Work energy and power

Kinetic Energy and the Work-Energy Theorem

We'll start with some definitions.

What this second definition means is that work equals the product of the distance an object travels and the component of the force acting on that object directed parallel to the object's direction of motion. That sounds more complicated than it really is: an example will help.
A box is pulled along the floor, as shown in Figure 14.1. It is pulled a distance of 10 m, and the force pulling it has a magnitude of 5 N and is directed 30° above the horizontal. So, the force component that is PARALLEL to the 10 m displacement is (5 N)(cos 30°).

One newton. meter is called a joule, abbreviated as 1 J.

• Work is a scalar. So is energy.
• The units of work and of energy are joules.
• Work can be negative … this just means that the force is applied in the direction opposite displacement.

This means that the kinetic energy of an object equals one half the object's mass times its speed squared.

The net work done on an object is equal to that object's change in kinetic energy. Here's an application:

Here, because the only horizontal force is the force of the brakes, the work done by this force is W_net.

Let's pause for a minute to think about what this value means. We've just calculated the change in kinetic energy of the train car, which is equal to the net work done on the train car. The negative sign simply means that the net force was opposite the train's displacement. To find the force:

Potential Energy

Potential energy comes in many forms: there's gravitational potential energy, spring potential energy, electrical potential energy, and so on. For starters, we'll concern ourselves with gravitational potential energy.
Gravitational PE is described by the following equation:

PE = mgh

In this equation, m is the mass of an object, g is the gravitational field of 10 N/kg on Earth, and h is the height of an object above a certain point (called "the zero of potential").³ That point can be wherever you want it to be, depending on the problem. For example, let's say a pencil is sitting on a table. If you define the zero of potential to be the table, then the pencil has no gravitational PE. If you define the floor to be the zero of potential, then the pencil has PE equal to mgh, where h is the height of the pencil above the floor. Your choice of the zero of potential in a problem should be made by determining how the problem can most easily be solved.
REMINDER: h in the potential energy equation stands for vertical height above the zero of potential.
Practice problems for these concepts can be found at: Energy Conservation Practice Problems for AP Physics B & C


kinetic-energy-and-potential-energy

Work and energy Test



Momentum, Work, Energy, And Power Practice Test

1. Consider a minor parking-lot accident. Car A backs out at 30 cm/s toward the west, and car B looks for a place to park, driving north at 40 cm/s. Both cars mass 1,000 kg. What is the total system momentum before the collision? Remember that momentum is a vector quantity. Also, be careful with your units.

(a) 700 kg · m/s, generally northwest

(b) 100 kg · m/s, generally northwest

(c) 500 kg · m/s, generally northwest

(d) There is not enough information to answer this.

2. Impulse is the product of

(a) time and distance.

(b) time, mass, and acceleration.

(c) time, mass, and velocity.

(d) time and velocity.

3. Consider a hockey player skating down the ice at 10.0 m/s. His mass is 82.0 kg. What is his kinetic energy?

(a) 820 J

(b) 410 J

(c) 8.20 × 10 ⁴ J

(d) 4.10 × 10 ³ J

4. An object whose mass is 10.0 kg is lifted through a distance of 4.000 m on a planet where the gravitational acceleration is 6.000 m/s ² . How much work is required to do this?

(a) 60.0 J

(b) 24.0 J

(c) 40.0 J

(d) 240 J

5. Suppose that an object is pushed with steady force along a frictionless surface. When you multiply the object’s mass by the length of time for which it is pushed and then multiply the result by the object’s acceleration over that period of time, you get

(a) momentum.

(b) velocity.

(c) impulse.

(d) a meaningless quantity.

6. According to the law of conservation of momentum, in an ideal closed system,

(a) when two objects collide, the system neither loses nor gains any total momentum.

(b) when two objects collide, neither object loses or gains any momentum.

(c) when two objects collide, the magnitudes of their momentum vectors add.

(d) when two objects collide, the magnitudes of their momentum vectors multiply.

7. When making calculations in which all the quantities have their units indicated throughout the entire process,

(a) the units multiply and divide just like the numbers.

(b) the units cannot cancel out.

(c) the units can be multiplied but not divided.

(d) the units can be added and subtracted, but not multiplied or divided.

8. One joule, reduced to base units, is equivalent to

(a) one kilogram-meter per second squared.

(b) one kilogram-meter.

(c) one kilogram-meter squared per second squared.

(d) one meter per second squared.

9. A 5,000-kg motorboat sits still on a frictionless lake. There is no wind to push against the boat. The captain starts the motor and runs it steadily for 10.00 seconds in a direction straight forward and then shuts the motor down. The boat has attained a speed of 5.000 meters per second straight forward. What is the impulse supplied by the motor?

(a) 2.500 × 10 ⁵ kg · m/s

(b) 2.500 × 10 ⁴ kg · m/s

(c) 2,500 kg · m/s

(d) 6.250 × 10 ⁴ kg · m/s

10. Which of the following does not have an effect on the momentum of a moving spherical particle?

(a) The speed of the particle

(b) The diameter of the particle

(c) The direction in which the particle travels

(d) The mass of the particle

 

Answers

1. c

2. b

3. d

4. d

5. c

6. a

7. a

8. c

9. b

10. b