Mechanical Advantage and Efficiency

1. Mechanical Advantage and Efficiency Machines

2. 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. • You may think of a machine as a complex gadget that runs on electricity, but a machine can be as simple as a shovel or even a ramp.

3. Making Work Easier • 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. • You might say that a machine makes work easier by multiplying either force or distance, or by changing dirction.

4. Input and Output Force • When you do work with a machine, you exert a force over some distance. • For example, you exert a force on the handle when you use a shovel to lift mulch. • The force you exert on the machine is called the input force, or sometimes the effort force. • The machine then does work, by exerting a force over some distance. • The shovel, in this case, exerts a force to lift mulch. • This force exerted by the machine is the output force. • Sometimes the term resistance force is used, because the machine must overcome some resistance.

5. Multiplying Force • In some machines, the output force is greater than the input force. • How can you exert a smaller force than is necessary for a job if the amount of work is the same? • Remember Work = Force x Distance • If the amount of work stays the same, a decrease in force must mean an increase in distance. • If a machine allows you to use less force to do work, you must apply the input force over a greater distance. • In the end, you do as much work with the machine as you would without the machine, but the work is easier to do.

6. Think about this… • What kind of device might allow you to exert a smaller force over a longer distance? • Think about e. • Suppose you have to lift a piano onto he stage in your school auditorium. • You could try to lift it vertically, or you could push it up a ramp. • If you use the ramp, the distance over which you must exert your force is greater than if you lift the piano directly. • This is because the length of the ramp is greater than the height of the stage. • The advantage of the ramp is that it allows you to exert a smaller force to push the piano than to lift it.

7. Multiplying Distance • In some machines, the output force is less than the input force. • Why would you want to use a machine like this? • The advantage of this kind of machine is that it 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.

8. Think about this… • When would you use this kind of machine? • Think about taking a shot with a hockey stick. You move your hands a short distance, but the other end of the stick moves a greater distance to hit the puck. • The hockey puck moves much faster than your hands. • What happens when you fold up a sheet of paper and wave it back and forth to fan yourself? • You move your hand a short distance, but the other end of the paper moves a longer distance, to cool you off on a warm day.

9. Changing Direction • Some machines don’t multiply either force or distance. • What could be the advantage of these machines? • Think about raising a sail on a boat. • You could raise the sail by climbing the mast of the boat and pulling up on the sail with a rope. • But it is much easier to stand on the deck and pull down than to lift up. • By running a rope through the top of the mast as shown on page 112, you can raise the sail by pulling down on the rope. • This rope system is a machine that makes your job easier by changing the direction in which you exert your force.

10. Mechanical Advantage • If you compare the input force to the output force, you can determine the advantage of using a machine. • A machine’s mechanical advantage is the number of times a force exerted on a machine is multiplied by the machine. • Finding the ratio of output force to input force gives you the mechanical advantage of a machine. • Mechanical advantage = output force input force

11. Mechanical Advantage of Multiplying Forces • For a machine that multiplies force, the mechanical advantage is greater than 1. • That is because the output force is greater than the input force. • For example, suppose you would have to exert 3200 N to lift a piano. If you use a ramp, you might need to exert only 1600 N. • The mechanical advantage of this ramp is 3200 N divided by 1600N or 2. • The ramp doubles the force that you exert.

12. Mechanical Advantage of Multiplying Distance • For a machine that multiplies distance, the output force is less than the input force. • So in this case, the mechanical advantage is less than 1. • If, for example you exert an input force of 20 N and the machine produces an output force of 10 N, the mechanical advantage is 10 N divided by 20 N or .5. • The output force of the machine is half your input force, but the machine exerts that force over a longer distance.

13. Mechanical Advantage of Changing Direction • What can you predict about the mechanical advantage of a machine that changes the direction of the force? • If only the direction changes, the input force will be the same as the output force. • The mechanical advantage will be 1.

14. Efficiency of Machines • So far you have leaned that the work you put into a machine (input work) is exactly equal to the work done by the machine (output work). • In an ideal situation this is true. • In a real situation, however, the output work is always less than the input work. • This is due to the force of friction. • In any machine, some work is wasted overcoming friction. • The less friction there is, the closer the output work is to the input work.

15. Efficiency • The efficiency of a machine compares the output work to the input work. • Efficiency is expressed as a percent. • The higher the percent, the more efficient the machine is. • If you are cutting a piece of paper with tight scissors, you are losing a great deal of efficiency. Suppose the efficiency of the scissors was 60%, a little more than half the work you do goes into cutting the paper. • The rest is wasted overcoming the friction in the scissors. • A machine that has an efficiency of 95% loses very little work. • An ideal machine would have an efficiency of 100%.

16. The Formula for Efficiency You cut the lawn with a hand lawn mower. You do 200,000 j of work to move the mower. If the work done by the mower in cutting the lawn is 250,000 j, what is the efficiency of the lawnmower? Efficiency = output x 100% input Efficiency = 200,000 x 100% 250,000 Efficiency = .8 x 100% = 80%

17. Actual and Ideal Mechanical Advantage • The mechanical advantage that a machine provides in a real situation is called the actual mechanical advantage. • You can only determine the actual mechanical advantage by measuring the true input and output forces. • It cannot be determined in advance because the actual values depend on the efficiency of the machine.

18. The Ideal Mechanical Advantage • Although you cannot predict the actual mechanical advantage of a machine, you can predict the quantity related to the actual mechanical advantage if you ignore losses due to friction. • The mechanical advantage of a machine without friction is called the ideal mechanical advantage of the machine. • The more efficient a machine is, the closer the actual mechanical advantage is to the ideal mechanical advantage. • By keeping a machine clean and well lubricated, you can make its operation closer to ideal, increase the machine’s efficiency, and make your own work easier.