Mechanical Advantage and Efficiency Machine – a device with which you can do work in a way that is easier or more effective. 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.

What is a Machine? Input force – the force you exert on the machine. Output force – the force exerted by the machine.

Multiplying Force In some machines, the output force is greater than the input force. If a machine allows you to use less force to do some amount of work, you must apply the force over a greater distance.

Multiplying Distance In some machines, the output force is less than the input force. The advantage of this kind of a machine is that it allows you to exert your input force over a shorter distance than you would without a machine.

Changing Direction Some machines do not multiply force or distance. They change the direction of the force. The machines allow you to use your body weight to help lift things.

Mechanical Advantage A machine’s mechanical advantage is the number of times a force exerted on a machine is multiplied by the machine. Mechanical Advantage- the ratio of the output force to the input force.

Efficiency of Machines Efficiency – a comparison of the output work to the input work of a machine.

Sample Problem – You cut the lawn with a hand lawn mower Sample Problem – You cut the lawn with a hand lawn mower. You do 250,000 J of work to move the mower. If the work done by the mower in cutting the lawn is 200,000 J, what is the efficiency of the lawnmower. Analyze You are given the input work and the output work. You are asked to find the efficiency. Write the formula Efficiency = Output work x 100% Input work Sub. & Solve Efficiency = 200,000 J x 100% 250,000 J Efficiency = 0.8 x 100% = 80%

Practice Problem #1- You do 1,500 J of work in using a hammer Practice Problem #1- You do 1,500 J of work in using a hammer. The hammer does 825 J of work on a nail. What is the efficiency of the hammer. Analyze You are given the input work and the output work. You are asked to find the efficiency. Write the formula Efficiency = Output work x 100% Input work Sub. & Solve Efficiency = 825 J x 100% 1,500 J Efficiency = 0.55 x 100% = 55%

Practice Problem #2 – Suppose you left your lawn mower outdoors all winter. It’s now rusty. Of your 250,000 J of work, only 100,000 go to cutting the lawn. What is the efficiency of the lawn mower now? Analyze You are given the input work and the output work. You are asked to find the efficiency. Write the formula Efficiency = Output work x 100% Input work Sub. & Solve Efficiency = 100,000 J x 100% 250,000 J Efficiency = 0.4 x 100% = 40%

Actual and Ideal Mechanical Advantage Actual Mechanical Advantage – the mechanical advantage that a machine provides in a real situation. The mechanical advantage of a machine without friction is called the ideal mechanical advantage of the machine. Ideal Mechanical Advantage – the mechanical advantage a machine would have without friction.