Q: A 2 kg object moves in a circle of radius 3 m at a speed of 4 m/s. What is the magnitude of the centripetal force acting on the object?

$$F_c = \dfrac{mv^2$}{r} = \dfrac{2 \times 16}{3} = 10.67\ \text{N}$$

Q: A force $$\vec{F} = (3\hat{i} + 4\hat{j})\ \text{N}$$ acts on a particle that moves from the origin to the point $$(2, 1) m. $$What is the work done by the force?

$$W = \vec{F} \cdot \vec{d} = 3 \times 2 + 4 \times 1 = 10\ \text{J}$$

Q: A block slides down a rough incline and comes to rest after traveling a distance $$d. If $$the coefficient of kinetic friction is $$\mu_k$$, what is the work done by friction?

$$W_{fric} = -\mu_k mgd \cos\theta$$

Q: A 3 kg object moving at 2 m/s collides and sticks to a 2 kg object at rest. What is the final velocity of the combined mass?

$$v_f = \dfrac{3 \times 2}{3 + 2} = 1.2\ \text{m/s}$$

Q: A force $$F(x) = 4x N $$acts on a particle as it moves from $$x = 0 to$$ $$x = 3 m. $$What is the work done by this force?

$$W = \$$int_0$$^3 4x\ dx = 18\ \text{J}$$

Q: A 1 kg object is attached to a string and swung in a vertical circle of radius 2 m. What is the minimum speed at the top of the circle to keep the string taut?

$$v_{min} = \sqrt{gR} = \sqrt{9.8 \times 2} \approx 4.43\ \text{m/s}$$

Q: A 0.2 kg ball is thrown vertically upward with a speed of 10 m/s. What is the maximum height reached by the ball?

$$h = \dfrac{v^2$}{2g} = \dfrac{100}{19.6} \approx 5.1\ \text{m}$$

Q: A 1 kg object moves with velocity $$\vec{v} = (3\hat{i} + 4\hat{j}) m/s. $$What is its kinetic energy?

$$KE = \dfrac{1}{2}mv^2$ = \dfrac{1}{2} \times 1 \times (3^2$ + 4^2$) = 12.5\ \text{J}$$

Question 1

A car of mass $$m$$ travels around a flat circular track of radius $$r at $$constant speed $$v. $$What is the minimum coefficient of static friction $$\mu_s$$ required to prevent the car from sliding off the track?

Accepted Answer

$$\mu_s = \dfrac{v^2$}{rg}$$

Question 2

A satellite orbits the Earth at a distance $$R$$ from the center of the Earth. If the mass of the Earth is $$M$$ and the gravitational constant is $$G$$, what is the speed $$v of $$the satellite in its circular orbit?

Accepted Answer

$$v = \sqrt{\dfrac{GM}{R}}$$

Question 3

A block of mass $$m is $$attached to a spring with spring constant $$k$$ and is pulled a distance $$x$$ from equilibrium and released. What is the potential energy stored in the spring at this position?

Accepted Answer

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

Question 4

A 2 kg object moves in a circle of radius 3 m at a speed of 4 m/s. What is the magnitude of the centripetal force acting on the object?

Accepted Answer

$$F_c = \dfrac{mv^2$}{r} = \dfrac{2 	imes 16}{3} = 10.67\ 	ext{N}$$

Question 5

A ball is dropped from a height $$h$$ above the ground. Neglecting air resistance, what is the speed of the ball just before it hits the ground?

Accepted Answer

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

Question 6

A force $$\vec{F} = (3\hat{i} + 4\hat{j})\ 	ext{N}$$ acts on a particle that moves from the origin to the point $$(2, 1) m. $$What is the work done by the force?

Accepted Answer

$$W = \vec{F} \cdot \vec{d} = 3 	imes 2 + 4 	imes 1 = 10\ 	ext{J}$$

Question 7

A 0.5 kg ball moving at 6 m/s collides elastically with a stationary 0.5 kg ball. What is the velocity of the first ball after the collision?

Accepted Answer

$$0\ 	ext{m/s}$$

Question 8

A block slides down a rough incline and comes to rest after traveling a distance $$d. If $$the coefficient of kinetic friction is $$\mu_k$$, what is the work done by friction?

Accepted Answer

$$W_{fric} = -\mu_k mgd \cos	heta$$

Question 9

A planet has twice the mass and half the radius of Earth. What is the acceleration due to gravity on its surface?

Accepted Answer

$$g' = \dfrac{GM}{R^2$} \rightarrow g' = \dfrac{2GM_E}{(0.5R_E)^2$} = 8g_E$$

Question 10

A 3 kg object moving at 2 m/s collides and sticks to a 2 kg object at rest. What is the final velocity of the combined mass?

Accepted Answer

$$v_f = \dfrac{3 	imes 2}{3 + 2} = 1.2\ 	ext{m/s}$$

Question 11

A force $$F(x) = 4x N $$acts on a particle as it moves from $$x = 0 to$$ $$x = 3 m. $$What is the work done by this force?

Accepted Answer

$$W = \$$int_0$$^3 4x\ dx = 18\ 	ext{J}$$

Question 12

A 1 kg object is attached to a string and swung in a vertical circle of radius 2 m. What is the minimum speed at the top of the circle to keep the string taut?

Accepted Answer

$$v_{min} = \sqrt{gR} = \sqrt{9.8 	imes 2} \approx 4.43\ 	ext{m/s}$$

Question 13

A 5 kg object is acted on by a force that increases its velocity from 2 m/s to 6 m/s. What is the change in kinetic energy?

Accepted Answer

$$\Delta KE = \dfrac{1}{2}m(v_f^2$ - v_i^2$) = \dfrac{1}{2} 	imes 5 	imes (36 - 4) = 80\ 	ext{J}$$

Question 14

A 0.2 kg ball is thrown vertically upward with a speed of 10 m/s. What is the maximum height reached by the ball?

Accepted Answer

$$h = \dfrac{v^2$}{2g} = \dfrac{100}{19.6} \approx 5.1\ 	ext{m}$$

Question 15

A 1 kg object moves with velocity $$\vec{v} = (3\hat{i} + 4\hat{j}) m/s. $$What is its kinetic energy?

Accepted Answer

$$KE = \dfrac{1}{2}mv^2$ = \dfrac{1}{2} 	imes 1 	imes (3^2$ + 4^2$) = 12.5\ 	ext{J}$$

Question 16

A 2 kg block slides at 5 m/s on a frictionless surface and collides with a spring of $$k = 200 N/m. $$What is the maximum compression of the spring?

Accepted Answer

$$x_{max} = \sqrt{\dfrac{mv^2$}{k}} = \sqrt{\dfrac{2 	imes 25}{200}} = 0.5\ 	ext{m}$$

Question 17

A 0.1 kg bullet moving at 400 m/s embeds itself in a 2 kg block at rest on a frictionless surface. What is the final velocity of the block-bullet system?

Accepted Answer

$$v_f = \dfrac{0.1 	imes 400}{2.1} \approx 19.05\ 	ext{m/s}$$

Question 18

A 3 kg object moves east at 4 m/s and a 2 kg object moves north at 6 m/s. What is the magnitude of the velocity of the center of mass?

Accepted Answer

$$v_{cm} = \sqrt{\left(\dfrac{3 	imes 4}{5}\$$right)^2$$ + \left(\dfrac{2 	imes 6}{5}\$$right)^2$$} = \sqrt{(2.4)^2$ + (2.4)^2$} = 3.4\ 	ext{m/s}$$

Physics with Calculus: Exam 2 Study Guide (Chapters 5–9)

Study Guide - Practice Questions

Study Guide - Flashcards