Q: A car accelerates from rest at a constant rate of $$2\ \mathrm{m/s^2$}$$ for $$5\ \mathrm{s}. $$What is its final velocity?

$$v = v_0$ + at = 0 + 2 \times 5 = 10\ \mathrm{m/s}$$

Q: A ball is thrown straight up with an initial velocity of $$20\ \mathrm{m/s}. $$Neglecting air resistance, what is the maximum height reached by the ball? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$h = \frac{v_0$^2}{2g} = \frac{20^2$}{2 \times 9.8} = 20.4\ \mathrm{m}$$

Q: A 0.5 kg ball is attached to a string and swung in a horizontal circle of radius 2 m at a constant speed of 4 m/s. What is the tension in the string?

$$T = m\frac{v^2$}{r} = 0.5 \times \frac{4^2$}{2} = 4\ \mathrm{N}$$

Q: A crate weighing 500 N is pulled at constant velocity across a floor with a coefficient of kinetic friction $$\mu_k = 0.40. $$What is the minimum force required if the rope is pulled horizontally?

$$F = \mu_k F_N = 0.40 \times 500 = 200\ \mathrm{N}$$

Q: A 1.5 kg fish is hung from a spring scale that stretches 1.00 cm for a 12.0 N weight. How far does the spring stretch for the fish?

$$\Delta L = \frac{F}{k} = \frac{1.5 \times 9.8}{12.0/0.01} = 0.01225\ \mathrm{m} = 1.23\ \mathrm{cm}$$

Q: A car of mass 1000 kg rounds a flat curve of radius 50 m. If the coefficient of static friction is $$\mu_s = 0.8$$, what is the maximum speed the car can have without sliding?

$$v_{max} = \sqrt{\mu_s g r} = \sqrt{0.8 \times 9.8 \times 50} = 19.8\ \mathrm{m/s}$$

Q: A 10 g mass and a 0.5 kg mass are separated by 0.05 m. What is the gravitational force between them? ($$G = 6.674 \times 10$$^{-11}$$\ \mathrm{N\cdot m^2$/kg^2$$}$)

$$F = \frac{G m_1$ m_2$}{r^2$} = \frac{6.674 \times 10$$^{-11}$$ \times 0.01 \times 0.5}{0.05^2$} = 1.33 \times 10$$^{-11}$$\ \mathrm{N}$$

Question 1

Which of the following best describes the difference between a real baseball in flight and an idealized model of the baseball, as shown in the images above?

Accepted Answer

The real baseball experiences air resistance, wind, and variable gravitational force, while the idealized model ignores air resistance and assumes constant gravity.

Question 2

A student uses a laser pointer to measure the distance light travels in a vacuum in a given time. According to the current SI definition, how is one meter defined?

Accepted Answer

The distance light travels in vacuum in $$1/299792458$$ seconds.

Question 3

Which of the following is a vector quantity?

Accepted Answer

Displacement

Question 4

A hiker walks 3 km east and then 4 km north. What is the magnitude of the hiker's displacement from the starting point?

Accepted Answer

$$\sqrt{3^2$ + 4^2$} = 5 km$$

Question 5

A car accelerates from rest at a constant rate of $$2\ \mathrm{m/s^2$}$$ for $$5\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v = v_0$ + at = 0 + 2 	imes 5 = 10\ \mathrm{m/s}$$

Question 6

A ball is thrown straight up with an initial velocity of $$20\ \mathrm{m/s}. $$Neglecting air resistance, what is the maximum height reached by the ball? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{20^2$}{2 	imes 9.8} = 20.4\ \mathrm{m}$$

Question 7

A 0.5 kg ball is attached to a string and swung in a horizontal circle of radius 2 m at a constant speed of 4 m/s. What is the tension in the string?

Accepted Answer

$$T = m\frac{v^2$}{r} = 0.5 	imes \frac{4^2$}{2} = 4\ \mathrm{N}$$

Question 8

A satellite orbits Earth at a radius $$r$$ with speed $$v. $$Which equation correctly relates the gravitational force to the required centripetal force for circular motion?

Accepted Answer

$$\frac{G M_E m}{r^2$} = m \frac{v^2$}{r}$$

Question 9

A crate weighing 500 N is pulled at constant velocity across a floor with a coefficient of kinetic friction $$\mu_k = 0.40. $$What is the minimum force required if the rope is pulled horizontally?

Accepted Answer

$$F = \mu_k F_N = 0.40 	imes 500 = 200\ \mathrm{N}$$

Question 10

A 1.5 kg fish is hung from a spring scale that stretches 1.00 cm for a 12.0 N weight. How far does the spring stretch for the fish?

Accepted Answer

$$\Delta L = \frac{F}{k} = \frac{1.5 	imes 9.8}{12.0/0.01} = 0.01225\ \mathrm{m} = 1.23\ \mathrm{cm}$$

Question 11

A car of mass 1000 kg rounds a flat curve of radius 50 m. If the coefficient of static friction is $$\mu_s = 0.8$$, what is the maximum speed the car can have without sliding?

Accepted Answer

$$v_{max} = \sqrt{\mu_s g r} = \sqrt{0.8 	imes 9.8 	imes 50} = 19.8\ \mathrm{m/s}$$

Question 12

A 10 g mass and a 0.5 kg mass are separated by 0.05 m. What is the gravitational force between them? ($$G = 6.674 	imes 10$$^{-11}$$\ \mathrm{N\cdot m^2$/kg^2$$}$)

Accepted Answer

$$F = \frac{G m_1$ m_2$}{r^2$} = \frac{6.674 	imes 10$$^{-11}$$ 	imes 0.01 	imes 0.5}{0.05^2$} = 1.33 	imes 10$$^{-11}$$\ \mathrm{N}$$

Question 13

A projectile is launched with an initial velocity $$v_0 at an $$angle $$	heta$$ above the horizontal. Which equation gives the time of flight until it returns to the same vertical level?

Accepted Answer

$$t = \frac{2 v_0$ \sin 	heta}{g}$$

Question 14

A block of mass $$m$$ slides down a frictionless incline of angle $$\alpha. $$What is the acceleration of the block?

Accepted Answer

$$a = g \sin \alpha$$

Question 15

A 2 kg object falls through air and reaches terminal velocity. If the drag force is $$F_D = D v^2$ and g = 9.8$$\ \mathrm{$$m/s^2$$}$$, what is the terminal velocity v_T$?

Accepted Answer

$$v_T = \sqrt{\frac{mg}{D}}$$

Question 16

A car accelerates uniformly from $$10\ \mathrm{m/s} to$$ $$30\ \mathrm{m/s} in$$ $$5\ \mathrm{s}. $$What is the acceleration?

Accepted Answer

$$a = \frac{v_2$ - v_1$}{t} = \frac{30 - 10}{5} = 4\ \mathrm{m/s^2$}$$

Question 17

A 60 kg passenger rides a Ferris wheel of radius 8 m, making one revolution in 10 s. What is the normal force on the passenger at the top of the wheel? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$N = mg - m \frac{v^2$}{R}$$, where $$v = \frac{2\pi R}{T}$$

Physics with Calculus: Models, Measurements, and Vectors

Study Guide - Practice Questions

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