Q: A $$2\ \mathrm{kg}$$ block slides down a frictionless incline of height $$5\ \mathrm{m}. $$What is its speed at the bottom?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5} \approx 9.9\ \mathrm{m/s}$$

Q: A $$3\ \mathrm{kg}$$ object moves in a circle of radius $$2\ \mathrm{m} at a $$constant speed of $$4\ \mathrm{m/s}. $$What is the magnitude of the net force acting on the object?

$$F = m \dfrac{v^2$}{r} = 3 \times \dfrac{16}{2} = 24\ \mathrm{N}$$

Q: A $$5\ \mathrm{kg}$$ object is moving at $$10\ \mathrm{m/s}. $$What is its kinetic energy?

$$K = \dfrac{1}{2} m v^2$ = \dfrac{1}{2} \times 5 \times 100 = 250\ \mathrm{J}$$

Q: A $$2\ \mathrm{kg}$$ block slides $$4\ \mathrm{m}$$ across a horizontal surface with a coefficient of kinetic friction $$\mu_k = 0.3. $$How much work is done by friction?

$$W = -\mu_k m g d = -0.3 \times 2 \times 9.8 \times 4 = -23.52\ \mathrm{J}$$

Q: A $$0.2\ \mathrm{kg}$$ ball is attached to a string and swung in a horizontal circle of radius $$0.5\ \mathrm{m} at$$ $$3\ \mathrm{m/s}. $$What is the tension in the string?

$$T = m \dfrac{v^2$}{r} = 0.2 \times \dfrac{9}{0.5} = 3.6\ \mathrm{N}$$

Q: A $$10\ \mathrm{kg}$$ box is pulled across a rough floor at constant speed by a force of $$40\ \mathrm{N}. $$What is the coefficient of kinetic friction?

$$\mu_k = \dfrac{F}{mg} = \dfrac{40}{10 \times 9.8} \approx 0.41$$

Q: A $$0.5\ \mathrm{kg}$$ mass is attached to a string and swung in a vertical circle of radius $$1\ \mathrm{m}. $$What is the minimum speed at the top of the circle to keep the string taut?

$$v = \sqrt{g r} = \sqrt{9.8 \times 1} \approx 3.13\ \mathrm{m/s}$$

Question 1

A car accelerates uniformly from rest to a velocity of $$20\ \mathrm{m/s} in$$ $$5\ \mathrm{s}. $$What is the magnitude of its acceleration?

Accepted Answer

$$2\ \mathrm{m/s^2$}$$

Question 2

A projectile is launched from the ground at an angle of $$53^\circ$$ with an initial speed $$v_0. $$Neglecting air resistance, which equation gives the time of flight until it lands back on level ground?

Accepted Answer

$$t = \dfrac{2 v_0$ \sin 53^\circ}{g}$$

Question 3

A $$2\ \mathrm{kg}$$ block slides down a frictionless incline of height $$5\ \mathrm{m}. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5} \approx 9.9\ \mathrm{m/s}$$

Question 4

A stone is tied to a string and whirled in a horizontal circle of radius $$r at $$speed $$v. If $$the speed is doubled and the radius is halved, what happens to the centripetal acceleration?

Accepted Answer

It becomes eight times as great.

Question 5

A $$0.5\ \mathrm{kg}$$ ball is dropped from rest from a height $$h. If it $$rebounds to a height $$\dfrac{9}{16}h$$, what fraction of its initial kinetic energy does it retain after the bounce?

Accepted Answer

$$\dfrac{9}{16}$$

Question 6

A $$3\ \mathrm{kg}$$ object moves in a circle of radius $$2\ \mathrm{m} at a $$constant speed of $$4\ \mathrm{m/s}. $$What is the magnitude of the net force acting on the object?

Accepted Answer

$$F = m \dfrac{v^2$}{r} = 3 	imes \dfrac{16}{2} = 24\ \mathrm{N}$$

Question 7

A $$1.5\ \mathrm{kg}$$ mass is attached to a spring with spring constant $$k = 200\ \mathrm{N/m}. $$What is the period of oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\dfrac{m}{k}} = 2\pi \sqrt{\dfrac{1.5}{200}} \approx 0.545\ \mathrm{s}$$

Question 8

A $$5\ \mathrm{kg}$$ object is moving at $$10\ \mathrm{m/s}. $$What is its kinetic energy?

Accepted Answer

$$K = \dfrac{1}{2} m v^2$ = \dfrac{1}{2} 	imes 5 	imes 100 = 250\ \mathrm{J}$$

Question 9

A $$2\ \mathrm{kg}$$ block slides $$4\ \mathrm{m}$$ across a horizontal surface with a coefficient of kinetic friction $$\mu_k = 0.3. $$How much work is done by friction?

Accepted Answer

$$W = -\mu_k m g d = -0.3 	imes 2 	imes 9.8 	imes 4 = -23.52\ \mathrm{J}$$

Question 10

A $$0.2\ \mathrm{kg}$$ ball is attached to a string and swung in a horizontal circle of radius $$0.5\ \mathrm{m} at$$ $$3\ \mathrm{m/s}. $$What is the tension in the string?

Accepted Answer

$$T = m \dfrac{v^2$}{r} = 0.2 	imes \dfrac{9}{0.5} = 3.6\ \mathrm{N}$$

Question 11

A $$10\ \mathrm{kg}$$ box is pulled across a rough floor at constant speed by a force of $$40\ \mathrm{N}. $$What is the coefficient of kinetic friction?

Accepted Answer

$$\mu_k = \dfrac{F}{mg} = \dfrac{40}{10 	imes 9.8} \approx 0.41$$

Question 12

A $$0.5\ \mathrm{kg}$$ mass is attached to a string and swung in a vertical circle of radius $$1\ \mathrm{m}. $$What is the minimum speed at the top of the circle to keep the string taut?

Accepted Answer

$$v = \sqrt{g r} = \sqrt{9.8 	imes 1} \approx 3.13\ \mathrm{m/s}$$

Question 13

A $$2\ \mathrm{kg}$$ object is moving at $$5\ \mathrm{m/s}$$ and collides elastically with a stationary $$3\ \mathrm{kg}$$ object. What is the velocity of the $$2\ \mathrm{kg}$$ object after the collision?

Accepted Answer

$$v = \dfrac{(2-3)}{2+3} 	imes 5 = -1\ \mathrm{m/s}$$

Question 14

A $$1\ \mathrm{kg}$$ mass is attached to a spring and oscillates with amplitude $$0.1\ \mathrm{m}$$ and period $$2\ \mathrm{s}. $$What is the maximum speed?

Accepted Answer

$$v_{max} = \dfrac{2\pi A}{T} = \dfrac{2\pi 	imes 0.1}{2} = 0.314\ \mathrm{m/s}$$

Question 15

A $$0.5\ \mathrm{kg}$$ ball is thrown vertically upward with an initial speed of $$10\ \mathrm{m/s}. $$What is the maximum height reached?

Accepted Answer

$$h = \dfrac{v_0$^2}{2g} = \dfrac{100}{19.6} \approx 5.1\ \mathrm{m}$$

Question 16

A $$2\ \mathrm{kg}$$ object is acted on by a net force of $$10\ \mathrm{N}$$ for $$3\ \mathrm{s}. $$What is the change in momentum?

Accepted Answer

$$\Delta p = F \Delta t = 10 	imes 3 = 30\ \mathrm{kg\cdot m/s}$$

Question 17

A $$1\ \mathrm{kg}$$ mass is attached to a string and swung in a circle of radius $$2\ \mathrm{m} at$$ $$4\ \mathrm{m/s}. $$What is its angular momentum?

Accepted Answer

$$L = m v r = 1 	imes 4 	imes 2 = 8\ \mathrm{kg\cdot m^2$/s}$$

Question 18

A $$0.5\ \mathrm{kg}$$ mass is attached to a spring with $$k = 100\ \mathrm{N/m}. $$What is the potential energy stored when the spring is stretched $$0.2\ \mathrm{m}$$?

Accepted Answer

$$U = \dfrac{1}{2} k x^2$ = \dfrac{1}{2} 	imes 100 	imes 0.04 = 2\ \mathrm{J}$$

Physics with Calculus Exam Practice – Step-by-Step Guidance

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