WORK AND POWERWHEN OBJECTS MOVE

October Sky Quiz 11. How did those living in Homer’s hometown make a living? 2. What was Homer’s daily job before school? 3. What happened to Homer’s grandfather in the mine? 4. When Homer wasn’t playing in the mountains, what did he enjoy doing

most? 5. What was Homer’s nickname? 6. What was Sputnik?7. Which country was responsible for Sputnik? 8. Give one detail of the fight between Homer and his brother Jim

explained in chapter 2. 9. In what sport did Homer’s brother Jim excel? 10. Why did Homer’s mom want him to be successful at building a rocket?

Changes in Motion

Any change in an object’s motion is caused by a FORCE.

When we apply a force on an object to cause this motion, we do WORK on the object

Work done is a result of a force over a DISTANCE

Work Work is done only if the force

causes an object to move in the SAME direction as the force

Concept CheckState whether work is done in each of the following situations:

1. A teacher applies a force to a wall and becomes exhausted.

2. A book falls off a table and free falls to the ground.

3. A waiter carries a tray full of meals above his head by one arm straight across the room at a constant speed. (Careful! This is a difficult question.)

4. A rocket accelerates through space.

Doing Work

When a weight lifter raises a heavy barbell, he does work on the barbell.

Doing WorkWhen a weight lifter simply holds a barbell overhead, he does NO work on the barbell.

Calculating Work

Work = F x d

Force applied(N) X Distance (m)

Example Problem 1

Bud, a very large man of mass 130 kg, stands on a pogo stick. How much work is done as Bud compresses the spring of the pogo stick 0.50 m?

Work done at an ANGLE

Remember that a force is a vector quantity

The work done is parallel to the direction of the objects motion.

This is the horizontal component of the force

Calculating Work at an Angle

FORCE (N)

X: direction of motion

Equation

The angle is always between the force and the displacement

dFW cos

The Waiter To do work the force

must cause the displacement

A vertical force does not cause a horizontal displacement

dFW cos

No work is done because the cosine of 90 degrees is ZERO.

UNIT of Work

The unit for work is the Newton-meter We call the newton-meter the joule (J)

for short. One joule of work is done when a force of

one Newton is exerted over a distance of one meter.

1 J = 1 Nm

Example Problem 2

A force of 50 N acts on the block at the angle shown in the diagram. The block moves a horizontal distance of 3.0 m. How much work is done by the applied force?

W = F (cosɵ)d W = (50 N)(cos 30)(3 m) W = 129.9 Joules  

Example 3 Renatta Gass is out with her friends. Misfortune occurs

and Renatta and her friends find themselves getting a workout. They apply a cumulative force of 1080 N to push the car 218 m to the nearest fuel station. Determine the work done on the car.

W = F x d W = (1080 N)(218 m) W = 2.35 x 105 Joules  

Example 4

A student with a mass of 80.0 kg runs up three flights of stairs in 12.0 sec. The student has gone a vertical distance of 8.0 m. Determine the amount of work done by the student to elevate his body to this height. Assume that her speed is constant.

W = F x d W = (80kg x 9.8m/s2) (8 m) W = 6272 Joules  

Example 5

Hans Full is pulling on a rope to drag his backpack to school across the ice. He pulls upwards and rightwards with a force of 22.9 Newtons at an angle of 35 degrees above the horizontal to drag his backpack a horizontal distance of 129 meters to the right. Determine the work (in Joules) done upon the backpack.

W = F (cosɵ)d W = (22.9 N)(cos 35)(129 m) W = 2420 Joules  

Example 6

Ben Travlun carries a 200-N suitcase up three flights of stairs (a height of 10.0 m) and then pushes it with a horizontal force of 50.0 N at a constant speed of 0.5 m/s for a horizontal distance of 35.0 meters. How much work does Ben do on his suitcase during this entire motion?

W = F x d W = (200 N)(10 m) W = 2000 Joules

W = F x d W = (50 N)(35.0 m) W = 1750 Joules

3750 J