Q: A $$10\ \mathrm{kg}$$ box is at rest on a horizontal surface. The coefficient of static friction is $$0.4. $$What is the maximum force that can be applied before the box starts to move?

$$f_s = \mu_s N = 0.4 \times 98 = 39.2\ \mathrm{N}$$

Q: A $$2\ \mathrm{kg}$$ mass is lifted to a height of $$5\ \mathrm{m}. $$What is the change in gravitational potential energy?

$$\Delta U_g = mgh = 2 \times 9.8 \times 5 = 98\ \mathrm{J}$$

Q: A force of $$50\ \mathrm{N} is $$applied at an angle of $$60^\circ to a $$lever arm of length $$0.5\ \mathrm{m}. $$What is the torque produced?

$$\tau = rF\sin\phi = 0.5 \times 50 \times \sin 60^\circ = 21.65\ \mathrm{N\cdot m}$$

Question 1

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

Accepted Answer

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

Question 2

A ball is thrown vertically upward with an initial velocity of $$15\ \mathrm{m/s}. $$What is the maximum height it reaches? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$11.5\ \mathrm{m}$$

Question 3

A $$5\ \mathrm{kg}$$ box is pulled across a horizontal surface with a force of $$30\ \mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal. What is the horizontal component of the force?

Accepted Answer

$$30\cos 30^\circ = 25.98\ \mathrm{N}$$

Question 4

A block slides down a frictionless incline of angle $$	heta = 20^\circ. $$What is the acceleration of the block?

Accepted Answer

$$a = g\sin 20^\circ$$

Question 5

Which of the following is the correct expression for the moment of inertia of a solid sphere of mass $$M$$ and radius $$R$$?

Accepted Answer

$$I = \frac{2}{5}MR^2$

Question 6

A $$2\ \mathrm{kg}$$ object moves in a circle of radius $$4\ \mathrm{m} at a $$constant speed of $$6\ \mathrm{m/s}. $$What is the magnitude of the centripetal force?

Accepted Answer

$$18\ \mathrm{N}$$

Question 7

A $$0.5\ \mathrm{kg}$$ ball is attached to a string and swung in a horizontal circle of radius $$2\ \mathrm{m} at an $$angular velocity of $$3\ \mathrm{rad/s}. $$What is the linear speed of the ball?

Accepted Answer

$$v = r\omega = 6\ \mathrm{m/s}$$

Question 8

A $$10\ \mathrm{kg}$$ box is at rest on a horizontal surface. The coefficient of static friction is $$0.4. $$What is the maximum force that can be applied before the box starts to move?

Accepted Answer

$$f_s = \mu_s N = 0.4 	imes 98 = 39.2\ \mathrm{N}$$

Question 9

A $$0.2\ \mathrm{kg}$$ ball moving at $$5\ \mathrm{m/s}$$ collides elastically with a stationary $$0.1\ \mathrm{kg}$$ ball. What is the final velocity of the $$0.2\ \mathrm{kg}$$ ball?

Accepted Answer

$$v_{1f} = \frac{m_1$ - m_2$}{m_1$ + m_2$} v_{1i} = \frac{0.2 - 0.1}{0.2 + 0.1} 	imes 5 = 1.67\ \mathrm{m/s}$$

Question 10

A force of $$10\ \mathrm{N} is $$applied to a spring, stretching it by $$0.05\ \mathrm{m}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{F}{\Delta x} = \frac{10}{0.05} = 200\ \mathrm{N/m}$$

Question 11

A $$3\ \mathrm{kg}$$ object is moving with a velocity of $$4\ \mathrm{m/s}. $$What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2}mv^2$ = 24\ \mathrm{J}$$

Question 12

A $$2\ \mathrm{kg}$$ mass is lifted to a height of $$5\ \mathrm{m}. $$What is the change in gravitational potential energy?

Accepted Answer

$$\Delta U_g = mgh = 2 	imes 9.8 	imes 5 = 98\ \mathrm{J}$$

Question 13

A $$0.5\ \mathrm{kg}$$ mass attached to a spring oscillates with a maximum displacement of $$0.1\ \mathrm{m}. If $$the spring constant is $$200\ \mathrm{N/m}$$, what is the maximum potential energy stored in the spring?

Accepted Answer

$$U_s = \frac{1}{2}kx^2$ = 1\ \mathrm{J}$$

Question 14

A $$4\ \mathrm{kg}$$ object is acted on by two forces: $$F_1 = 10$$\ \mathrm{N}$$ east and F_2$ = 6\ \mathrm{N}$$ north. What is the magnitude of the net force?

Accepted Answer

$$F_{net} = \sqrt{10^2$ + 6^2$} = 11.66\ \mathrm{N}$$

Question 15

A satellite orbits Earth at a radius $$r$$ from the center of the planet. What is the expression for its orbital speed?

Accepted Answer

$$v = \sqrt{\frac{GM}{r}}$$

Question 16

A force of $$50\ \mathrm{N} is $$applied at an angle of $$60^\circ to a $$lever arm of length $$0.5\ \mathrm{m}. $$What is the torque produced?

Accepted Answer

$$	au = rF\sin\phi = 0.5 	imes 50 	imes \sin 60^\circ = 21.65\ \mathrm{N\cdot m}$$

Question 17

A $$2\ \mathrm{kg}$$ object moving at $$3\ \mathrm{m/s}$$ collides inelastically with a $$1\ \mathrm{kg}$$ object at rest. What is their final velocity?

Accepted Answer

$$v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{2 	imes 3 + 1 	imes 0}{2 + 1} = 2\ \mathrm{m/s}$$

Question 18

A $$5\ \mathrm{kg}$$ object is acted on by a net force of $$20\ \mathrm{N}$$ for $$4\ \mathrm{s}. $$What is the impulse delivered to the object?

Accepted Answer

$$J = F_{avg} \Delta t = 20 	imes 4 = 80\ \mathrm{N\cdot s}$$

Fundamental Concepts in Mechanics: Motion, Forces, Energy, and Rotational Dynamics

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