Q: A ball is thrown vertically upward with an initial velocity of $$15\ \mathrm{m/s}. $$Ignoring air resistance, what is the maximum height reached by the ball? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$h = \frac{v^2$}{2g} = \frac{15^2$}{2 \times 9.8} \approx 11.5\ \mathrm{m}$$

Q: A student lifts a $$50\ \mathrm{kg}$$ box to a height of $$2\ \mathrm{m}. $$How much work is done against gravity?

$$W = mgh = 50 \times 9.8 \times 2 = 980\ \mathrm{J}$$

Q: Two ice skaters push off from each other. Skater A has mass $$60\ \mathrm{kg}$$ and skater B has mass $$40\ \mathrm{kg}. If $$skater A moves at $$3\ \mathrm{m/s}$$, what is skater B's velocity?

$$v_B = -\frac{m_A v_A}{m_B} = -\frac{60 \times 3}{40} = -4.5\ \mathrm{m/s}$$

Question 1

A car accelerates uniformly from rest along a straight line for 10 seconds, reaching a final velocity of 20 m/s. What is the car's acceleration?

Accepted Answer

$$a = \frac{20}{10} = 2\ \mathrm{m/s^2$}$$

Question 2

A ball is thrown vertically upward with an initial velocity of $$15\ \mathrm{m/s}. $$Ignoring air resistance, what is the maximum height reached by the ball? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{15^2$}{2 	imes 9.8} \approx 11.5\ \mathrm{m}$$

Question 3

A hockey puck slides across frictionless ice with a constant velocity. Which of Newton's Laws best explains why the puck continues moving?

Accepted Answer

Newton's First Law: An object in motion remains in motion unless acted upon by a net force.

Question 4

A 2 kg block is pushed with a force of 10 N on a frictionless surface. What is its acceleration?

Accepted Answer

$$a = \frac{F}{m} = \frac{10}{2} = 5\ \mathrm{m/s^2$}$$

Question 5

A car of mass $$1000\ \mathrm{kg}$$ traveling at $$20\ \mathrm{m/s}$$ collides with a stationary truck of mass $$3000\ \mathrm{kg}. If $$they stick together after the collision, what is their final velocity?

Accepted Answer

$$v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{1000 	imes 20 + 3000 	imes 0}{4000} = 5\ \mathrm{m/s}$$

Question 6

A satellite orbits Earth in a circular path. Which force provides the necessary centripetal acceleration?

Accepted Answer

Gravitational force: $$F = G\frac{m_1$ m_2$}{r^2$}$$

Question 7

A student lifts a $$50\ \mathrm{kg}$$ box to a height of $$2\ \mathrm{m}. $$How much work is done against gravity?

Accepted Answer

$$W = mgh = 50 	imes 9.8 	imes 2 = 980\ \mathrm{J}$$

Question 8

A spinning disk has a moment of inertia $$I$$ and angular velocity $$\omega. $$What is its rotational kinetic energy?

Accepted Answer

$$K = \frac{1}{2} I \$$omega^2$$

Question 9

A block slides down a frictionless incline of height $$h. $$What is its speed at the bottom?

Accepted Answer

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

Question 10

Two ice skaters push off from each other. Skater A has mass $$60\ \mathrm{kg}$$ and skater B has mass $$40\ \mathrm{kg}. If $$skater A moves at $$3\ \mathrm{m/s}$$, what is skater B's velocity?

Accepted Answer

$$v_B = -\frac{m_A v_A}{m_B} = -\frac{60 	imes 3}{40} = -4.5\ \mathrm{m/s}$$

Question 11

A pendulum swings with a period $$T. If $$its length is quadrupled, what happens to the period?

Accepted Answer

$$T' = 2T$$

Question 12

A car rounds a curve of radius $$50\ \mathrm{m} at$$ $$10\ \mathrm{m/s}. $$What is the required centripetal acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{r} = \frac{10^2$}{50} = 2\ \mathrm{m/s^2$}$$

Question 13

A $$5\ \mathrm{kg}$$ object is dropped from a height of $$10\ \mathrm{m}. $$What is its velocity just before hitting the ground? (Ignore air resistance)

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} \approx 14\ \mathrm{m/s}$$

Question 14

A $$0.2\ \mathrm{kg}$$ ball moving at $$5\ \mathrm{m/s}$$ collides elastically with a stationary $$0.3\ \mathrm{kg}$$ ball. What is the velocity of the $$0.2\ \mathrm{kg}$$ ball after the collision?

Accepted Answer

$$v_1$$' = \frac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$ = \frac{0.2 - 0.3}{0.5} 	imes 5 = -1\ \mathrm{m/s}$$

Question 15

A $$10\ \mathrm{kg}$$ object is moving at $$4\ \mathrm{m/s}. $$What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2} m v^2$ = \frac{1}{2} 	imes 10 	imes 16 = 80\ \mathrm{J}$$

Question 16

A $$2\ \mathrm{kg}$$ mass attached to a $$0.5\ \mathrm{m}$$ string rotates in a horizontal circle at $$3\ \mathrm{m/s}. $$What is the tension in the string?

Accepted Answer

$$T = \frac{m v^2$}{r} = \frac{2 	imes 9}{0.5} = 36\ \mathrm{N}$$

Question 17

A $$1\ \mathrm{kg}$$ object is dropped from rest and falls for $$3\ \mathrm{s}. $$What is its velocity just before hitting the ground? (Ignore air resistance)

Accepted Answer

$$v = g t = 9.8 	imes 3 = 29.4\ \mathrm{m/s}$$

Question 18

A $$0.5\ \mathrm{kg}$$ ball is thrown horizontally from a $$20\ \mathrm{m}$$ high cliff with a speed of $$8\ \mathrm{m/s}. $$How far from the base of the cliff does it land? (Ignore air resistance)

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} \approx 2.02\ \mathrm{s}$$;\ d = v t = 8 	imes 2.02 \approx 16.2\ \mathrm{m}$

Physics 1050: Course Syllabus and Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard