Simple Machines

And EfficiencyPhysics Chapter 10d

Machine

Makes doing work easier by changing direction of applied force or amount of applied force

Simple machines have no or few moving parts and no engine

Simple machines can be combined to form complex machines

Some terms: Wo=output work.

Wo is always less than Wi

Wi=input work Wi is always more than Wo

Simple Machines

There are six basic simple machines: Lever family:

Lever: a long pole or rod that moves around a fixed point (fulcrum)

Pulley: grooved wheel with a rope or chain attached to the load

Wheel and axle: wheel and axle attached Inclined plane family:

Inclined plane: ramp Wedge: 2 inclined planes forming a wedge Screw: inclined plane wound around a cylinder

InventorsToolbox: The Elements of Machines

Types of Simple Machines

http://www.edheads.org/activities/simple-machines/

Mechanical Advantage

Ratio of the force needed to do the work to the force the machine uses on the load

Some terms: Effort force= Fe: The force exerted by the

person using the machine Resistance force=Fr: The force exerted by the

machine on the load Mechanical advantage (MA) MA= Fr/Fe

Ideal Mechanical Advantage

Uses the definition of Work to describe mechanical advantage

Ideal mechanical advantage is equal to the displacement of the effort force divided by the displacement of the load

IMA = de/dr

Efficiency

Compares input work to output work Eff = W

o/W

i x 100 (given as a percent)

All real machines have efficiency less than 100%

Because Wo/W

i = F

rd

r/F

ed

e And F

r/F

e=MA and d

e/d

r=IMA

So Eff = MA x 100 IMA

Sample Problem

You examine the rear wheel of a bicycle. It has a radius of 35.6 cm and has a gear with a radius of 4 cm. When the chain is pulled with a force of 155 N, the wheel rim moves 14 cm.The efficiency of this part of the bicycle is 95%.

What is the IMA of the wheel and gear? What is the MA of the wheel and gear? What is the reistance force? How far was the chain pulled to move the rim

14 cm?

What is the IMA of the wheel and gear?

What you know: de (for a wheel, this is radius) = 4 cm dr = 35.6 cm

What equation will you use? IMA=de/dr

Substitute IMA=4 cm/35.6 cm

Solve and check for units 0.112 (no units for MA or IMA)

What is the MA of the wheel and gear?

What you know IMA = 0.112 Eff = 0.95 Fe = 155 N

Write the equation We don't know Fr, so use Eff = MA/IMA Re-write as MA = (Eff)(IMA)

Substitute MA = (0.95)(0.112)

Solve and check units MA = 0.1067 (no units)

What is the reistance force?

What you know MA = 0.1067 Fe = 155 N

Equation MA = Fr/Fe So Fr = (MA)(Fe)

Substitute Fr= (0.1067)(155 N)

Solve and check units Fr = 16.5 N

How far was the chain pulled to move the rim 14 cm?

What we know dr = 14 cm IMA = 0.112

What equation IMA = de/dr So de = (IMA)(dr)

Substitute de = (0.112)(14 cm)

Solve and check units de = 1.568 cm