Q: A 1,000 kg car is parked on a hill. The force of gravity acting on the car is given by $$F = mg. If$$ $$g = 9.8\ \mathrm{m/s^2$}$$, what is the magnitude of the gravitational force on the car?

$$F = 1,000\ \mathrm{kg} \times 9.8\ \mathrm{m/s^2$} = 9,800\ \mathrm{N}$$

Q: A 0.5 kg ball is swung in a horizontal circle of radius 2 m at a constant speed of 4 m/s. What is the magnitude of the net force required to maintain this circular motion?

$$F = m \frac{v^2$}{r} = 0.5\ \mathrm{kg} \times \frac{(4\ \mathrm{m/s})^2$}{2\ \mathrm{m}} = 4\ \mathrm{N}$$

Q: Which of the following is the correct mathematical expression for the scalar (dot) product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

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

Q: A force of $$10\ \mathrm{N}$$ acts at an angle of $$60^\circ to $$the direction of displacement of $$5\ \mathrm{m}. $$What is the work done by the force?

$$W = Fd \cos \theta = 10 \times 5 \times \cos 60^\circ = 25\ \mathrm{J}$$

Question 1

A hockey puck slides across a frictionless ice surface at a constant velocity. Which of Newton's laws best explains why the puck continues moving without slowing down?

Accepted Answer

Newton's first law: An object in motion remains in motion at constant velocity unless acted upon by a net external force.

Question 2

A 2 kg object is acted on by a net force of 10 N to the right. What is its acceleration?

Accepted Answer

$$a = \frac{F}{m} = \frac{10\ \mathrm{N}}{2\ \mathrm{kg}} = 5\ \mathrm{m/s^2$} to $$the right

Question 3

Which of the following statements correctly distinguishes between mass and weight?

Accepted Answer

Mass is a measure of the amount of matter in an object and is independent of location; weight is the force of gravity on that object and depends on the local gravitational field.

Question 4

A 5 kg box rests on a horizontal table. Which force is responsible for supporting the box against gravity, and what is its direction?

Accepted Answer

Normal force; upward, perpendicular to the surface of the table

Question 5

A 1,000 kg car is parked on a hill. The force of gravity acting on the car is given by $$F = mg. If$$ $$g = 9.8\ \mathrm{m/s^2$}$$, what is the magnitude of the gravitational force on the car?

Accepted Answer

$$F = 1,000\ \mathrm{kg} 	imes 9.8\ \mathrm{m/s^2$} = 9,800\ \mathrm{N}$$

Question 6

According to Newton's law of universal gravitation, what is the direction of the gravitational force between two masses?

Accepted Answer

The force is always attractive and directed along the line joining the centers of the two masses.

Question 7

A 0.5 kg ball is swung in a horizontal circle of radius 2 m at a constant speed of 4 m/s. What is the magnitude of the net force required to maintain this circular motion?

Accepted Answer

$$F = m \frac{v^2$}{r} = 0.5\ \mathrm{kg} 	imes \frac{(4\ \mathrm{m/s})^2$}{2\ \mathrm{m}} = 4\ \mathrm{N}$$

Question 8

Which of the following best describes a resistive force acting on a car moving through air at high speed?

Accepted Answer

A force opposite to the direction of motion, with magnitude proportional to the square of the speed: $$F_{	ext{resistive}} = -bv^2$

Question 9

A skydiver of mass 80 kg reaches terminal speed while falling through the air. If the resistive force is given by $$F_{	ext{resistive}} = bv$$ and $$g = 9.8\ \mathrm{m/s^2$}$$, what is the terminal speed $$v_t$$?

Accepted Answer

$$v_t = \frac{mg}{b}$$

Question 10

Which of the following is the correct mathematical expression for the scalar (dot) product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

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

Question 11

A force of $$10\ \mathrm{N}$$ acts at an angle of $$60^\circ to $$the direction of displacement of $$5\ \mathrm{m}. $$What is the work done by the force?

Accepted Answer

$$W = Fd \cos 	heta = 10 	imes 5 	imes \cos 60^\circ = 25\ \mathrm{J}$$

Question 12

A block attached to a spring is pulled so that the spring is stretched by $$0.2\ \mathrm{m}$$ from its equilibrium position. If the spring constant is $$k = 100\ \mathrm{N/m}$$, what is the work done by the spring as the block is released and returns to equilibrium?

Accepted Answer

$$W = -\frac{1}{2} k x^2$ = -\frac{1}{2} 	imes 100 	imes (0.2)^2$ = -2\ \mathrm{J}$$

Question 13

Which of the following is a correct expression for the gravitational potential energy of an object of mass $$m at $$height $$h$$ above Earth's surface?

Accepted Answer

$$U_g = mgh$$

Question 14

Which of the following is an example of a non-conservative force?

Accepted Answer

Friction

Question 15

A roller coaster car of mass 500 kg starts from rest at a height of 20 m. Neglecting friction, what is its speed at the bottom of the hill? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 20} \approx 19.8\ \mathrm{m/s}$$

Question 16

Which of the following statements about energy conservation is correct for an isolated system where only conservative forces act?

Accepted Answer

$$E_{	ext{mechanical, initial}} = E_{	ext{mechanical, final}}$$

Question 17

A person lifts a 10 kg box vertically upward at constant speed for 2 m. What is the work done by the person? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$W = mgh = 10 	imes 9.8 	imes 2 = 196\ \mathrm{J}$$

Question 18

Which of the following is the correct formula for average power delivered by a force doing work $$W$$ over a time interval $$\Delta t$$?

Accepted Answer

$$P_{	ext{avg}} = \frac{W}{\Delta t}$$

Question 19

A cyclist applies a constant force of 200 N to move a bike at a constant velocity of 10 m/s. What is the power delivered by the cyclist?

Accepted Answer

$$P = Fv = 200 	imes 10 = 2,000\ \mathrm{W}$$

Physics Study Guide: Newton's Laws, Forces, Gravitation, Work, Energy, and Power

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