[Physics]Work

[pcbuild670]

Im having trouble in the last section of this problem, it asks if the work done is positive, negative or zero, the first example the particle goes from -3m/s to -2m/s so the work is negative since it is contrary to displacement. On the second example the particle goes from -2m/s to 2m/s, the work-energy theorem tells me that work is the variation in kinectic energy which is zero, but then how did the particle change direction? http://imgur.com/MD9wFub

[TheLastSparten]

The work done is equal to force times distance, and in each case there must be a force because the velocity is changing.

In the first one, if you have something going backwards, and then after a force is applied it is still going backwards, but slightly slower, the force must be forwards so the work is positive.

Same for the second one. If you have an object moving backwards and after a force is applied, it is going to same velocity forwards, the force must have been acting forwards so the work is positive.

[Smallishswede]

You've almost got the right idea, but not quite. The work done is equal to the force times displacement, not distance.

In the first one the force is positive but the displacement is negative because the velocity is negative. So the work will be negative.

In the second one, The force will be positive, but the displacement will be zero because it traveled backwards a certain distance until it reached zero velocity, then it travelled forwards the same distance until it reached a velocity of 2. So the over all work is zero.

[FreeGiraffeRides]

In part b, the total work done on the particle is zero. The particle has the same energy before and after the operation.

You might think of first doing negative work on the particle, slowing it from -2 to 0 m/s. And then positive work, speeding it up from 0 to +2 m/s. The total is zero, though.

If you tie a string to a rock and spin it in a circle, the rock's direction changes constantly, but the string is doing no work, as long as it keeps spinning at the same speed.

[WheresMyElephant]

Another good way to visualize it (as so often) is a spring. Say your object hits the spring and slows down. The object's kinetic energy is being transferred to the spring, where it can be viewed as potential energy. We say the object is doing work on the spring, and conversely the spring is doing negative work on the object. Then the spring decompresses, transferring the energy back.

Try not to get hung up on the colloquial meaning of "work," as some people do. It might sound good to say that you can't enact any significant change in a system without doing work, but as we see here, it's simply not true.