1. And Efficiency Physics Chapter 10d
Simple Machines
And Efficiency
Physics Chapter 10d

2. 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

3. 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

4. InventorsToolbox: The Elements of Machines

5. Types of Simple Machines

6. 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

7. 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

8. Efficiency Compares input work to output work
Eff = Wo/Wi x 100 (given as a percent)‏
All real machines have efficiency less than 100%
Because Wo/Wi = Frdr/Fede
And Fr/Fe=MA and de/dr=IMA
So Eff = MA x IMA

9. 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?

10. 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)‏

11. 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 = (no units)‏

12. What is the reistance force?
What you know
MA =
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

13. 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 = cm