Mechanical Advantage and Efficiency Machines

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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%.

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%

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.

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.