Work

Work, Machines and Energy
Chapter 5

Work

Relates to forces, motion, and energy

Two conditions must be met for work to be done on an object:

The object moves

A force must act on the object in the direction the object moves.

Are you doing work when

You are walking?

yes

Standing?

no

Sitting?

no

Lifting up a shovel?

yes

Throwing a ball?

yes

Catching a ball?

no

Skills Workout
page 108

Which task is more work: lifting a 2 N box 1 m or lifting a 1 N box 2 m? On what did you base you prediction?

Answer: The amount of work is the equal.

Energy is needed to rake leaves or to do any kind of work. In fact, energy is defined as the ability to do work. Are you doing work right now?

Answer: Though reading this takes effort, it is not work because it does not produce motion.

Measuring Work

Mathematical formula

Work = force x distance

W = F x d

Units:

W is a Newton meter or Joule

Measures energy

F is a Newton

d is a meter

Power

Rate at which work is done.

Formula:

Power = Work / time

P = W / t

Units:

P is J / s or Watt

W is Nm

t is second

James Watt ( 1736 – 1819 )

The SI unit of power was named for James Watt, a Scottish engineer. Watt coined the term " Horsepower " ( hp ), which is used to rate electric motors and gasoline engines. He defined one horsepower as the amount of work a horse could do in one second. One horsepower is equal to 745.56 W.

Math Connection

James Watt used the English unit of force, the pound, to define work in terms of foot-pounds, or horsepower. A foot-pound is the work done by moving one pound over a distance of one foot. One horsepower is equal to 745.56 Nm/s. One Newton is 0.225 pounds at the earth’s surface, and one meter is 3.28 feet. What is one horsepower?

Answer: 745.56 Nm/s x 0.225 pounds/N x 3.28 ft/m = 550.22 ft-lbs/s

Figure this out !

Suppose the electric company supplies 1000 watts of electricity for one hour for $0.08. If you were paid this rate for your work mowing the lawn, how much would you make for providing one-half horsepower for one hour?

Answer: Since 1 horsepower – 746 watts, ½ horsepower = 373 watts. At $0.08 per kilowatt-hour, you would be paid about 3 cents.

$.08 x [ 373 W / 1000W ]

Skills Warmup
page 112

You have been asked to lift a lawn mower onto the back of a pickup truck. The lawn mower is too heavy to lift directly. How will you move the lawn mower onto the truck?

Answer: Using a ramp would be the simplest. Ropes and pulleys. Answers vary.

Machines

Make work easier.

Changes the direction or the size of the force needed to do work.

Two forces involved when using a machine

Effort force

Resistance force

Machines do not save work

Lets you apply less force to overcome a resistance

Force must be applied over a greater distance

Mechanical Advantage

M.A. is the number of times a machine multiples an effort force.

M.A. less than 1 increase the distance or speed of motion.

M.A. = resistance force

effort force

M.A. = R / E

Mechanical Efficiency

Amount of work put ( W _I) into a machine is always greater than the amount of work done ( W_O ) by a machine.

Some of the work put into a machine must overcome friction.

W_I = F_Ex d_E

W_O = F_R x d_R

Mechanical efficiency is always less than 100%.

Mechanical Efficiency = W_O / W_I x 100%

Archimedes
( 287 –21 B.C. )

" Give me a place to stand on and I will move the earth. "

Inclined Plane

Has a sloping surface

Figure 5.7, page 116

Will not change the amount of work.

Reduces the effort force

A.M.A. = F _R / F _E

I.M.A. = Length of plane / Height of plane

Or I.M.A. = d _E / d _R

Wedge and Screw

Wedge is and inclined plane that can move.

E.g. is an ax

Screw is also an inclined plane.

A series on inclined planes with a pitch

E.g. is a car jack.

Levers

Fulcrum – a fixed point.

A machine that do work by moving around a fixed point are called levers.

There are three classes of levers.they are classified according to the location of the fulcrum, the effort force, and the resistance force.

First Class Lever

Fulcrum is always between the effort force and resistance force.

Multiplies the effort force and also change its direction.

R F E

Second Class Lever

The resistance force is between the fulcrum and the effort force.

Distance from the fulcrum to the resistance force is less than the distance from the fulcrum to the effort force.

Multiply the effort force without changing its direction.

FRE

Third Class Lever

The effort force is between the fulcrum and the resistance force.

The effort force is greater than the resistance force.

M.A. = less than 1

Examples: Rake, fishing pole

M. A. of Levers

M.A. = Distance of the effort force from the fulcrum

Distance of the resistance force from the fulcrum

or

M.A. = d_E / d_R

M.A. of first and second class levers is usually greater than 1.

The M.A. of the third class levers is less than 1.

Third class levers do not multiply force.

Wheel and Axle

Two circular objects

Steering mechanism of a car

Wheel has larger radius than the axle

M.A. is always greater than 1

Examples:

Door knob

Ferris wheel

wheelchair

Formula:

M.A. = radius of wheel divided by radius of axle

Pulleys

A pulley is a rope wrapped around a grooved wheel.

Two types of pulleys:

Fixed pulley – attached to a stationary structure

M.A. = 1 because it does not multiply the effort force

Movable pulleys – is hung on a rope and hooked top a resistance

Can multiply the effort force

M.A. = 2

Figures 5.9, 5.10, 5.11, page 119

Pulley system:

Two or more pulleys are used

M.A. varies due to number of ropes

Compound Machines

Is a system of two or more simple machines working together.

The M.A. is much greater than that of a simple machine.

Multiples the total M.A.

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