Since a pulley is involved, shouldn't the work done be 1/2 of the original force, and thus 100J?
aamc official guide #74
- Thread starter sanguinee
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You can't change the work done by using a machine. That would violate energy conservation by the work-energy theorem. If you can increase an object's potential energy by the same amount by inputting less work, then potential energy wouldn't be a state function.
I'm not sure if that specific number is correct, since I hate pulley problems but I do know that Fout is not the same as Fin - that's the point of the pulley and that's the basis of mechanical advantage.
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Intuitively, you know that the amount of work to do something is the same regardless of how you do it.
Work = ∆KE + ∆PE
For example, the work, the change in KE + change PE, of a skier starting from rest on top of the mountain until she skis (w/o friction) to the bottom is the same as dropping that skier off a building of an equal height as the mountain. The final velocity is the same in both cases. In the first, her acceleration is smaller but it occurs over a longer distance (the length of the slope) rather than straight downwards. And, since she reaches the bottom, the change in PE is the same, too.
In this case, the work done is the same kind of thing. This time, KE is 0 at both the start and end (bring a box up 5m, it's initial and final velocities are both 0), so the only thing that matters is change in PE.
PEo = mass * g * height (= 0) = 0 J
PE f= mass * g * height = 4 * 5 * 10 = 200 J
The change in PE = 200 J regardless of how you lift the thing upward. Pulley or no pulley. The work done, then, is 200J.
As a last point, remember the question is asking about work and not about the force needed. Mechanical advantage means that the force you have to exert is less, but, since the work done is the same, the distance you have to apply that force is longer--much like in the skier example.
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Work by simple definition is the force x distance. In this example, you can think of it in terms of KE and PE; however, you can make it more simple than that and just say that the force is vertical (mg) and the height is 5.
4x10x5=200J
4x10x5=200J
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The point of any machine (pulley, lever (all 3 classes) or inclined plane) is to accomplish a given amount of work (output) for a given amount of work (input).
These 2 values Work in must be > or = Work out else you have created some kind of magical energy generating machine and have solved all of our energy problems forever.
What you should know, is that the FORCES required to accomplish this work need not be equal. Think of torque wrenches. By lengthening a torque wrench handle I can get the same torque (t = rFsin(theta)) with a much lower F in, even though I will get the same torque (measured in N*m, same as Work) output, my input force is smaller.
The is the entire bases for mechanical advantage (http://www.edinformatics.com/math_science/simple_machines/lever.htm). MA = Output F /Input F. By using pulleys, levers or inclined planes we can exert less force to accomplish the same work. lifting an mass m straight up to a height h requires the work mgh. i can use a ladder or a ramp but the work done isn't changing, just our ease in accomplishing that work is.
Hope this helps, good luck!
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