How Everything Works
How Everything Works How Everything Works
 

QUESTIONS AND ANSWERS
 
Question 1062

Please explain ideal mechanical advantage and actual mechanical advantage. How can I demonstrate these two ideas? — S
Mechanical advantage is any process that allows you to exchange force for distance (or torque for angle) while performing a particular task. The amount of mechanical work you must do (i.e., the amount of energy you must supply) to perform that task won't change, but the relationship of force and distance (or torque and angle) will. For example, you can increase the altitude of a wooden block by 1 meter either by lifting it straight upward 1 meter or by pushing it several meters uphill along a ramp. In the first case, you'll have to exert a large upward force on the block but you won't have to move it very far to complete the task. In the second case, you'll have to exert a much smaller uphill force on the block but you'll have to move it a long way along the ramp. If you multiply the force you exert on the block times the distance that block travels while rising 1 meter, you'll find that it's exactly the same in either case. You've simply calculated the work required to raise the block 1 meter and that work won't change, regardless of how you perform the task! That's the crucial issue with mechanical advantage—it doesn't let you avoid doing the work, it just lets you do that work with a small (or larger) force exerted over a longer (or shorter) distance. In a situation involving rotation, mechanical advantage lets you do the same work with a smaller (or larger) torque exerted over a larger (or smaller) angle. In all of these cases, you're doing the same amount of work but you're making it more palatable by adjusting the balance between force and distance or between torque and angle.

As for actual mechanical advantage, it's simply a recognition that any mechanical system involves imperfections. The work that you do with the help of a machine doesn't all go toward your goal. Instead, you end up doing some work against sliding friction or air resistance and that work is lost to thermal energy. For example, when you slide a block up a ramp, friction with the ramp wastes some of your energy. If you multiply the uphill force you exert on the block while pushing it up the hill times the distance it travels along the ramp, you'll find that you must do somewhat more work while raising the block 1 meter than you would have done by simply lifting the block directly upward that 1 meter. So ideal mechanical advantage assumes no change in the work you do while actual mechanical advantage recognizes that you're going to end up doing extra work whenever you employ a machine to obtain mechanical advantage.

         

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