Q: A simple pendulum of length $$L is $$released from rest at an angle $$\theta$$ from the vertical. What is the expression for the maximum speed $$v_{max} of $$the pendulum bob at the lowest point?

$$v_{max} = \sqrt{2gL(1-\cos\theta)}$$

Q: A 60-kg jogger runs up a flight of stairs with a vertical height of 4.5 m in 4.0 s. What is the average power output of the jogger?

$$P = \frac{mgh}{\Delta t} = \frac{60 \times 9.8 \times 4.5}{4.0} = 660\ \text{W}$$

Q: A 700 kg buggy is pulled at a constant speed of 3 m/s against a friction force of 400 N. How much power is required?

$$P = Fv = 400 \times 3 = 1200\ \text{W}$$

Q: A 2000 kg car changes its velocity from $$-15.0 m/s to$$ $$+2.60 m/s in 0.05 s. $$What is the average force exerted on the car?

$$F_{ave} = \frac{\Delta p}{\Delta t} = \frac{2000 \times (2.60 - (-15.0))}{0.05} = 704,000\ \text{N}$$

Q: Which of the following is the correct SI unit for power?

$$1\ \text{W} = 1\ \text{J}/\text{s}$$

Question 1

A simple pendulum of length $$L is $$released from rest at an angle $$	heta$$ from the vertical. What is the expression for the maximum speed $$v_{max} of $$the pendulum bob at the lowest point?

Accepted Answer

$$v_{max} = \sqrt{2gL(1-\cos	heta)}$$

Question 2

Which of the following best describes the period $$T of a $$simple pendulum for small angles?

Accepted Answer

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

Question 3

A 60-kg jogger runs up a flight of stairs with a vertical height of 4.5 m in 4.0 s. What is the average power output of the jogger?

Accepted Answer

$$P = \frac{mgh}{\Delta t} = \frac{60 	imes 9.8 	imes 4.5}{4.0} = 660\ 	ext{W}$$

Question 4

Which of the following statements about the period of a simple pendulum is correct?

Accepted Answer

The period is independent of the mass of the bob.

Question 5

A 700 kg buggy is pulled at a constant speed of 3 m/s against a friction force of 400 N. How much power is required?

Accepted Answer

$$P = Fv = 400 	imes 3 = 1200\ 	ext{W}$$

Question 6

If a force acts on an object for a time $$\Delta t$$, the impulse delivered to the object is:

Accepted Answer

$$J = F \Delta t$$

Question 7

A 2000 kg car changes its velocity from $$-15.0 m/s to$$ $$+2.60 m/s in 0.05 s. $$What is the average force exerted on the car?

Accepted Answer

$$F_{ave} = \frac{\Delta p}{\Delta t} = \frac{2000 	imes (2.60 - (-15.0))}{0.05} = 704,000\ 	ext{N}$$

Question 8

Which of the following best explains why airbags reduce injuries in car crashes?

Accepted Answer

They increase the time over which the momentum changes, reducing the average force.

Question 9

The impulse delivered to a particle by a force is equal to:

Accepted Answer

The area under the force vs. time curve.

Question 10

A pendulum clock is moved from Earth to the Moon, where gravity is about $$1/6$$ that of Earth. What happens to the period of the pendulum?

Accepted Answer

The period increases by a factor of $$\sqrt{6}.$$

Question 11

Which of the following is the correct SI unit for power?

Accepted Answer

$$1\ 	ext{W} = 1\ 	ext{J}/	ext{s}$$

Question 12

A motor must lift an elevator (mass 1600 kg) and passengers (mass 200 kg) at a constant speed of 3.00 m/s. If friction is 4000 N, what power must the motor deliver?

Accepted Answer

$$P = (Mg + f)v = (1800 	imes 9.8 + 4000) 	imes 3.00 = 6.49 	imes 10^4$\ 	ext{W}$$

Question 13

Which of the following is a correct statement about impulse and momentum?

Accepted Answer

Impulse equals the change in momentum: $$\vec{J} = \Delta \vec{p}$$

Question 14

If the force acting on an object is not constant, how is the impulse calculated?

Accepted Answer

$$J = \int_{t_i}^{t_f} F(t) dt$$

Question 15

A pendulum is released from a small angle $$	heta. $$For small angles, which approximation is valid for $$\sin	heta$$?

Accepted Answer

$$\sin	heta \approx 	heta (in $$radians)

Question 16

Which of the following best describes the relationship between average power $$\bar{P}$$, work $$W$$, and time $$\Delta t$$?

Accepted Answer

$$\bar{P} = \frac{W}{\Delta t}$$

Simple Pendulum, Power, and Impulse: Study Notes for College Physics

Study Guide - Practice Questions

Study Guide - Flashcards