Q: Given two forces $$\vec{F}_1$$ and $$\vec{F}_2$$ acting at an angle $$\theta to $$each other, what is the dot product $$\vec{F}_1 \cdot \vec{F}_2$$?

$$\vec{F}_1 \cdot \vec{F}_2 = F_1$ F_2$ \cos \theta$$

Q: A 2 kg object is moving at 3 m/s. What is its kinetic energy?

$$KE = \frac{1}{2} \times 2 \times 3^2$ = 9 J$$

Question 1

A box of mass $$m is $$pushed across a rough surface with a constant force $$F$$ over a distance $$d. If $$the coefficient of kinetic friction between the box and the surface is $$\mu_k$$, what is the net work done on the box?

Accepted Answer

$$W = Fd - \mu_k mgd$$

Question 2

Which of the following best describes the physical meaning of the dot product between two vectors, such as force and displacement?

Accepted Answer

It gives the amount of one vector in the direction of the other.

Question 3

A spring with spring constant $$k is $$compressed by a distance $$x. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2}kx^2$

Question 4

A ball is dropped from a height $$h$$ and bounces back to a height $$h' \u003c h. $$Which of the following best explains the energy transformation during the bounce?

Accepted Answer

Some energy is lost to non-conservative forces such as heat and sound during the bounce.

Question 5

Given two forces $$\vec{F}_1$$ and $$\vec{F}_2$$ acting at an angle $$	heta to $$each other, what is the dot product $$\vec{F}_1 \cdot \vec{F}_2$$?

Accepted Answer

$$\vec{F}_1 \cdot \vec{F}_2 = F_1$ F_2$ \cos 	heta$$

Question 6

A car of mass $$m$$ accelerates from rest to velocity $$v$$ over a distance $$d. $$Ignoring friction, what is the work done by the net force on the car?

Accepted Answer

$$W = \frac{1}{2}mv^2$

Question 7

Which of the following is true about conservative and non-conservative forces?

Accepted Answer

Conservative forces allow energy to be recovered; non-conservative forces dissipate energy as heat or sound.

Question 8

A 2 kg object is moving at 3 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} 	imes 2 	imes 3^2$ = 9 J$$

Question 9

A system of two particles, each of mass $$m$$, moves with velocities $$\vec{v}_1$$ and $$\vec{v}_2. $$What is the total momentum of the system?

Accepted Answer

$$m(\vec{v}_1 + \vec{v}_2)$$

Question 10

In a perfectly elastic collision between two objects, which of the following is conserved?

Accepted Answer

Both momentum and kinetic energy

Question 11

A bullet of mass $$m is $$fired into a block of mass $$M at $$rest. The bullet embeds in the block, and they move together after the collision. What is the final velocity $$v_f of $$the combined system?

Accepted Answer

$$v_f = \frac{m v_{bullet}}{m + M}$$

Question 12

A ball of mass $$m$$ moving at velocity $$v$$ collides elastically with a stationary ball of equal mass. What is the velocity of the first ball after the collision?

Accepted Answer

$$0$$

Question 13

Which equation represents the work-energy theorem?

Accepted Answer

$$W = \Delta KE$$

Question 14

A force $$\vec{F}$$ acts on an object for a time $$\Delta t. $$What is the impulse delivered to the object?

Accepted Answer

$$J = \vec{F} \Delta t$$

Question 15

A 0.5 kg ball moving at 4 m/s collides inelastically with a 1 kg ball at rest. What is their final velocity after the collision?

Accepted Answer

$$v_f = 1.33 m/s$$

Question 16

Which of the following statements about the impulse-momentum theorem is correct?

Accepted Answer

Impulse is equal to the change in momentum.

Question 17

A roller coaster car of mass $$m$$ starts from rest at height $$h$$ and descends to a lower height $$h'. $$Ignoring friction, what is its speed at height $$h'$$?

Accepted Answer

$$v = \sqrt{2g(h - h')}$$

Question 18

Which of the following is a correct application of the conservation of momentum in a two-object system?

Accepted Answer

The total momentum before collision equals the total momentum after collision.

Question 19

A person jumps off a stationary boat of mass $$M$$ with velocity $$v$$ relative to the water. What is the velocity of the boat after the jump?

Accepted Answer

$$v_{boat} = -\frac{m}{M}v$$

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