Q: A 2 kg object moves in a circle of radius 3 m at a constant speed of 4 m/s. What is the magnitude of the centripetal force acting on the object?

$$F_c = \frac{m v^2$}{r} = \frac{2 \times 16}{3} = 10.67\ \mathrm{N}$$

Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the maximum range $$R on $$level ground?

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

Q: A 5 kg object is dropped from rest from a height of 10 m. What is its speed just before hitting the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

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

Q: A student measures the period of a pendulum to be 2 s. If the length of the pendulum is doubled, what is the new period?

$$T_{new} = 2 \pi \sqrt{\frac{2L}{g}} = 2 \times T = 2 \times 2 = 2.83\ \mathrm{s}$$

Question 1

A ball is thrown vertically upward with an initial velocity of $$v_0. $$Neglecting air resistance, which equation best describes the maximum height $$h$$ reached by the ball?

Accepted Answer

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

Question 2

A car of mass $$m$$ accelerates from rest under a constant force $$F$$ for a time $$t. $$What is the final velocity $$v of $$the car?

Accepted Answer

$$v = \frac{F t}{m}$$

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

A student pushes a box across a horizontal floor with a force $$F at an $$angle $$	heta$$ below the horizontal. If the box moves a distance $$d$$, what is the work $$W$$ done by the student?

Accepted Answer

$$W = F d \cos 	heta$$

Question 6

A ball of mass $$m is $$dropped from a height $$h$$ and rebounds to a height $$h/2. $$What is the change in mechanical energy due to the collision with the ground?

Accepted Answer

$$\Delta E = -\frac{1}{2} m g h$$

Question 7

A 2 kg object moves in a circle of radius 3 m at a constant speed of 4 m/s. What is the magnitude of the centripetal force acting on the object?

Accepted Answer

$$F_c = \frac{m v^2$}{r} = \frac{2 	imes 16}{3} = 10.67\ \mathrm{N}$$

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

A block of mass $$m$$ slides on a horizontal surface with coefficient of kinetic friction $$\mu_k. $$What is the frictional force acting on the block?

Accepted Answer

$$f = \mu_k m g$$

Question 11

A 5 kg object is dropped from rest from a height of 10 m. What is its speed just before hitting the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

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

Question 12

A force $$F is $$applied to a mass $$m at $$rest on a frictionless surface for a time $$t. $$What is the impulse delivered to the mass?

Accepted Answer

$$J = F t$$

Question 13

A ball of mass $$m$$ moving at velocity $$v$$ collides elastically with a stationary ball of equal mass. What is the velocity of the first ball after the collision?

Accepted Answer

$$0$$

Question 14

A student uses a ramp to lift a box of mass $$m to a $$height $$h. If $$the ramp is frictionless, what is the minimum force $$F$$ required to move the box up the ramp at constant speed?

Accepted Answer

$$F = m g \sin 	heta$$

Question 15

A disk of radius $$R$$ rotates with angular velocity $$\omega. $$What is the linear speed $$v at $$the edge of the disk?

Accepted Answer

$$v = \omega R$$

Question 16

A 0.5 kg mass attached to a spring oscillates with amplitude 0.2 m and spring constant $$k = 50\ \mathrm{N/m}. $$What is the maximum speed of the mass?

Accepted Answer

$$v_{max} = A \sqrt{\frac{k}{m}} = 0.2 \sqrt{\frac{50}{0.5}} = 0.2 	imes 10 = 2\ \mathrm{m/s}$$

Question 17

A fluid flows through a pipe with cross-sectional area $$A$$ and speed $$v. $$What is the volume flow rate $$Q$$?

Accepted Answer

$$Q = A v$$

Question 18

A block of mass $$m is $$attached to a string and swung in a horizontal circle of radius $$r. $$What is the tension $$T in $$the string?

Accepted Answer

$$T = \frac{m v^2$}{r}$$

Question 19

A student measures the period of a pendulum to be 2 s. If the length of the pendulum is doubled, what is the new period?

Accepted Answer

$$T_{new} = 2 \pi \sqrt{\frac{2L}{g}} = 2 	imes T = 2 	imes 2 = 2.83\ \mathrm{s}$$

AP Physics 1 Reference Sheet: Constants, Formulas, and Key Concepts

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