Q: A ball is thrown vertically upward with an initial velocity of $$10\ \mathrm{m/s}. $$Neglecting air resistance, what is the maximum height reached by the ball? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$h = \frac{v^2$}{2g} = \frac{(10)^2$}{2 \times 9.8} \approx 5.1\ \mathrm{m}$$

Q: A 2 kg block slides down a frictionless incline of height 3 m. What is its speed at the bottom?

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

Q: A 3 kg object is attached to a spring and oscillates with a period of 2 seconds. What is the spring constant $$k$$?

$$k = \frac{4\pi^2$ m}{T^2$} = \frac{4 \times \pi^2$ \times 3}{4} \approx 29.6\ \mathrm{N/m}$$

Q: A cyclist increases her speed from $$5\ \mathrm{m/s} to$$ $$15\ \mathrm{m/s}$$ over a distance of $$50\ \mathrm{m}. $$What is her acceleration, assuming it is constant?

$$a = \frac{v^2$ - u^2$}{2s} = \frac{(15^2$ - 5^2$)}{2 \times 50} = \frac{225 - 25}{100} = 2\ \mathrm{m/s^2$}$$

Q: A 10 kg object is lifted vertically by 2 meters. What is the work done against gravity? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$W = mgh = 10 \times 9.8 \times 2 = 196\ \mathrm{J}$$

Question 1

A car accelerates uniformly from rest to a speed of 20 m/s in 5 seconds. What is the car's acceleration?

Accepted Answer

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

Question 2

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

Accepted Answer

An object will remain at rest or in uniform motion unless acted upon by a net external force.

Question 3

A ball is thrown vertically upward with an initial velocity of $$10\ \mathrm{m/s}. $$Neglecting air resistance, what is the maximum height reached by the ball? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{(10)^2$}{2 	imes 9.8} \approx 5.1\ \mathrm{m}$$

Question 4

A 2 kg block slides down a frictionless incline of height 3 m. What is its speed at the bottom?

Accepted Answer

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

Question 5

Which equation correctly relates impulse ($$J) to $$change in momentum ($$\Delta p$$)?

Accepted Answer

$$J = \Delta p$$

Question 6

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

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 7

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

Accepted Answer

Gravitational force

Question 8

A student pushes a box across a rough floor at constant speed. Which statement is true about the forces acting on the box?

Accepted Answer

The applied force is equal in magnitude and opposite in direction to the frictional force.

Question 9

Which of the following is the correct expression for kinetic energy ($$KE) of an $$object of mass $$m$$ moving at velocity $$v$$?

Accepted Answer

$$KE = \frac{1}{2}mv^2$

Question 10

A 3 kg object is attached to a spring and oscillates with a period of 2 seconds. What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{4\pi^2$ m}{T^2$} = \frac{4 	imes \pi^2$ 	imes 3}{4} \approx 29.6\ \mathrm{N/m}$$

Question 11

A cyclist increases her speed from $$5\ \mathrm{m/s} to$$ $$15\ \mathrm{m/s}$$ over a distance of $$50\ \mathrm{m}. $$What is her acceleration, assuming it is constant?

Accepted Answer

$$a = \frac{v^2$ - u^2$}{2s} = \frac{(15^2$ - 5^2$)}{2 	imes 50} = \frac{225 - 25}{100} = 2\ \mathrm{m/s^2$}$$

Question 12

Which of the following statements about work is correct?

Accepted Answer

Work is done when a force causes displacement in the direction of the force.

Question 13

A 10 kg object is lifted vertically by 2 meters. What is the work done against gravity? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$W = mgh = 10 	imes 9.8 	imes 2 = 196\ \mathrm{J}$$

Question 14

Which of the following is the correct formula for gravitational force between two masses $$m_1$$ and $$m_2$$ separated by distance $$r$$?

Accepted Answer

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

Question 15

A spinning ice skater pulls in her arms and spins faster. Which physical principle explains this change?

Accepted Answer

Conservation of angular momentum

Question 16

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

Accepted Answer

The period doubles: $$T' = 2T$$

Question 17

A block of mass $$m is $$attached to a spring with spring constant $$k$$ and oscillates with angular frequency $$\omega. $$Which equation is correct?

Accepted Answer

$$\omega = \sqrt{\frac{k}{m}}$$

Question 18

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the maximum range on level ground?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2	heta}{g}$$

PH-UY 1013 Mechanics: Syllabus and Study Guide

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