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

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

Q: A block slides down a frictionless incline of height $$h = 3\ \mathrm{m}. $$What is its speed at the bottom? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 3} = 7.67\ \mathrm{m/s}$$

Q: A cyclist exerts a constant power of 200 W to climb a hill 50 m high. If the total mass of the cyclist and bicycle is 80 kg, what is the minimum time required to reach the top? (Neglect friction, $$g = 9.8\ \mathrm{m/s^2$})$$

$$t = \frac{mgh}{P} = \frac{80 \times 9.8 \times 50}{200} = 196\ \mathrm{s}$$

Q: A rotating disk has an angular velocity of $$10\ \mathrm{rad/s}$$ and a moment of inertia of $$2\ \mathrm{kg\cdot m^2$}. $$What is its rotational kinetic energy?

$$K = \frac{1}{2}I\$$omega^2$$ = \frac{1}{2} \times 2 \times 10^2$ = 100\ \mathrm{J}$$

Q: A 3 kg object moving at $$4\ \mathrm{m/s}$$ collides inelastically with a 2 kg object at rest. What is the final velocity of the combined mass?

$$v_f = \frac{m_1v_1 + m_2v_2}{m_1$ + m_2$} = \frac{3 \times 4 + 2 \times 0}{3 + 2} = 2.4\ \mathrm{m/s}$$

Question 1

A car accelerates from rest to a speed of 20 m/s in 10 seconds along a straight road. What is the car's average acceleration during this time?

Accepted Answer

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

Question 2

Which of the following best describes Newton's First Law of Motion?

Accepted Answer

An object in motion will remain in motion unless acted upon by an external force.

Question 3

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

Accepted Answer

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

Question 4

A 5 kg object is acted upon by a net force of 20 N. What is its acceleration?

Accepted Answer

$$a = \frac{F}{m} = \frac{20}{5} = 4\ \mathrm{m/s^2$}$$

Question 5

A block slides down a frictionless incline of height $$h = 3\ \mathrm{m}. $$What is its speed at the bottom? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 3} = 7.67\ \mathrm{m/s}$$

Question 6

A 2 kg ball moving at $$3\ \mathrm{m/s}$$ collides elastically with a stationary 1 kg ball. What is the velocity of the 1 kg ball after the collision?

Accepted Answer

Question 7

A satellite orbits Earth in a circular path of radius $$r. $$Which equation gives the gravitational force acting on the satellite?

Accepted Answer

$$F = G \frac{Mm}{r^2$}$$

Question 8

A 0.5 kg mass attached to a spring oscillates with a period of 2 seconds. What is the spring constant $$k$$?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}} \Rightarrow k = \frac{4\pi^2$ m}{T^2$} = \frac{4 	imes \pi^2$ 	imes 0.5}{4} = \pi^2$ \approx 9.87\ \mathrm{N/m}$$

Question 9

A cyclist exerts a constant power of 200 W to climb a hill 50 m high. If the total mass of the cyclist and bicycle is 80 kg, what is the minimum time required to reach the top? (Neglect friction, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \frac{mgh}{P} = \frac{80 	imes 9.8 	imes 50}{200} = 196\ \mathrm{s}$$

Question 10

A rotating disk has an angular velocity of $$10\ \mathrm{rad/s}$$ and a moment of inertia of $$2\ \mathrm{kg\cdot m^2$}. $$What is its rotational kinetic energy?

Accepted Answer

$$K = \frac{1}{2}I\$$omega^2$$ = \frac{1}{2} 	imes 2 	imes 10^2$ = 100\ \mathrm{J}$$

Question 11

A 3 kg object moving at $$4\ \mathrm{m/s}$$ collides inelastically with a 2 kg object at rest. What is the final velocity of the combined mass?

Accepted Answer

$$v_f = \frac{m_1v_1 + m_2v_2}{m_1$ + m_2$} = \frac{3 	imes 4 + 2 	imes 0}{3 + 2} = 2.4\ \mathrm{m/s}$$

Question 12

A pendulum of length $$L$$ swings with small amplitude. What is the period of oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\frac{L}{g}}$$

Question 13

A 10 kg box is pulled across a horizontal floor with a force of 50 N at an angle of $$30^\circ$$ above the horizontal. If the coefficient of kinetic friction is 0.2, what is the acceleration of the box? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$a = \frac{F\cos	heta - \mu_k mg}{m} = \frac{50 	imes 0.866 - 0.2 	imes 10 	imes 9.8}{10} = \frac{43.3 - 19.6}{10} = 2.37\ \mathrm{m/s^2$}$$

Question 14

A car rounds a curve of radius 50 m at a speed of 20 m/s. What is the required centripetal force if the car's mass is 1000 kg?

Accepted Answer

$$F_c = \frac{mv^2$}{r} = \frac{1000 	imes 400}{50} = 8000\ \mathrm{N}$$

Question 15

A student lifts a 15 kg box vertically upward by 2 meters. How much work is done against gravity?

Accepted Answer

$$W = mgh = 15 	imes 9.8 	imes 2 = 294\ \mathrm{J}$$

Question 16

A 0.2 kg mass attached to a string moves in a horizontal circle of radius 0.5 m at a constant speed of 3 m/s. What is the tension in the string?

Accepted Answer

$$T = \frac{mv^2$}{r} = \frac{0.2 	imes 9}{0.5} = 3.6\ \mathrm{N}$$

Question 17

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

Accepted Answer

$$U = \frac{1}{2}kx^2$ = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ \mathrm{J}$$

Question 18

A 0.5 kg object moves in simple harmonic motion with amplitude 0.2 m and angular frequency $$\omega = 4\ \mathrm{rad/s}. $$What is its maximum kinetic energy?

Accepted Answer

$$K_{max} = \frac{1}{2}m\$$omega^2$$A^2$$ = \frac{1}{2} 	imes 0.5 	imes 16 	imes 0.04 = 0.16\ \mathrm{J}$

PH-UY 1013 Mechanics: Syllabus and Study Guide

Guida di studio - Domande di pratica

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