Work and Machines

Chap 5

Work

5.1

What is Work?Work

transfer of energy that occurs when a force makes an object move

W = FdW: work (J)F: force (N)d: distance (m)

1 J = 1 N·m

Distance must be in direction of force!

FWd

Doing Work If you push on your desk and

nothing moves, have you done work?No

Conditions for work to be done:Force must make object moveThe movement must be in the

same direction as the applied force.

Which is Work?Lifting books?Walking with books?

Work and EnergyWhen work is done, a transfer

of energy always occurs. If you carry a heavy box up a

flight of stairs, you transfer energy form your moving muscles to the box (increasing its PE by increasing its height).

Lifting ProblemBrett’s backpack weighs 30 N. How much

work is done on the backpack when he lifts it 1.5 m from the floor to his back?

GIVEN:

F = 30 N

d = 1.5 m

W = ?

WORK:

W = F·d

W = (30 N)(1.5 m)

W = 45 J

FWd

Dancing is WorkA dancer lifts a 40 kg ballerina 1.4 m in the

air and walks forward 2.2 m. How much work is done on the ballerina during and after?

GIVEN:

m = 40 kg

d = 1.4 m - during

d = 2.2 m - after

W = ?

WORK:

W = F·d F = m·a

F =(40kg)(9.8m/s2)=392 N

W = (392 N)(1.4 m)

W = 549 J during lift

No work after lift. “d” is not in the direction of the force. F

Wd

PowerPower

rate at which work is donemeasured in watts (W)

t

WP

P: power (W)W: work (J)t: time (s)

Power in Skating A figure skater lifts his partner, who

weighs 450 N, 1.5 m in 3.0 s. How much power is required?

GIVEN:

F = 450 N

d = 1.5 m

t = 3.0 s

WORK:

P = W ÷ t

W = F·d

W = (450 N)(1.5 m) = 675 J

P = 675 J ÷ 3.0 s

P = 225 W

P

W

t

Videoshttp://www.brainpop.com/

science/motionsforcesandtime/work/

Self Check 5.11. The amount of work done

depends on what two things?

2. You push a box with a force of 100 N. If it moves 5 m while you are pushing, how much work was done?

Using Machines

5.2

What is a Machine?

Machinedevice that makes work easierchanges the size and/or

direction of the exerted force

Making Work Easier Machines make work easier by:

increasing the force that can be applied to an object

car jack increasing the distance over which

a force can be applied ramp

changing the direction of an applied forcewedge-shaped blade of ax

Input and Output Forces

Input Force (Fin)force applied to the machine“what you do”

Output Force (Fout)force applied by the machine“what the machine does”

Force and WorkWork Input (Win)

work done on a machine

Work Output (Wout)

work done by a machine

Win = Fin × din

Wout = Fout × dout

Conserving EnergyConservation of Energy

can never get more work out than you put in

trade-off between force and distance

Win = Wout

Fin × din = Fout × dout

Ideal Machines In an ideal machine...

But in the real world…some energy is lost as friction

Win = Wout

Win > Wout

Mechanical AdvantageMechanical Advantage (MA)

number of times a machine increases the input force

€

MA =FoutFin

MA > 1 : force is increasedMA < 1 : distance is increasedMA = 1 : only direction is changed

Open a Window A worker applies an input force of 20 N

to open a window with a output force of 500 N. What is the crowbar’s MA?

GIVEN:

Fin = 20 N

Fout = 500 N

MA = ?

WORK:

MA = Fout ÷ Fin

MA = (500 N) ÷ (20 N)

MA = 25

MA

Fout

Fin

Mechanical Advantage Find the input force needed to lift a

2000 N rock using a jack with a mechanical advantage of 10.

GIVEN:

Fin = ?

Fout = 2000 N

MA = 10

WORK:

Fin = Fout ÷ MA

Fin = (2000 N) ÷ (10)

Fin = 200 N

MA

Fout

Fin

Mechanical AdvantageWindow blinds change direction

of the input force.The input and output forces

are equal, so the MA = 1

EfficiencyEfficiency

measure of how completely work input is converted to work output

100%W

WEfficiency

in

out

In real machines, it is always less than 100% due to friction

Ramps A worker exerts a force of 500 N to push

a 1500 N sofa 4.0 m along a ramp that is 1.0 m high. What is the ramp’s efficiency?

GIVEN:

Fin = 500 N

din = 4.0 m

Fout = 1500 N

dout = 1.0 m

WORK:

Win = (500N)(4.0m) = 2000 J

Wout = (1500N)(1.0m) = 1500 J

E = 1500 J × 100% 2000 J

E = 75%

1.0m

1500N

4.0m500N

100%in

out

W

WE

Increasing EfficiencyMachines can be made more

efficient by reducing friction. A lubricant fills in the gaps

between surfaces, enabling them to slide past each other more easily.

Videos

Self Check 5.2Why is the work output always

less than the input in a real machine?

Calculate the mechanical advantage of a hammer if the input force is 125 N and the output force is 2000 N.

Simple Machines

5.3

Simple MachinesA simple machine is a machine

that does work with only one movement of the machine.

There are six types of simple machines: levers, pulleys, wheel and

axle, inclined planes, screws, and wedges.

LeversLever

a bar that is free to pivot or turn around a fixed point

The fixed point the lever pivots on is called a fulcrum

Types of LeversFirst class lever

fulcrum in middle

Second class leverFout in middle

Third class leverFin in middle

IMA of a Lever Ideal Mechanical Advantage

length of input arm divided by length of output arm

Videohttp://

www.enchantedlearning.com/physics/machines/Levers.shtml

PulleysPulley

grooved wheel with a rope or chain running along the groove

a “flexible first-class lever”axel of pulley is the fulcrum

Lin Lout

F

IMA of a Pulley Ideal Mechanical Advantage (IMA)

equal to the number of supporting ropes

IMA = 0 IMA = 1 IMA = 2

Fixed PulleysFixed Pulley

does not increase force

changes direction of force

IMA = 1

Movable PulleysMovable Pulley

increases force

doesn’t change direction

IMA = 2

Comparing PulleysFor a fixed pulley, the distance

you pull the rope downward equals the distance the weight moves upward.

For a movable pulley, the distance you pull the rope upward is twice the distance the weight moves upward.

Block and Tackle PulleysBlock & Tackle

combination of fixed & movable pulleys

may or may not change direction

IMA = 4

Wheel and AxleWheel and Axle

two wheels of different sizes that rotate together

a pair of “rotatinglevers”

Wheel

Axle

Wheel and Axle Is this skateboard a good

example of a wheel and axel machine?No because

the axle is fixed.

IMA Wheel and Axle Ideal Mechanical Advantage (IMA)

effort force is applied applied to at rim of wheel

axle moves less distance but with greater force

r

e

r

rIMA

effort radius

resistance radius

Inclined Planes Inclined Plane

sloping surface used to raise objects

hl

h

lIMA

ScrewScrew

inclined plane wrapped in a spiral around a cylinderinput force by turning screwoutput force on threads

WedgeWedge

a moving inclined plane with 1 or 2 sloping sideschanges direction of the input force

Compound MachinesCompound Machine

combination of 2 or more simple machines

A. Compound MachinesRube Goldberg Machine

Rube Goldberg walks in his sleep, strolls through a cactus field in his bare feet, and screams out an idea for self-operating napkin: As you raise spoon of soup (A) to your mouth it pulls string (B), thereby jerking 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 automatic cigar lighter (J), setting off sky-rocket (K) which causes sickle (L) to cut string (M) and allow pendulum with attached napkin to swing back and forth thereby wiping off your chin. After the meal, substitute a harmonica for the napkin and you'll be able to entertain the guests with a little music.

Videos http://www.brainpop.com/technology/simplemachines/

levers/ http://www.brainpop.com/technology/simplemachines/

pulley/ http://www.brainpop.com/technology/simplemachines/

wheelandaxle/ http://www.brainpop.com/technology/simplemachines/

inclinedplane/ http://computerkiddoswiki.pbworks.com/Simple-Machines http://www.edheads.org/activities/odd_machine/

Self Check 5.31. Identify the simple machines in

this bicycle.

Problems You use a 160 cm plank to lift a large

rock. If the rock is 20 cm from the fulcrum, what is the plank’s IMA?

GIVEN:

Lr = 20 cm

Le = 140 cm

IMA = ?

WORK:

IMA = Le ÷ Lr

IMA = (140 cm) ÷ (20 cm)

IMA = 7

IMA

Le

Lr

20cm

160cm

Problems A crank on a pasta maker has a radius

of 20 cm. The turning shaft has a radius of 5 cm. What is the IMA of this wheel and axle?

GIVEN:

re = 20 cm

rr = 5 cm

IMA = ?

WORK:

IMA = re ÷ rr

IMA = (20 cm) ÷ (5 cm)

IMA = 4

IMA

re

rr

5 cm 20 cm

Problems A steering wheel requires a mechanical

advantage of 6. What radius does the wheel need to have if the steering column has a radius of 4 cm?

GIVEN:

IMA = 6

re = ?

rr = 4 cm

WORK:

re = IMA · rr

re = (6)(4 cm)

re = 24 cm

IMA

re

rr

rr re

Problems You need to lift a 150 N box using only

15 N of force. How long does the lever need to be if the resistance arm is 0.3m?

GIVEN:

Fr = 150 N

Fe = 15 N

Lr = 0.3 m

Le = ?

MA = 10

WORK:

Le = IMA · Lr

Le = (10)(0.3)

Le = 3 m

Total length = Le + Lr

Total length = 3.3 m IMA

Le

Lr

0.3m

?

150N

15N

Problems How much force must be exerted to

push a 450 N box up a ramp that is 3 m long and 1.2 m high?

GIVEN:

Fe = ?

Fr = 450 N

l = 3 m

h = 1.2 m

WORK:IMA = l ÷ hIMA = (3 m)÷(1.2 m)IMA = 2.5

IMA

l

hMA

Fr

Fe

Fe = Fr ÷ MAFe = (450 N)÷(2.5)Fe = 180 N

WedgeZipper

2 lower wedges push teeth together1 upper wedge pushes teeth apart