Instructor’s Copy
Worksheet: The Advantage and Efficiency of Machines
Solve the following problems.
An inclined plane is 4 meters long and 1 meter high. A force of 1200 N is needed to move a
3200 N box.
1. Calculate input work.
IW = DE X E
= (4m)(1200 N)
= 4800 J
2. Calculate output work.
OW = DR X R
= (1 m)(3200 N)
= 3200 J
3. Calculate IMA.
IMA = DE/DR
= 4m/1m
=4
4. Calculate AMA.
AMA = R/E
= 3200/1200
= 2.7
5. Calculate the efficiency of the machine.
Efficiency = WO/WI X 100
= 3200 J/4800 J X 100
= 66.7%
For pulleys, the ideal mechanical advantage is the number of supporting strands.
6. What is the IMA of the pulley system shown to the right?
3
7. If the system is used to lift a 500 N weight, how much force would you need to apply?
166.7 N (Force applied/3)
8. If you wanted to lift the mass 10 meters, how much rope would you need to pull through your
hands. 30 m (resistance distance X 3)
9. Calculate the input work.
IW = DE X E
= (30 m)(166.7 N)
= 5001 J
10. Calculate the output work.
OW = DR X R
= (10 m)(500 N)
= 5000 J
11. Calculate the efficiency of the machine.
Efficiency = OW/IW X 100
= 5000 J/5001 J
= 99.9 %
12. The radius of a wheel is 18 inches. The radius of the axle is 3 inches. What is the mechanical
advantage of the wheel and axle system if the formula is rw/ra?
IMA = rw/ra
= 18 inches/3 inches
=6
13. For the mechanical advantage of a gear system, you take the number of teeth (or possibly the
diameter of the gear) of the effort gear/the number of teeth (or diameter) of the resistance gear.
The best system occurs where the effort gear is bigger.
14. Calculate the mechanical advantage of the gear
system shown to the left.
40 teeth/16 teeth = 2.5
For a lever, the DE is the distance from the fulcrum to the effort. The DR is the distance from the
fulcrum to the object being moved. While using a lever, the effort force is exerted through a
distance of 45 cm while the resistance moves 5 cm. An effort force of 20 N was used.
15. What is the mechanical advantage of the machine?
IMA = DE/DR
= 45 cm/5 cm
=9
16. What is the maximum weight of the object this lever can move?
DE X E = DR X R (Law of Conservation of energy)
(45 cm)(20 N) = (5 cm)(R)
R = 180 N