Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the time of flight until it lands back at the same height?

$$t = \frac{2 v_0$ \sin \theta}{g}$$

Q: A block of mass $$m is $$pulled up a rough incline of angle $$\theta$$ and coefficient of kinetic friction $$\mu_k at $$constant speed. What is the required pulling force?

$$F = m g (\sin \theta + \mu_k \cos \theta)$$

Question 1

A car accelerates uniformly from rest to a velocity $$v in $$time $$t. $$Which equation correctly relates the displacement $$x to $$the acceleration $$a$$ and time $$t$$?

Accepted Answer

$$x = \frac{1}{2} a t^2$

Question 2

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the time of flight until it lands back at the same height?

Accepted Answer

$$t = \frac{2 v_0$ \sin 	heta}{g}$$

Question 3

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

Accepted Answer

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

Question 4

Which of the following equations represents the work done by a constant force $$F$$ acting over a displacement $$d at an $$angle $$	heta to $$the direction of motion?

Accepted Answer

$$W = Fd \cos 	heta$$

Question 5

A ball is thrown vertically upward with initial velocity $$v_0. $$What is the maximum height reached?

Accepted Answer

$$h = \frac{v_0$^2}{2g}$$

Question 6

A car of mass $$m$$ moves in a circle of radius $$r$$ with constant speed $$v. $$What is the required centripetal force?

Accepted Answer

$$F = \frac{mv^2$}{r}$$

Question 7

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

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}}$$

Question 8

A force $$F is $$applied to a mass $$m$$ causing an acceleration $$a. $$Which equation correctly relates these quantities?

Accepted Answer

$$F = ma$$

Question 9

A satellite orbits Earth at a distance $$r$$ from the center of the Earth. What is the gravitational force acting on it?

Accepted Answer

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

Question 10

A block slides across a rough surface and comes to rest due to friction. Which equation gives the work done by friction if the coefficient of kinetic friction is $$\mu_k$$, the normal force is $$N$$, and the distance is $$d$$?

Accepted Answer

$$W = -\mu_k N d$$

Question 11

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 12

A car of mass $$m$$ traveling at speed $$v$$ comes to a stop. What is the kinetic energy lost?

Accepted Answer

$$KE = \frac{1}{2} m v^2$

Question 13

A force $$F is $$applied to a lever arm of length $$r at an $$angle $$	heta to $$the arm. What is the torque produced?

Accepted Answer

$$	au = F r \sin 	heta$$

Question 14

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

Accepted Answer

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

Question 15

A mass $$m is $$attached to a string and swung in a horizontal circle of radius $$r at $$constant speed $$v. $$What is the tension in the string?

Accepted Answer

$$T = \frac{mv^2$}{r}$$

Question 16

A block of mass $$m is $$dropped from height $$h. $$What is the potential energy lost by the block?

Accepted Answer

$$PE = mgh$$

Question 17

A car rounds a curve of radius $$r at $$speed $$v. $$What is the minimum coefficient of friction $$\mu$$ required to prevent slipping?

Accepted Answer

$$\mu = \frac{v^2$}{rg}$$

Question 18

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

Accepted Answer

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

Question 19

A ball is thrown horizontally from a cliff of height $$h$$ with initial speed $$v_0. $$How far from the base of the cliff does it land?

Accepted Answer

$$d = v_0$ \sqrt{\frac{2h}{g}}$$

Question 20

A block of mass $$m is $$pulled up a rough incline of angle $$	heta$$ and coefficient of kinetic friction $$\mu_k at $$constant speed. What is the required pulling force?

Accepted Answer

$$F = m g (\sin 	heta + \mu_k \cos 	heta)$$

Physics 140/211 Midterm 1 Equation Sheet: Core Concepts and Formulas

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