Q: A crate of mass 8.0 kg is given an initial speed of 5.0 m/s at the bottom of a 2.5 m ramp inclined at 30°. It slides 1.6 m up the ramp before stopping. What is the magnitude of the friction force acting on the crate?

$$f = \frac{\frac{1}{2} m v^2$ - m g s \sin \theta}{s}$$

Q: A 1000 kg car travels north at 15 m/s and collides with a 2000 kg truck traveling east at 10 m/s. What is the magnitude of the total momentum just before the collision?

$$P = \sqrt{(1.5 \times 10^4$)^2 + (2.0$$ \times $$10^4)^2$} = 2.5 \times 10^4$ \text{ kg m/s}$$

Q: A CD spins at 7200 rev/min. What is its angular velocity in radians per second?

$$\omega = 7200 \times \frac{2\pi}{60} = 754 \text{ rad/s}$$

Question 1

A crate of mass 8.0 kg is given an initial speed of 5.0 m/s at the bottom of a 2.5 m ramp inclined at 30°. It slides 1.6 m up the ramp before stopping. What is the magnitude of the friction force acting on the crate?

Accepted Answer

$$f = \frac{\frac{1}{2} m v^2$ - m g s \sin 	heta}{s}$$

Question 2

Which of the following statements about momentum is correct?

Accepted Answer

Momentum is a vector quantity and has the same direction as velocity.

Question 3

A 1000 kg car travels north at 15 m/s and collides with a 2000 kg truck traveling east at 10 m/s. What is the magnitude of the total momentum just before the collision?

Accepted Answer

$$P = \sqrt{(1.5 	imes 10^4$)^2 + (2.0$$ 	imes $$10^4)^2$} = 2.5 	imes 10^4$ 	ext{ kg m/s}$$

Question 4

In a perfectly elastic collision between two gliders on a frictionless track, which quantities are conserved?

Accepted Answer

Both momentum and kinetic energy are conserved.

Question 5

Two astronauts push each other in space where no external forces act. What happens to their total momentum?

Accepted Answer

It remains constant.

Question 6

A bullet of mass $$m_B$$ collides inelastically with a block of mass $$m_W$$ suspended as a pendulum. After the collision, the block rises to height $$y. $$What is the initial speed $$v_1 of $$the bullet?

Accepted Answer

$$v_1$$ = \frac{m_B + m_W}{m_B} \sqrt{2 g y}$$

Question 7

In a completely inelastic collision, what happens to the kinetic energy of the system?

Accepted Answer

It decreases.

Question 8

If two objects stick together after a collision, which type of collision is this?

Accepted Answer

Completely inelastic collision

Question 9

A 0.50 kg glider moving at 2.0 m/s collides with a 0.30 kg glider moving at -2.0 m/s. If they stick together, what is their final velocity?

Accepted Answer

$$v_{2x} = \frac{(0.50)(2.0) + (0.30)(-2.0)}{0.50 + 0.30} = 0.5 	ext{ m/s}$$

Question 10

For a one-dimensional elastic collision where object B is initially at rest, what is the final velocity of object A?

Accepted Answer

$$v_{A2x} = \frac{m_A - m_B}{m_A + m_B} v_{A1x}$$

Question 11

In a collision between two objects of equal mass, where one is initially at rest, what happens to the moving object's velocity after an elastic collision?

Accepted Answer

It becomes zero.

Question 12

Which formula gives the position vector of the center of mass for a system of particles?

Accepted Answer

$$\vec{r}_{cm} = \frac{m_1$ \vec{r}_1 + m_2$ \vec{r}_2 + m_3$ \vec{r}_3 + \cdots}{m_1$ + m_2$ + m_3$ + \cdots}$$

Question 13

A CD spins at 7200 rev/min. What is its angular velocity in radians per second?

Accepted Answer

$$\omega = 7200 	imes \frac{2\pi}{60} = 754 	ext{ rad/s}$$

Question 14

If the vector sum of external forces on a system is zero, what can be said about the system's momentum?

Accepted Answer

The total momentum is constant.

Question 15

In a real-world car crash, why are collisions designed to be inelastic?

Accepted Answer

To absorb energy and reduce injury.

Question 16

Which of the following best describes the motion of the center of mass when external forces act on a system?

Accepted Answer

It moves as if all mass were concentrated at that point and acted on by the net external force.

Question 17

A rotating disc reaches an angular velocity of 754 rad/s in 4.0 s from rest. What is its average angular acceleration?

Accepted Answer

$$\alpha_{avg} = \frac{754}{4.0} = 189 	ext{ rad/s}^2$$

Question 18

Which equation relates the total momentum of a system to the velocity of its center of mass?

Accepted Answer

$$\vec{P}_{total} = M_{total} \vec{v}_{cm}$$

Work, Energy, and Momentum: Study Notes for College Physics

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