*_{2}**v**_{2}= 0*m*_{1}**v**_{1}−*m*_{2}**v**_{2}= 0*m*_{1}**v**_{1}+*m*_{2}**v**_{2}=*m*_{1}**v**_{1}′*m*_{1}**v**_{1}+*m*_{2}**v**_{2}=*m*_{1}**v**_{2}

- Momentum is the sum of mass and velocity. Impulse is the change in momentum.
- Momentum is the sum of mass and velocity. Impulse is the rate of change in momentum.
- Momentum is the product of mass and velocity. Impulse is the change in momentum.
- Momentum is the product of mass and velocity. Impulse is the rate of change in momentum.

What is the equation for conservation of momentum along the *x*-axis for 2D collisions in terms of mass and velocity, where one of the particles is initially at rest?

*m*_{1}**v**_{1}=*m*_{1}**v**_{1}′cos*θ*_{1}*m*_{1}**v**_{1}=*m*_{1}**v**_{1}′cos*θ*_{1}+*m*_{2}**v**_{2}′cos*θ*_{2}*m*_{1}**v**_{1}=*m*_{1}**v**_{1}′cos*θ*_{1}−*m*_{2}**v**_{2}′cos*θ*_{2}*m*_{1}**v**_{1}=*m*_{1}**v**_{1}′sin*θ*_{1}+*m*_{2}**v**_{2}′sin*θ*_{2}

What is the equation for conservation of momentum along the *y*-axis for 2D collisions in terms of mass and velocity, where one of the particles is initially at rest?

- 0 =
*m*_{1}**v**_{1}′sin*θ*_{1} - 0 =
*m*_{1}**v**_{1}′sin*θ*_{1}+*m*_{2}**v**_{2}′sin*θ*_{2} - 0 =
*m*_{1}**v**_{1}′sin*θ*_{1}−*m*_{2}**v**_{2}′sin*θ*_{2} - 0 =
*m*_{1}**v**_{1}′cos*θ*_{1}+*m*_{2}**v**_{2}′cos*θ*_{2}

### Extended Response

#### 8.1 Linear Momentum, Force, and Impulse

- No, because momentum is independent of the velocity of the object.
- No, because momentum is independent of the mass of the object.
- Yes, if the lighter object’s velocity is considerably high.
- Yes, if the lighter object’s velocity is considerably low.

- The softer surface increases the duration of the magnitude, thereby reducing the effect of the force.
- The softer surface decreases the duration of the impact, thereby reducing the effect of the force.
- The softer surface increases the duration of the impact, thereby increasing the effect of the force.
- The softer surface decreases the duration of the impact, thereby increasing the effect of the force.

Can we use the equation ${\text{F}}_{\text{net}}=\frac{\text{\Delta}p}{\text{\Delta}t}$ when the mass is constant?

- No, because the given equation is applicable for the variable mass only.
- No, because the given equation is not applicable for the constant mass.
- Yes, and the resultant equation is F =
*m***v** - Yes, and the resultant equation is F =
*ma*

#### 8.2 Conservation of Momentum

Why does a figure skater spin faster if he pulls his arms and legs in?

- Due to an increase in moment of inertia
- Due to an increase in angular momentum
- Due to conservation of linear momentum
- Due to conservation of angular momentum

#### 8.3 Elastic and Inelastic Collisions

- He should speed up.
- He should slow down.
- He should speed up and then slow down just before the collision.
- He should slow down and then speed up just before the collision.

What approach would you use to solve problems involving 2D collisions?

- Break the momenta into components and then choose a coordinate system.
- Choose a coordinate system and then break the momenta into components.
- Find the total momenta in the x and y directions, and then equate them to solve for the unknown.
- Find the sum of the momenta in the x and y directions, and then equate it to zero to solve for the unknown.