If W = FD, and W/F = D, that means that as force increases, displacement decreases. I was just having a hard time understanding why thats so. Similarly F = ma and F/m = a, so as (m) increases (a) decreases. That makes sense, since the more the mass the less the acceleration. However, wouldn't it be true that the more the Force the greater the displacement in the Work equation? Just need a proper conceptual explanation. Thanks.
[Physics] Why is force inversely proportional to distance when calculating work
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I agree with CuriousOne that the example is more confusing than helpful, but this is the way I would explain it.
Suppose you take a spring, place it on the ground then compress it. If you now suddenly let go of the spring it will rebound and bounce upwards off the ground:
The spring clearly has work done on it because its kinetic energy increases and that increase must have come from somewhere. However the ground can't have done any work on the spring because the ground hasn't moved. It should be obvious that the potential energy in the compressed spring has been converted into kinetic energy of the uncompressed spring - in effect the spring has done work on itself. This is what your book means by:
transfers of energy from one type to another inside the object
i.e. potential energy of the compressed spring has been converted into kinetic energy of the uncompressed spring.
In the case of the skater the skater's arms correspond to the spring and the rail corresponds to the ground. The skater's arm isn't a spring, of course, because it's chemical energy not potential energy being converted to kinetic energy by the skater's muscles. Nevertheless the same principle applies.
Yes, increasing the -ve charge increases the force of attraction, requiring more work to separate the two charges. The potential energy becomes more -ve because more work is required to separate them.
You are confusing two meanings of "increase" : an increase in magnitude and an increase in sign.
Potential energy increases in magnitude if it gets further away from zero. This is equivalent to the force between the two charges becoming stronger - regardless of whether it is attractive or repulsive. PE increases in sign if it becomes more positive (and decreases if it becomes more negative). This is equivalent to the force between the two charges becoming less attractive and more repulsive.
Increasing the -ve charge makes the potential energy increase in magnitude (the force becomes stronger) but decrease in sign (the force becomes more attractive).
Best Answer
You should keep in mind that the amount of work is constant (so you can do the "if I increase this that other thing decreases"). Then, if you increase the force you exert, but the work you do ought to be constant, then you can only move the object so far.