Question 1

Which of the following best describes the scalar (dot) product of two vectors $$\vec{A}$$ and $$\vec{B} as $$shown in the first image?

Accepted Answer

$$\vec{A} \cdot \vec{B} = AB \cos \phi$$

Question 2

A block of mass $$1\ \mathrm{kg} is at $$rest on a frictionless surface. You push it with a constant force $$F so $$that after being displaced by $$1\ \mathrm{m}$$, its speed is $$1\ \mathrm{m/s}. $$What is the magnitude of the force $$F$$ you must apply?

Accepted Answer

$$F = 0.5\ \mathrm{N}$$

Question 3

If a force $$\vec{F} is $$applied at an angle $$\alpha to $$the direction of displacement $$\Delta \vec{s}$$, what is the work done by the force?

Accepted Answer

$$W = F \Delta s \cos \alpha$$

Question 4

A block slides on a horizontal surface with initial speed $$5\ \mathrm{m/s}$$ and comes to rest due to kinetic friction ($$\mu_k = 0.1). $$How far does it travel before stopping? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$d = 25.5\ \mathrm{m}$$

Question 5

Which of the following statements about the work done by the weight force is correct?

Accepted Answer

It is zero if the object moves horizontally.

Question 6

A block of mass $$m is $$released from rest at height $$h on a $$frictionless ramp. What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 7

The gravitational potential energy for an object of mass $$m at a $$distance $$r$$ from the center of the Earth is given by:

Accepted Answer

$$U = -\dfrac{G M_E m}{r}$$

Question 8

What is the escape speed from the surface of a planet of mass $$M$$ and radius $$R$$?

Accepted Answer

$$v_{esc} = \sqrt{\dfrac{2GM}{R}}$$

Question 9

A block of mass $$1\ \mathrm{kg} is $$attached to a spring with force constant $$k = 2000\ \mathrm{N/m}$$ and stretched by $$4\ \mathrm{cm}. $$What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = 1.6\ \mathrm{J}$$

Question 10

A $$5\ \mathrm{g}$$ bullet is fired at $$400\ \mathrm{m/s}$$ into a $$1\ \mathrm{kg}$$ crate on a frictionless surface. What is the speed of the crate (with bullet embedded) immediately after the collision?

Accepted Answer

$$v = 2.0\ \mathrm{m/s}$$

Question 11

Which of the following is true about the work done by the normal force on an object moving along a surface?

Accepted Answer

It is zero because the normal force is perpendicular to the displacement.

Question 12

A block of mass $$m is $$attached to a spring (force constant $$k) $$and released from rest at extension $$x_0. $$What is the maximum speed attained by the block?

Accepted Answer

$$v_{max} = \sqrt{\dfrac{k}{m}} x_0$

Question 13

Which of the following is a correct statement of the Work-Energy Theorem for a particle of mass $$m$$?

Accepted Answer

$$\dfrac{1}{2} m v_f^2$ - \dfrac{1}{2} m v_i^2$ = \sum \vec{F} \cdot \Delta \vec{s}$$

Question 14

A $$100\ \mathrm{g}$$ ball approaches a wall at $$4\ \mathrm{m/s}$$ and bounces off elastically. If the collision lasts $$0.1\ \mathrm{s}$$, what is the magnitude of the average force exerted by the ball on the wall?

Accepted Answer

$$8\ \mathrm{N}$$

Question 15

Which of the following is always conserved in an isolated system with no external forces?

Accepted Answer

Mechanical energy and momentum

Question 16

A block slides down a frictionless curved ramp and then moves onto a rough horizontal surface. Which principle(s) should be used to find the distance it travels before stopping?

Accepted Answer

Conservation of mechanical energy for the ramp, work-energy theorem for the rough surface

Question 17

A $$350\ \mathrm{kg}$$ roller coaster car starts from rest at height $$h$$ and slides down a frictionless loop-the-loop. What is its speed at the bottom of the loop (radius $$R$$)?

Accepted Answer

$$v = \sqrt{2g h}$$

Question 18

Which of the following is true about the conservation of momentum in a system where the net external force in the $$x-$$direction is zero, but not in $$y or$$ $$z$$?

Accepted Answer

Momentum is conserved only in the $$x-$$direction.

Work, Energy, and Momentum: Theorems and Conservation Laws in Mechanics

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