Chapter 14

Work, Power, and Machines

14-1 Work Objectives: Write and answer the objectives on

page 134.14.1 Objectives

1. When does a force do work?Before:After:2. How are work and power related?Before:After:

I. What is Work?

- Work is a quantity that measures the effects of a force acting over a distance.

- Work is only done when force causes a change in the motion of an object.

Work = Force x Distance

W = F x d

- If you try to lift a car, you might apply a large force, but if the difference that the car moves is equal to zero, the work done on the car is also equal to zero.

- However, once the car moves even a small amount, you have done some work on it.

II. Work is Measured in Joules

- Because work is calculated as force times distance, it is measured in units of Newtons times meters; N m.

- These units are also called joules (J).- 1J is equal to 1 kg m2/s2

- You do about 1J of work when you slowly lift an apple; which weighs about 1N, from your waist to the top of your head; a distance of about 1m.

- 3 push-ups require about 1,000J of work.

Examples:1. A crane uses an average force of 5,200N to lift a girder 25m. How much work does the crane do on the girder?

W = ?F = 5200Nd = 25m

W = Fd W = (5200)(25) W = 1.3 x 105 JW = 130,000 J

2. An apple weighing 1N falls through a distance of 1m. How much work is done on the apple by the force of gravity?

W = ? F = 1Nd = 1m

W = FdW = (1)(1)W = 1 J

3. The brakes on a bicycle apply 125N of frictional force to the wheels as the bicycle travels 14.0m. How much work have the brakes done on the bicycle?

W = ? F = 125Nd = 14.0m

W = FdW = (125)(14.0)W = 1750 J

III.Power

- Power is a quantity that measures the rate at which work is done.

- Running up a flight of stairs doesn’t require any more work than walking up slowly, but it is definitely more exhausting.

- The amount of time it takes to get work done is another important factor when considering work and machines.

- The quantity that measures this is Power.Power = Work / Time

P = W / t

IV.Power is Measured in Watts

- Power is measured in SI units called Watts.

- A Watt is the amount of power required to do 1J of work in 1s.

Examples:1. While rowing in a race, John does 3960J of work on the oars in 60.0s. What is the Power output in watts?

P = ? W = 3960Jt = 60.0s

P = W/tP = 3960/60.0P = 66 W

2. Using a jack, a mechanic does 5350J of work to lift a car 0.500m in 50s. What is the mechanic’s power output?

P = ? W = 5350Jt = 50s

P = W/tP = 5350/50P = 107 W

3.Suppose you are moving a 300N box of books. Calculate your power output in the following situations:A. You exert a force of 60N to push the box 12m in 20s.

P = ? F = 60Nd = 12mt = 20s

W = FdW = (60)(12)W = 720J P = W/t

P = 720/20P = 36 W

B. You lift the box 1m onto a truck in 3s.P = ? F = 300Nd = 1mt = 3s

W = FdW = (300)(1)W = 300J P = W/t

P = 300/3P = 100 W

Go back to the 14-1 Objectives on page 78 and answer them

again.

1. When does a force do work?2. How are work and power

related?

** WORK AND POWER QUIZ TOMORROW**

14-2 Work and MachinesAnswer the following on a

separate sheet of paper.Objectives:1. How do machines make work

easier?2. How are work input and work

output related for a machine?

Machines

Which is easier:A. lifting a car yourselfB. Using a car jack

- Which requires more work?:Using a jack does not require less work:You do the same amount of work either way, but the jack makes the work easier by allowing you to apply less force at any given moment.

-Machines multiply and redirect forces

:Machines help us do work by redistributing the work that we put into them.

:Machines can change the direction of an input force, or they can increase an output force by changing the distance over which the force is applied.

-Work input equals work output

:A car jack and a loading ramp make doing work easier by increasing the distance over which the force is applied.

:As a result, the force required at any point is reduced.

:But the amount of work you put into the machine - the work input - is equal to the amount you get out - the work output.

-Mechanical advantage tells us how much a machine multiplies force or increases distance.

: A ramp makes doing work easier by increasing the distance over which the force is applied.

: But how long should the ramp be?A. long ramp- use little force, longer

distanceB. short ramp- would be too steep

Equations

• Woutput = Oforce x Odistance

• Winput = Iforce x Idistance

Go back to the 14-2 Objectives and answer them again.

1. How do machines make work easier?

2. How are work input and work output related for a machine?

14-3 Mechanical Advantage and Efficiency

Answer on a separate sheet of paper

Objectives:1. How does the actual mechanical

advantage of a machine compare to its ideal mechanical advantage?

2. Why is the efficiency of a machine always less than 100 percent?

Mechanical Advantage

• Mechanical advantage of a machine is the number of times that the machine increases an input force.MA = Output force / Input forceMA = Input distance / Output distance

A woman drives her car up onto wheel ramps to perform some repairs. If she

drives a distance of 1.8meters along the ramp to raise the car .3meters, what is the mechanical advantage?

• MA = ?• Input Distance = 1.8

m• Output Distance

= .3m

• MA = Id / Od• MA = 1.8m / .3m• MA = 6

If you exert 100 N on a jack to lift a 10,000N car, what would the jack’s MA be?

• MA = ?• Input Force = 100N• Output Force =

10,000N

• MA = Of / If• MA = 10,000N /

100N• MA = 100

Efficiency

• Efficiency is the percentage of the work input that becomes work output.

• Because there is always some friction, the efficiency of any machine is always less than 100%.

• Efficiency = (Work output / Work input) x 100

You have just designed a machine that uses 1000 J of work from a motor for every 800J of useful work the machine supplies. What is the efficiency?

• Efficiency = ?• Work Output =

800 J• Work Input =

1000J

• Efficiency = (Wo / Wi) x 100• Efficiency = (800 / 1000) x 100

• Efficiency = 80%

Go back to the 14-3 Objectives and answer

them again.Objectives:1. How does the actual

mechanical advantage of a machine compare to its ideal mechanical advantage?

2.Why is the efficiency of a machine always less than 100 percent?

On Page 150, write down and answer the 14-4 Simple Machines Objectives

14.4 Objectives:1.What are the 6 types of simple

machines?Before:After:2.What determines the MA of the 6 types of

simple machines?Before:After:

*Simple Machines are divided into 2 families:

1. The Lever Family2. The Inclined Plane Family

II. The Lever Family

-Consists of the simple lever, pulley, and wheel and axle.

-To understand how levers do work, imagine using a claw hammer to pull out a nail.

-As you pull on the handle of the hammer, the head turns around the point where it meets the wood.

-The force you apply to the handle is transferred to the claw on the other end of the hammer. The claw then does the work on the nail.

Levers

http://lpc1.clpccd.cc.ca.us/lpc/DivisionIII/images/DSNT/Levers.jpg

-Levers are divided into 3 classes

:All levers have a rigid ARM that turns around a point called the FULCRUM.

:Force is transferred from one part of the arm to another.

:Levers are divided into 3 classes depending on the location of the fulcrum and of the input / output force.

1st Class Lever

Examples: Hammer, Pliers and scissors are 2 1st class levers joined together

Input force applied on one end.Fulcrum in the middle.Output force on other end.

2nd Class Levers

Examples: Wheelbarrow, nutcrackers, and hinged doors

Input force applied on one end.Fulcrum on the other end.Output force in the middle.

3rd Class Levers

Examples: Human Forearm (Biceps), tweezers

Input force applied in the middle.Fulcrum at one end.Output force on the other end.

PulleysPulleysPulleysPulleys

Fixed PulleyFixed Pulley::•Wheel attached to surface

•Changes the direction of the applied force

•NO mechanical advantage – same amount of force is required

Movable PulleyMovable Pulley:

• Pulley moves along the rope

• Wheel supports the load

• Effort is in the same direction as movement

• Reduces the forces needed to move an object

http://www.swe.org/iac/LP/pulley_03.html

In the second picture, the weight is held by two ropes instead of one. That means the weight is split equally between the two ropes, so each one holds only half

the weight.

Combined Combined (double) Pulley(double) Pulley:

•Has at least two wheels

•The more complex the pulley, the more the effort needed to move the object decreases

Pulleys are used to gain mechanical advantage

trading the amount of rope you have to pull to lift an object for how heavy the

object can be.

http://www.swe.org/iac/LP/pulley_03.html

The more lines of support (ropes) a pulley has, the more mechanical advantage it has!

The Wheel & Axle

The Wheel & Axlea wheel connected to a rigid

pole

• The Wheel & axle is a modified lever:– The center of the axle acts as a

fulcrum – making the wheel a lever that rotates around in a circle.

The Inclined Plane Family

consists of : the inclined plane, the wedge, and the screw

The Inclined Plane

• The Inclined Plane is a sloping surface, such as a ramp.

• It is one of the most important machines in industry.

• The inclined plane makes lifting or moving an object easier.

The Inclined Plane

• If you push an object up a ramp, you must move it a longer distance than if you tried to lift it straight up, but less effort is needed to move it.

• By using the inclined plane, the same amount of work is done, but the work is done in an easier way.

The Inclined Planea sloping surface that does not

move

• An inclined plane provides for NOT Less work but less effort. 

• The trade off is greater distance to travel.

The Inclined Plane

• Used to reduce the force needed to overcome the force of gravity when lifting or lowering a heavy object.

• MA = distance of plane / height

The Inclined Plane

The Wedge

The Wedgean inclined plane that tapers to a

sharp edge

• The wedge used to increase force.  • The material remains in place while

the wedge moves through it. • A wedge changes the direction of the

input force.

The Wedge• - A wedge is a small inclined

plane used as a tool.• - It acts as a moving inclined

plane.• - A wedge is usually a piece of

wood or metal that tapers to a thin edge.

The Wedge• It is used to raised an object or to split

an object apart.• -For example, when a door wedge is

jammed under a door, it raises the door slightly and exerts a strong force against it.

• An axe is a wedge attached to a shaft.

The Wedge• It changes a forward movement

into a parting movement that can split a log.

• Nearly all cutting machines make use of the wedge, including scissors, saws, and knives. A nail is a wedge too.

The Wedge

• Wedges can be forced between two things to hold them tightly together, like nails or a doorstop.

• Wedges can be used to split, cut or fasten.

The Screw

The Screw

• A screw is an inclined plane wrapped around a cylinder.

• Like pushing an object up a ramp, tightening a screw with gently sloping threads requires a small force acting over a large distance.

The Screw

• Tightening a screw with steeper threads requires more force.

• Jar lids are screws that people use everyday. Spiral staircases are also common screws.

The Screwan inclined plane wrapped around

a central cylinder

• A Screw has two (2) parts: – The Body – Cylinder Post – The Thread – Inclined Plane wrapped

around the cylinder.

The Screw

• Functions of the screw– To fasten things – the standard screw

or nuts & bolts.– Drill bits are screws used to make

holes. – A jackscrew is used to lift heavy

objects; car jack.

The Screw

• When you turn a screw:– The input force is changed by the

threads into an output force.– The output force pulls the screw into

the materials.– Friction between the threads & the

material holds the screw in place.

The Screw

Go back to the 14-4 Objectives and answer them again.

Objectives:1. What are the 6 types of

simple machines?2. What determines the MA of

the 6 types of simple machines?