Q: A 5 kg box is at rest on a horizontal surface. The coefficient of static friction between the box and the surface is 0.4. What is the maximum horizontal force that can be applied to the box before it starts to move?

$$F_{s,\text{max}} = \mu_s N = 0.4 \times 5 \times 9.8 = 19.6\ \text{N}$$

Q: A car of mass 1200 kg moves around a flat circular track of radius 50 m at a constant speed of 15 m/s. What is the magnitude of the friction force required to keep the car moving in a circle?

$$F_{\text{friction}} = m \frac{v^2$}{R} = 1200 \times \frac{15^2$}{50} = 5400\ \text{N}$$

Q: A satellite orbits Earth at a radius of $$7.0 \times 10^6$ m. Given G = 6.674$$ \times $$10^{-11}$$\ \text{N}\cdot\text{m}^2/\text{kg}^2$$ and M_E = 5.97$$ \times $$10^{24} kg$$, what is the satellite's orbital speed?

$$v = \sqrt{\frac{GM_E}{r}} = \sqrt{\frac{6.674 \times 10$$^{-11}$$ \times 5.97 \times 10$$^{24}$$}{7.0 \times 10^6$}} \approx 7.56\ \text{km/s}$$

Q: A 2 kg object is dropped from a height of 10 m. What is its kinetic energy just before hitting the ground? (Neglect air resistance, $$g = 9.8\ \text{m/s}^2)$$

$$K = mgh = 2 \times 9.8 \times 10 = 196\ \text{J}$$

Q: A block slides down a frictionless incline of height 5 m. If the block has a mass of 3 kg, what is its speed at the bottom?

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

Q: A spring with a spring constant $$k = 200\ \text{N/m} is $$compressed by 0.1 m. What is the elastic potential energy stored in the spring?

$$U_e = \frac{1}{2} k x^2$ = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\ \text{J}$$

Q: A 1 kg object moves in a circle of radius 2 m at a speed of 4 m/s. What is the required centripetal force?

$$F_{\text{net}} = m \frac{v^2$}{R} = 1 \times \frac{16}{2} = 8\ \text{N}$$

Q: A 0.2 kg puck slides on ice with a velocity of 3 m/s and collides head-on with a 0.3 kg puck moving at -2 m/s. What is the total momentum before the collision?

$$p_{\text{tot}} = m_1$ v_1$ + m_2$ v_2$ = 0.2 \times 3 + 0.3 \times (-2) = 0.6 - 0.6 = 0\ \text{kg}\cdot\text{m/s}$$

Q: A 1 kg ball is attached to a string and swung in a horizontal circle of radius 2 m at a speed of 6 m/s. What is the tension in the string?

$$T = m \frac{v^2$}{R} = 1 \times \frac{36}{2} = 18\ \text{N}$$

Question 1

A 5 kg box is at rest on a horizontal surface. The coefficient of static friction between the box and the surface is 0.4. What is the maximum horizontal force that can be applied to the box before it starts to move?

Accepted Answer

$$F_{s,	ext{max}} = \mu_s N = 0.4 	imes 5 	imes 9.8 = 19.6\ 	ext{N}$$

Question 2

A car of mass 1200 kg moves around a flat circular track of radius 50 m at a constant speed of 15 m/s. What is the magnitude of the friction force required to keep the car moving in a circle?

Accepted Answer

$$F_{	ext{friction}} = m \frac{v^2$}{R} = 1200 	imes \frac{15^2$}{50} = 5400\ 	ext{N}$$

Question 3

A satellite orbits Earth at a radius of $$7.0 	imes 10^6$ m. Given G = 6.674$$ 	imes $$10^{-11}$$\ 	ext{N}\cdot	ext{m}^2/	ext{kg}^2$$ and M_E = 5.97$$ 	imes $$10^{24} kg$$, what is the satellite's orbital speed?

Accepted Answer

$$v = \sqrt{\frac{GM_E}{r}} = \sqrt{\frac{6.674 	imes 10$$^{-11}$$ 	imes 5.97 	imes 10$$^{24}$$}{7.0 	imes 10^6$}} \approx 7.56\ 	ext{km/s}$$

Question 4

A 2 kg object is dropped from a height of 10 m. What is its kinetic energy just before hitting the ground? (Neglect air resistance, $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$K = mgh = 2 	imes 9.8 	imes 10 = 196\ 	ext{J}$$

Question 5

A block slides down a frictionless incline of height 5 m. If the block has a mass of 3 kg, what is its speed at the bottom?

Accepted Answer

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

Question 6

A 0.5 kg ball moving at 4 m/s collides elastically with a stationary 0.5 kg ball. What is the velocity of the first ball after the collision?

Accepted Answer

$$v_{A,f} = 0\ 	ext{m/s}$$

Question 7

A 2 kg mass moving at 3 m/s collides inelastically with a 1 kg mass at rest. What is their final velocity after the collision?

Accepted Answer

$$v_f = \frac{m_1$ v_{1,i} + m_2$ v_{2,i}}{m_1$ + m_2$} = \frac{2 	imes 3 + 1 	imes 0}{2 + 1} = 2\ 	ext{m/s}$$

Question 8

A spring with a spring constant $$k = 200\ 	ext{N/m} is $$compressed by 0.1 m. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U_e = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ 	ext{J}$$

Question 9

A 1 kg object moves in a circle of radius 2 m at a speed of 4 m/s. What is the required centripetal force?

Accepted Answer

$$F_{	ext{net}} = m \frac{v^2$}{R} = 1 	imes \frac{16}{2} = 8\ 	ext{N}$$

Question 10

A 0.2 kg puck slides on ice with a velocity of 3 m/s and collides head-on with a 0.3 kg puck moving at -2 m/s. What is the total momentum before the collision?

Accepted Answer

$$p_{	ext{tot}} = m_1$ v_1$ + m_2$ v_2$ = 0.2 	imes 3 + 0.3 	imes (-2) = 0.6 - 0.6 = 0\ 	ext{kg}\cdot	ext{m/s}$$

Question 11

A 1 kg ball is attached to a string and swung in a horizontal circle of radius 2 m at a speed of 6 m/s. What is the tension in the string?

Accepted Answer

$$T = m \frac{v^2$}{R} = 1 	imes \frac{36}{2} = 18\ 	ext{N}$$

Question 12

A 0.5 kg ball is dropped from a height of 8 m. What is its velocity just before it hits the ground? ($$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 8} \approx 12.5\ 	ext{m/s}$$

Question 13

A 3 kg object is moving at 5 m/s. What is its momentum?

Accepted Answer

$$p = mv = 3 	imes 5 = 15\ 	ext{kg}\cdot	ext{m/s}$$

Question 14

A 2 kg block slides 4 m across a horizontal surface with a kinetic friction coefficient of 0.2. How much work is done by friction?

Accepted Answer

$$W = -f_k d = -\mu_k m g d = -0.2 	imes 2 	imes 9.8 	imes 4 = -15.68\ 	ext{J}$$

Question 15

A 1 kg mass is attached to a spring ($$k = 100\ 	ext{N/m}) $$and pulled 0.2 m from equilibrium. What is the total mechanical energy if released from rest at this position?

Accepted Answer

$$E = U_e = \frac{1}{2} k x^2$ = 0.5 	imes 100 	imes 0.04 = 2\ 	ext{J}$$

Question 16

A 2 kg object moving at 4 m/s collides elastically with a 1 kg object at rest. What is the velocity of the 2 kg object after the collision?

Accepted Answer

$$v_{A,f} = \frac{m_A - m_B}{m_A + m_B} v_{A,i} = \frac{2 - 1}{2 + 1} 	imes 4 = \frac{1}{3} 	imes 4 = 1.33\ 	ext{m/s}$$

College Physics I: Newton’s Laws, Circular Motion, Work & Energy, and Momentum – Study Notes

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