CH 7: work and simple machines

1

What is work?

It involves the exchange of energy for some change in a physical system.

2

In science, the word work has a different meaning than you may be familiar with.

Work and Energy

are so closely

related they have the

same unit - J (joule)

• a student doing homework at a desk

• a mouse pushing a piece of cheese with its nose across the floor

3

Work or Not? According to the scientific definition, what is work and what is not?

the exchange of energy for some change in a physical system.

most common form: mechanical work

4

Mechanical work (W):

using a force to move an object a distance (when both the force and the motion of the object are in the same direction.)

Two factors determine work: application of a force

displacement

5

The mouse is using a force to move the cheese a distance: both the force and motion are in the same direction

force motion

Is work being done?

Mowing the lawn

Weight-lifting

Moving furniture up a flight of stairs

Pushing against a locked door

Swinging a golf club

YES

YES

NO

YES

YES

How is work calculated ?

The product of the force applied to an object and the distance through which that

force is applied.

Work = Force (N) x Distance (m) or

W = Fd 1 Nm = Joule (J)

Do you do more work when you finish a job quickly? Work does NOT involve time, only force and distance.

No work is done when you stand in place holding an object.

Would you do more work if you ran up the stairs and skipped 2 at a time?

Formula for work

Work = Force x Distance

• The unit of force is Newtons

• The unit of distance is meters

• The unit of work is newton-meters

• One newton-meter = one joule

• So, the unit of work is a joule (J)

9

W = Fd

W=FD Calculate:

If a man pushes a concrete block 10 meters with a force of 20 N, how much work has he done?

200 joules

(W = 20N x 10m)

10

a couple more…

11

How much work is done when a force of 33N pulls a wagon 13 meters?

429 J (W = 33N x 13m)

12

Marge uses a force of 25 N to lift her grocery bag while doing 50 Joules of work. How far did she lift the grocery bags?

2 m (50 J = 25N x d)

Power • Power is the rate at which work is done.

• Power = Work*/Time *(force x

distance)

• The unit of power is the Watt (W).

13 P = W/∆t

power

How quickly work is done.

Amount of work done per unit time.

If two people mow two lawns of equal size and one does the job in half the time, who did more work?

Same work. Different power exerted.

POWER = WORK / TIME

Try a couple problems: Physics students, Ben and Bonnie are in the

weightlifting room. Ben lifts the 50 kg barbell over his head (approximately .60 m) 10 times in one minute; Bonnie lifts the 50 kg barbell the same distance over her head 10 times in 10 seconds.

Which student does the most work?

Which student delivers the most power?

Explain your answers. 15

16

Ben and Bonnie do the same amount of work; they apply the same force to lift the same barbell the same distance above their heads.

Yet, Bonnie is the most powerful since she does the same work in less time.

Power and time are inversely proportional.

17

Frank does 2400J of work in climbing a set of

stairs. If he does the work in 6 seconds, what is

his power output?

P = W/∆t

P = 2400/6

P = 400 W

How much power will it take to move a 10kg mass at an acceleration of 2 m/s/s a distance of 10 meters in 5 seconds?

(This problem requires you to use the formulas for

force, work, and power all in the correct order.)

Force=Mass x Acceleration

Work=Force x Distance

Power = Work/Time

18

How much power will it take to move a 10 kg mass at an acceleration of 2 m/s/s a distance of 10 meters in 5 seconds?

Force=Mass x Acceleration

Force=10 x 2 Force=20 N

Work=Force x Distance

Work = 20 x 10 Work = 200 Joules

Power = Work/Time

Power = 200/5

Power = 40 watts 19

P = W

t

But being “powerful” is not

only having a lot of force…it’s

also being fast

Recap…

21

• Work is done on an object only if it moves. If you hold an object in place you do not do any work. Also if you move an object at constant velocity at a constant height you do no work (because the force is up and the motion is sideways not in the same direction of the force).

• ***Work is only done when the force and displacement are in the same direction.***

• If Force and Displacement are at right angles then W = 0.

22

Power – is the work done divided by the time taken to do the work. It is denoted by “P”. It is measured in Watts.

P = W / t ; P = Fd / t

Watt – the unit of Power. It is equal to 1 Joule per second (J/s).

Power is often measured in Kilowatts

since a watt is so small. 1 KW = 1000 watts.

trail up the mountain = 9 km

Force to hike = 80 N

W = 80 N x 9 km

Work = 720 J

climb up the cliff = 6 km

Force to climb = 120 N

W = 1 20 N x 6 km

Work = 720 J

The amount of work is the same!

practice problem

How much work does the force of gravity do when a 25 N object falls a distance of 3.5 m?

858 J

Both the force and displacement are

in the same direction so:

F = mg (25)(9.8) = 245 N

W = Fd = (245 N)(3.5 m)

John and Zombie Bob run a distance of 100 m. John is running with a force of 300 N and Zombie Bob is running with a force of 600 N. Which of the two does more work?

30,000 J 60,000 J

Power practice problem

How much power is required for a figure skater to lift his partner and hold her for 3 seconds? (the skater weighs 400 N and will travel 1 m in the 3 s)

P = w/t P = 400 x 1

3

133 J/s

If John lifted a box weighing 500 N to a height of 8 m in 10 s, and Zombie Bob lifted a box weighing 250 N to a height of 4 m in 5 seconds, who exerts more power?

400 W 200 W

28

hard work

Before engines and motors were invented, people had to do things like lifting or pushing heavy loads by hand. Using an animal could help, but what they really needed were some clever ways to either make work easier or faster.

29

Ancient people invented simple machines that would help them overcome resistive forces and allow them to do the desired work against those forces.

What is a Simple Machine?

• A simple machine has few or no moving parts.

• Simple machines make work easier

• A machine can change the size, the direction, or the distance over which a force acts.

31

• Machines make work easier by accomplishing one or more of the following functions: • transferring a force from one place to another,

• changing the direction of a force,

• increasing the magnitude of a force, or

• increasing the distance or speed of a force.

32

No machine can increase both the magnitude and the distance of a force at the same time.

Why Use Simple Machines?

For the mechanical advantage… • Making something easier to do (less force

needed), but it takes a little longer to do it

• For example, going up a longer flight of

stairs instead of going straight up a ladder

Forces involved:

Input Force

FI

Force applied to a machine

Output Force

FO

Force applied by a machine to something else

Two forces, thus two types of work

Work Input

work done on a machine

=Input force x the distance through which that force acts (input distance)

Work Output

Work done by a machine

=Output force x the distance through which the resistance moves (output distance)

Can you get more work out than you put in?

Work output can never be greater than work input.

Remember Law of conservation of energy?

Efficiency No machine is 100% efficient.

Cannot convert all the

energy put in to same

amount of useable

energy or work out

W in = W out

Some work is always needed to overcome friction!!!

Calculating efficiency

38

A percentage comparison of work output to

work input:

work output (WO) / work input (WI)

efficiency = W out/W in x 100%

Machine efficiency is expressed as a percentage.

• It is useful to think about a machine in terms of the input force (the force you apply) – as the amount of force needed to move the load (resistance) effort force (Fe)

• and the output force (force being moved) – as the weight or load that the work is done on (the resistance) – the resistance force (Fr). 39

Mechanical Advantage

• Most machines are designed to make work easier by reducing the FORCE needed to accomplish the work.

40

Mechanical Advantage • When a machine takes a small input force and

increases the magnitude of the output force, a

mechanical advantage has been produced

A way to calculate mechanical advantage is to compare the force needed to directly do the work to the force applied when using a machine. In math language that looks like:

MA = weight (Fr) effort (Fe)

MA represents the number of times a machine multiplies the input force.

expressed in a

ratio WITH NO

UNITS!!

Try a problem

42

You need to move a piano onto a stage 2 m above the floor. The piano is 3300 N (740 lbs). This would require 6600 J of work!

You cannot exert that much effort force

unassisted. A machine could help by

making the amount of effort force less.

Using a pulley

reduces the

effort needed to

only 550 N. Now

you can lift the

piano.

What is the MA of the pulley?

MA = weight (Fr) effort (Fe)

MA = 3300 N 550 N MA = 6

Text, pg.154

Kisha applied 20N of force to turn an ice cream freezer crank. The crank’s resistance was 60 N. What was the mechanical advantage of the crank?

MA = 60 N

20 N

MA= 3

44

What about a machine that increases distance as a way to reduce force?

Distance principle

45

To conserve work and energy, simple

machines compensate for smaller effort by

exerting the force over a longer distance.

46

• The MA is the ratio of the output distance and input distance. MA = effort length (arm)/resistance length (arm)

MA

MA = effort arm resistance arm

Suppose you need to remove a nail from a board by using a claw hammer. If the effort length for a claw hammer is 11.0 cm and the resistance length is 2.0 cm. What is the mechanical advantage?

IMA= Effort arm Resistance arm

= 11.0 cm 2.0 cm

= 5.5

another one…

48

You use a crowbar to pry open a stuck door. If the mechanical advantage of the lever is 6.5 and the distance from the pivot point to the door jam is 4 cm, how long is the crowbar from your end to the pivot point?

MA = effort arm

resistance arm

6.5 = X X = 6.5(4)

4 cm

effort arm = 26 cm

49

• The six simple machines are:

• Lever

• Wheel and Axle

• Pulley

• Inclined Plane

• Wedge

• Screw

Simple machines

The Lever • A lever is a rigid bar that rotates around a

fixed point called the fulcrum.

• The bar may be either straight or curved.

• In use, a lever has both an effort (or applied) force and a load (resistant force).

input force

output force

Levers & Law of Moments

51

Moment or “Torque”

52

When a force causes an object to turn

on a fixed point, this turning effect is

called moments or torque

53

Even though it may not look like it, the motion of a

lever is a rotational movement around a fixed pivot

point.

This is the reason why pulleys and wheel and axles are “modified” levers.

Axis of

rotation

54

55

The turning effect or moment of a force is dependent

on both the size of the force and how far it is applied

from the pivot or fulcrum.

56

57

58

What if a moment existed on both sides of the

pivot point?

59

When a lever is balanced (in equilibrium) it has no tendency to move.

If there is torque on

both sides of the

fulcrum that are equal,

the forces are

balanced.

A net torque will

accelerate the lever in

the direction of the

larger moment.

The Law of Moments

60

You can determine the balance point (rotational

equilibrium) for any lever using the formula for the

Law of Moments:

F1l1 = F2l2

example problem 1

61

The ruler in the diagram below is supported at its

center.

If the ruler is balanced, what must be the lengths

of x and y?

A. 3cm (x) 5cm (y) B. 5cm (x) 3cm (y)

C. 6cm (x) 10cm (y) D. 12cm (x) 20cm (y)

example problem 2

62

The see-saw balances when Susan (320N) sits at A, Tom, weighing 540N, sits at B and Harry, weighing W, sits at C. Find W.

(320N x 3m) + (540N x 1m) = 1500Nm W x 3m

1500 Nm = W x 3m

1500Nm/3m = W

W = 500 N

• The class of a lever is determined by the location of the effort force and the load relative to the fulcrum.

63

3 classes of levers

3 classes of levers

64

To find the MA of a lever, divide the output force by the input force, or

divide the length of the resistance arm by the length of the effort arm.

location of the effort force and the load relative to the fulcrum

• the fulcrum is located at some point between the effort and resistance forces. • Common examples of first-class levers include

crowbars, scissors, pliers, tin snips and seesaws.

• A first-class lever always changes the direction of force

65

Effort

resistance

First class lever

a downward effort force on one end of the lever results in an upward movement of the resistance force

Fulcrum is between EF (effort) and RF (load) Effort moves farther than Resistance**. Multiplies EF and changes its direction

66

• the load is located between the fulcrum and the effort force.

• When the fulcrum is located closer to the load than to the effort force, an increase in force (mechanical advantage) results.

67

Second class lever

Resistance Force (load) is between fulcrum and Effort Force Effort moves farther than Resistance

Multiplies EF, but does not change its direction 68

Common examples include nut wheel barrows, doors, and bottle openers.

• the effort force is applied between the fulcrum and the resistance force.

• A third-class lever does not change the direction of force; third-class levers always produce a gain in speed and distance and a corresponding decrease in force.

69

Third class lever

EF is between fulcrum and RF (load) Does not multiply force Resistance moves farther than Effort. 70

Examples of third-class levers include tweezers, hammers, and shovels.

wheel & axle, pulleys

71

modified levers

• A wheel rigidly secured to a smaller wheel or shaft, called an axle.

• When either the wheel or axle turns, the other part also turns. One full revolution of either part causes one full revolution of the other part.

Wheel and axle

73

• a grooved wheel that turns freely in a frame called a block.

• A pulley can be used to simply change the direction of a force or to gain a mechanical advantage, depending on how the pulley is arranged.

pulley

74

A pulley is said to be a fixed pulley if it does not rise or fall with the load being moved. A fixed pulley changes the direction of a force; however, it does not create a mechanical advantage.

A moveable pulley rises and falls with the load that is being moved. A single moveable pulley creates a mechanical advantage; however, it does not change the direction of a force.

The mechanical advantage of a moveable pulley is equal to the number of ropes that support the moveable pulley.

Inclined Plane

• The Egyptians used simple machines to build the pyramids. One method was to build a very long incline out of dirt that rose upward to the top of the pyramid very gently. The blocks of stone were placed on large logs (another type of simple machine - the wheel and axle) and pushed slowly up the long, gentle inclined plane to the top of the pyramid.

• An inclined plane is an even sloping surface. The inclined plane makes it easier to move a weight from a lower to higher elevation.

78

An inclined plane that moves.

Mechanical advantage is increased by sharpening it.

wedge

• also a modified version of the inclined plane.

• think of the threads of the screw as a type of circular ramp (or inclined plane).

80

screw

81

MA of an screw can be calculated by dividing the number of

turns per inch.

Archimedes

screw

Summary Wedge Pushes material apart, cuts

Wheel

and Axle

Makes it easy to move things

by rolling them, and reducing friction

Lever Helps lift heavy weights

using longer distances

Inclined

Plane

Makes it easier to move objects upward;

a longer path, but easier lifting

Screw Turns rotation into lengthwise movement

Pulley

Makes lifting heavy weights easier

by redirecting force

Compound Machines

• Simple Machines can be put together in different ways to make complex machinery

GADGET ANATOMY What’s in a Machine?

84

RUBE GOLDBERG 85

86

“To invent, you need a good imagination and a pile of junk.” —Thomas Edison (1847-1931)

Rube Goldberg (1883-1970) was a Pulitzer

Prize winning cartoonist, sculptor, and

author.

• Born July 4, 1883 in San Francisco, CA

• Graduated from University of Calif. Berkeley in 1904 w/degree in Mining Engineering

• Hired by city of San Francisco as an engineer in the water department

• Quits after 6 months to become a sports cartoonist

• Drew cartoons for 5 newspapers

88

• Founding member and 1st president of the National Cartoonists

Society

• Won the Pulitzer Prize in 1948 for his Political Cartoons

Becomes very popular for cartoons such as Mike and Ike, Boob McNutt, Lala Palooza and

others. His character Professor Lucifer Gorgonzola Butts makes him very famous.

His cartoons were, (as he said),

“symbols of man's capacity for exerting maximum effort to

accomplish minimal results”

Rube believed that there were two ways to do things: the simple way

and the hard way, and that a surprisingly number of people preferred

doing things the hard way.

Rube Goldberg died on December 7, 1970 at the age of 87

91

Among many ways Rube influenced popular culture were the 1963 board game called “Mouse Trap” and a 1930 movie he wrote featuring his machines and starring the Three Stooges.

92

Today his work inspires international competitions in which

participants invent a complex machine that performs a simple task

What is a Rube Goldberg Device? • Rube Goldberg drew contraptions that make

simple tasks into difficult and complicated ones.

94

A Rube Goldberg device

is a comical, complicated invention

that performs a simple operation using a string of simple

machines.

Mealtime can be messy—but not with this self-operating napkin

95

Need to catch a bike thief? Check out this wacky contraption inspired by Rube Goldberg.

Go through steps 1 to 11 to see how the thief was nabbed!

When you slip on ice, your foot kicks paddle (A),

lowering finger (B), snapping turtle (C) extends neck

to bite finger, opening ice tongs (D) and dropping pillow (E),

thus allowing you to fall on something soft.

Safety Device for Walking on Icy Pavements

97 honda AP physics

This too shall pass

Myth busters

98

Every year, high school and college students compete in a Rube Goldberg Contest at Purdue University in Indiana.

Guiness record Jimmy Kimmel

2014 winner

Create your own

99

Illustrate a Rube Goldberg machine • Use 10 or more steps • include at least 4 out of 6 simple machines

(wheel & axle, pulley, screw, inclined plane, wedge, and lever.)

• Make up your own or do one from the list • Final drawing must be colored with steps numbered

and explained.

100

Professor Butts and the Self-Operating Napkin

The Napkin is activated when the Soup Spoon (A) is raised to mouth, pulling string (B) which jerks

ladle (C) which throws cracker (D) past parrot (E). Parrot jumps after cracker and perch (F) tilts,

upsetting seeds (G) into pail (H). Extra weight in pail pulls cord (I), which opens and lights a cigar

lighter (J), setting off a skyrocket (K) which causes sickle (L) to cut string (M) and allow the

pendulum with the attached napkin to swing back and forth, wiping chin.

Wee Village problems

102

LET’S REVIEW 103

Practice Questions

1. Explain who is doing more work and why: a bricklayer carrying bricks and placing them on the wall of a building being constructed, or a project supervisor observing and recording the progress of the workers from an observation booth.

2. How much work is done in pushing an object 7.0 m

across a floor with a force of 50 N and then pushing it back to its original position? How much power is used if this work is done in 20 sec?

3. Using a single fixed pulley, how heavy a load could you

lift? 104

Practice Questions

4. Give an example of a machine in which friction is both an advantage and a disadvantage.

5. Why is it not possible to have a machine with

100% efficiency?

6. What is effort force? What is work input?

Explain the relationship between effort force, effort distance, and work input.

105

Practice Questions 1. Explain who is doing more work and why: a bricklayer

carrying bricks and placing them on the wall of a building being constructed, or a project supervisor observing and recording the progress of the workers from an observation booth. Work is defined as a force applied to an object, moving that object a distance in the direction of the applied force. The bricklayer is doing more work.

2. How much work is done in pushing an object 7.0 m across a

floor with a force of 50 N and then pushing it back to its original position? How much power is used if this work is done in 20 sec? Work = 7 m X 50 N X 2 = 700 N-m or J; Power = 700 N-m/20 sec = 35 W

3. Using a single fixed pulley, how heavy a load could you

lift?Since a fixed pulley has a mechanical advantage of one, it will only change the direction of the force applied to it. You would be able to lift a load equal to your own weight, minus the negative effects of friction. 106

Practice Questions 4. Give an example of a machine in which friction is both an

advantage and a disadvantage. One answer might be the use of a car jack. Advantage of friction: It allows a car to be raised to a desired height without slipping. Disadvantage of friction: It reduces efficiency.

5. Why is it not possible to have a machine with 100% efficiency?

Friction lowers the efficiency of a machine. Work output is always less than work input, so an actual machine cannot be 100% efficient.

6. What is effort force? What is work input? Explain the relationship between effort force, effort distance, and work input. The effort force is the force applied to a machine. Work input is the work done on a machine. The work input of a machine is equal to the effort force times the distance over which the effort force is exerted. 107