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4-2 Mechanical Advantage and Efficiency

What is a Machine?
Shovels and bulldozers are examples of machines. A machine is a device with which you can do work in a way that is easier or more effective. Machines can be as simple as a shovel or a ramp, instead of a bulldozer or something like that. A machine doesn’t decrease the amount of work that is done. A machine makes work easier by changing the amount of force you exert, the distance over which you exert your force, or the direction in which you exert your force. (It makes work easier by multiplying either force or distance or by changing direction. The force you exert on a machine is called the input force, or the effort force. The machine does the work by exerting force over some distance. The force exerted by the machine is called the output force.

Multiplying Force
In some machines, the output force is greater than the input force. If the amount of work stays the same a decrease in force must mean an increase in distance. So if a machine allows you to use less force to do some amount of work, you must apply the input force over a greater distance. A ramp allows you to exert smaller force over a longer distance.

Multiplying Distance
In some machines, the output force is less than the input force. This kind of machine allows you to exert your input force over a shorter distance than you would without the machine. For you to apply a force over a shorter distance, you need to apply a greater force.

Changing Direction
Some machines don’t multiply either force or distance. A rope system is an example of this type of mechanical advantage.

Mechanical Advantage
A machine’s mechanical advantage is the number of times a force exerted on a machine is multiplied by the machine.
Output Force
Mechanical Advantage = -------------------
Input Force

Mechanical Advantage of Multiplying Force
For a machine that multiplies force, the mechanical advantage is greater than one (1). That is because the output force is greater than the input force. If you exert a force of 20 N on a can opener, and the opener exerts a force of 60 N on your can, you tripled your force.

Mechanical Advantage of Multiplying Distance
For a machine that multiplies distance, the output force is less than the input force. So mechanical advantage is less than one. If you exert an input force of 20 N and the machine produces an output force of 10 N, so the MA is .5.

Mechanical Advantage of Changing Direction
If only the direction changes, the input force will be the same as the output force, so the MA would be 1.

Efficiency of Machines
In real situations, output work is always less than the input force, because of things like friction. Some work is wasted overcoming friction. The less friction, the closer the output work is to the input work. The efficiency of a machine compares the output work to the input work, and it is expressed as a percent. A machine that has an efficiency of 95% loses very little work. An ideal machine would have an efficiency of 100%.

Calculating Efficiency
To calculate efficiency, divide the output work by the input work and multiply the result by 100%.
Output Work
Efficiency = -------------- x 100%
Input Work

Actual and Ideal Mechanical Advantage
The MA that a machine provides in a real situation is called the actual MA, which you can only determine by measuring the true input and output forces. The MA of a machine without friction is called the ideal mechanical advantage of the machine. If you keep a machine lubricated and clean, you can make it close to the idea MA.


Section Review
1. Machines make work easier when you exert force over a longer distance.
2. The actual MA is different because of friction, and that slows it down.
3. You need to know the things in bold.
Output Work
Efficiency = -------------- x 100%
Input Work
4. Machines can’t increase force and distance, because it’s only going to increase one or the other.


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