Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the formula for its horizontal range $$R$$?

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

Question 1

A ball is thrown horizontally from the top of a 45 m high cliff with an initial speed of 10 m/s. Neglecting air resistance, how far from the base of the cliff will the ball land? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\approx 30\ \mathrm{m}$$

Question 2

Which of the following correctly expresses the condition for translational equilibrium?

Accepted Answer

$$\sum \vec{F} = 0$$

Question 3

A car accelerates from rest at $$2\ \mathrm{m/s^2$}$$ for $$5\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$10\ \mathrm{m/s}$$

Question 4

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

Accepted Answer

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

Question 5

Which equation represents the work done by a constant force $$F$$ over a displacement $$d at an $$angle $$	heta$$?

Accepted Answer

$$W = Fd \cos 	heta$$

Question 6

A 2 kg object moves in a circle of radius 0.5 m at a speed of 4 m/s. What is the magnitude of the centripetal force?

Accepted Answer

$$F_c = 32\ \mathrm{N}$$

Question 7

Which formula gives the period $$T of a $$simple pendulum of length $$L$$?

Accepted Answer

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

Question 8

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the formula for its horizontal range $$R$$?

Accepted Answer

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

Question 9

A 5 kg object is dropped from rest from a height of 20 m. What is its kinetic energy just before hitting the ground? (Neglect air resistance)

Accepted Answer

$$980\ \mathrm{J}$$

Question 10

Which of the following is the correct expression for Newton's Law of Universal Gravitation?

Accepted Answer

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

Question 11

A 0.2 kg ball moving at 5 m/s collides elastically with a stationary 0.2 kg ball. What is the velocity of the first ball after the collision?

Accepted Answer

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

Question 12

Which equation represents the conservation of mechanical energy for a system with only conservative forces?

Accepted Answer

$$K_i + U_i = K_f + U_f$$

Question 13

A solid sphere rolls without slipping down an incline. Which condition must be satisfied for rolling without slipping?

Accepted Answer

$$v = R\omega$$

Question 14

A rocket expels gas at a rate of $$\dot{m}$$ with exhaust velocity $$v_e. $$What is the thrust produced?

Accepted Answer

$$F = \dot{m} v_e$$

Question 15

Which formula gives the pressure of an ideal gas in terms of number density $$n$$, Boltzmann constant $$k_B$$, and temperature $$T$$?

Accepted Answer

$$p = n k_B T$$

Question 16

A spring with spring constant $$k is $$compressed by a distance $$x. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$

Question 17

A 3 kg object moving at 4 m/s collides inelastically with a 2 kg object at rest. What is their final velocity after collision?

Accepted Answer

$$2.4\ \mathrm{m/s}$$

Question 18

Which equation gives the moment of inertia $$I of a $$solid sphere of mass $$M$$ and radius $$R$$ about its center?

Accepted Answer

$$I = \frac{2}{5} M R^2$

Question 19

A mass attached to a spring oscillates with angular frequency $$\omega. $$What is the period $$T of $$oscillation?

Accepted Answer

$$T = \frac{2\pi}{\omega}$$

Physics 145 Final Exam Reference Sheet: Core Equations and Concepts

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