Q: A 2 kg block slides down a frictionless incline from a height of 5 m. What is its speed at the bottom? (Assume $$g = 9.8 m/s$^2)$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5}$$

Q: A spring with $$k = 200 N/m is $$compressed by 0.1 m from equilibrium. What is the elastic potential energy stored in the spring?

$$U_s = \dfrac{1}{2} k \Delta x^2$ = \dfrac{1}{2} \times 200 \times (0.1)^2$

Q: A 3 kg object is dropped from a height of 10 m. Ignoring air resistance, what is the change in gravitational potential energy as it reaches the ground?

$$\Delta U_g = m g (h_f - h_i) = 3 \times 9.8 \times (0 - 10)$$

Q: A 0.5 kg ball is thrown vertically upward with an initial speed of 10 m/s. What is its maximum height above the launch point? (Ignore air resistance, $$g = 9.8 m/s$^2)$$

$$h = \dfrac{v^2$}{2g} = \dfrac{10^2$}{2 \times 9.8}$$

Q: A 4 kg object is acted upon by a constant force of 20 N over a distance of 5 m at an angle of 30° to the direction of motion. What is the work done by the force?

$$W = F d \cos \theta = 20 \times 5 \times \cos 30^\circ$$

Q: A 1 kg object is attached to a spring ($$k = 100 N/m) $$and pulled from equilibrium to $$x = 0.2 m. If $$released, what is its speed as it passes through equilibrium?

$$v = \sqrt{\dfrac{k x^2$}{m}} = \sqrt{\dfrac{100 \times (0.2)^2$}{1}}$$

Question 1

A 500 kg satellite orbits Earth at a height of 300 km above the surface. Given Earth's mass $$m_{planet} = 5.97 	imes 10$$^{24}$$ kg and radius r$$_{planet} = 6.37 	imes $$10^6 m$$, what is the velocity of the satellite in its stable circular orbit? (Use $$G = 6.67 	imes 10$$^{-11}$$ N·m^2$/kg^2$)

Accepted Answer

$$v_{obj} = \sqrt{\dfrac{G m_{planet}}{r_{planet} + h}} = \sqrt{\dfrac{6.67 	imes 10$$^{-11}$$ 	imes 5.97 	imes 10$$^{24}$$}{6.37 	imes 10^6$ + 3.00 	imes 10^5$}}$$

Question 2

A 2 kg block slides down a frictionless incline from a height of 5 m. What is its speed at the bottom? (Assume $$g = 9.8 m/s$^2)$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5}$$

Question 3

A spring with $$k = 200 N/m is $$compressed by 0.1 m from equilibrium. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U_s = \dfrac{1}{2} k \Delta x^2$ = \dfrac{1}{2} 	imes 200 	imes (0.1)^2$

Question 4

A 3 kg object is dropped from a height of 10 m. Ignoring air resistance, what is the change in gravitational potential energy as it reaches the ground?

Accepted Answer

$$\Delta U_g = m g (h_f - h_i) = 3 	imes 9.8 	imes (0 - 10)$$

Question 5

A 1 kg ball moving at 4 m/s collides elastically with a stationary 1 kg ball. What are their final velocities?

Accepted Answer

Ball 1: $$v_{f1} = 0$$, Ball 2: $$v_{f2} = 4 m/s$$

Question 6

A 2 kg object moving at 3 m/s collides inelastically with a 1 kg object at rest. What is their final velocity after sticking together?

Accepted Answer

$$v_f = \dfrac{m_1$ v_{1i} + m_2$ v_{2i}}{m_1$ + m_2$} = \dfrac{2 	imes 3 + 1 	imes 0}{2 + 1}$$

Question 7

A 0.5 kg ball is thrown vertically upward with an initial speed of 10 m/s. What is its maximum height above the launch point? (Ignore air resistance, $$g = 9.8 m/s$^2)$$

Accepted Answer

$$h = \dfrac{v^2$}{2g} = \dfrac{10^2$}{2 	imes 9.8}$$

Question 8

A 4 kg object is acted upon by a constant force of 20 N over a distance of 5 m at an angle of 30° to the direction of motion. What is the work done by the force?

Accepted Answer

$$W = F d \cos 	heta = 20 	imes 5 	imes \cos 30^\circ$$

Question 9

A 2 kg object moving at 5 m/s collides elastically with a stationary 8 kg object. What is the final velocity of the 2 kg object?

Accepted Answer

$$v_{f1} = \dfrac{m_1$ - m_2$}{m_1$ + m_2$} v_{i1} = \dfrac{2 - 8}{2 + 8} 	imes 5$$

Question 10

A 1 kg object is attached to a spring ($$k = 100 N/m) $$and pulled from equilibrium to $$x = 0.2 m. If $$released, what is its speed as it passes through equilibrium?

Accepted Answer

$$v = \sqrt{\dfrac{k x^2$}{m}} = \sqrt{\dfrac{100 	imes (0.2)^2$}{1}}$$

Question 11

A 5 kg object is moving at 2 m/s. What is its momentum?

Accepted Answer

$$p = m v = 5 	imes 2$$

Question 12

A 3 kg object experiences a force of 12 N for 0.5 s. What is the change in its momentum?

Accepted Answer

$$\Delta p = F \Delta t = 12 	imes 0.5$$

Question 13

A 2 kg object slides across a flat surface with a coefficient of kinetic friction $$\mu_k = 0.3$$ for 4 m. What is the work done by friction?

Accepted Answer

$$W_f = -\mu_k n d = -0.3 	imes 2 	imes 9.8 	imes 4$$

Question 14

A 1 kg object is moving at 6 m/s. If a net force acts for 2 s and brings it to rest, what is the average force applied?

Accepted Answer

$$F_{net} = \dfrac{m \Delta v}{\Delta t} = \dfrac{1 	imes (0 - 6)}{2}$$

Question 15

A 2 kg object is moving at 4 m/s. It collides and sticks to a 3 kg object at rest. What is the final velocity?

Accepted Answer

$$v_f = \dfrac{m_1$ v_{1i} + m_2$ v_{2i}}{m_1$ + m_2$} = \dfrac{2 	imes 4 + 3 	imes 0}{2 + 3}$$

Question 16

A 1 kg object moving at 2 m/s collides elastically with a 3 kg object at rest. What is the final velocity of the 3 kg object?

Accepted Answer

$$v_{f2} = \dfrac{2 m_1$}{m_1$ + m_2$} v_{i1} = \dfrac{2 	imes 1}{1 + 3} 	imes 2$$

Question 17

A 2 kg object is moving at 3 m/s east. A 1 kg object is moving at 4 m/s north. What is the total momentum magnitude of the system?

Accepted Answer

$$P = \sqrt{(2 	imes 3)^2$ + (1 	imes 4)^2$}$$

Question 18

A 1 kg object is dropped from 5 m onto a spring ($$k = 200 N/m). If $$the spring compresses by $$x m$$, what is the value of $$x at $$maximum compression? (Ignore energy losses)

Accepted Answer

$$m g h = \dfrac{1}{2} k x^2$ \Rightarrow x = \sqrt{\dfrac{2 m g h}{k}}$$

Question 19

A 2 kg object is moving at 5 m/s. If it is brought to rest by friction over 10 m, what is the coefficient of kinetic friction? ($$g = 9.8 m/s$^2)$$

Accepted Answer

$$\mu_k = \dfrac{\dfrac{1}{2} m v^2$}{m g d} = \dfrac{\dfrac{1}{2} 	imes 2 	imes 25}{2 	imes 9.8 	imes 10}$$

Exam 3 Review: Circular Motion, Gravitation, Work & Energy, and Linear Momentum

Guida di studio - Domande di pratica

Study guide - Flashcard