A machine cannot give you more work than you put in, but it can make a heavy job feel easy. Learn the numbers behind it.
A machine is a device that makes work easier by changing the size or direction of a force. Mechanical advantage (MA) = load ÷ effort. Velocity ratio (VR) = distance moved by the effort ÷ distance moved by the load. Efficiency = (work output ÷ work input) × 100%, which also equals MA ÷ VR × 100%.
An effort of 50 N lifts a load of 150 N. Find the mechanical advantage.
150 ÷ 50 = 3
The effort in that machine moves 4 m while the load moves 1 m. Find its velocity ratio and efficiency.
VR = 4 ÷ 1 = 4, and efficiency = 3 ÷ 4 × 100 = 75%
Why can the efficiency of a real machine never be 100%?
Friction and the weight of the moving parts waste some of the input work as heat
A lever is a rigid bar that turns about a fixed point called the fulcrum. In a class I lever the fulcrum lies between the load and the effort (scissors, see-saw, crowbar). In a class II lever the load lies between the fulcrum and the effort (wheelbarrow, nutcracker). In a class III lever the effort lies between the fulcrum and the load (tongs, fishing rod).
To which class does a pair of scissors belong, and why?
Class I, because the pivot (fulcrum) lies between the blades that carry the load and the handles where the effort is applied
A lever has an effort arm of 100 cm and a load arm of 20 cm. What is its ideal velocity ratio, and what effort lifts a 100 N load?
VR = 100 ÷ 20 = 5, so for an ideal lever the effort is 100 ÷ 5 = 20 N
A single fixed pulley has VR = 1 and only changes the direction of the effort. A single movable pulley has VR = 2. In a block and tackle the VR equals the number of rope strands supporting the load. For an inclined plane, VR = length of the plane ÷ height.
What is the VR of an inclined plane 5 m long and 1 m high?
5 ÷ 1 = 5
A block and tackle has 4 strands supporting the load. What is its velocity ratio?
4, equal to the number of supporting strands
A load of 80 N is lifted by an effort of 25 N in a machine with VR = 4. Find its efficiency.
MA = 80 ÷ 25 = 3.2, so efficiency = 3.2 ÷ 4 × 100 = 80%
1. Define the mechanical advantage of a machine.
2. Define the velocity ratio of a machine.
3. Write the expression for the efficiency of a machine.
4. An effort of 50 N lifts a load of 150 N. What is the mechanical advantage?
5. In a machine the effort moves 4 m while the load moves 1 m. What is the velocity ratio?
6. What is the efficiency of a machine with MA = 3 and VR = 4?
7. To which class of lever does a nutcracker belong?
8. What is the velocity ratio of a single movable pulley?
9. What is the velocity ratio of an inclined plane 5 m long and 1 m high?
10. Why does a real machine never have an efficiency of 100%?