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Let’s suppose that a man is anchored to the back of a spaceship, which is going forward in empty space (no friction) at 100 m/s. Now, this person throws a bag of potatoes applying 1N of force in the opposite direction of the spaceship velocity (and it takes 1 second to throw it). According to the Work formula (W = F * D, where W is Work, F is Force and D is Distance travelled while the force is applied) the work done on the spaceship should be 1N times the space travelled in one second, which is 100 meters (actually the force would accelerate the ship a bit, making the distance 100 meters + a small amount, but let’s ignore that for now). Therefore, the man does 100 Joules of work on the spaceship.

Now, let’s say that the spaceship is going at 1000 m/s and the man throws an identical bag of potatoes out of the ship in the same way, applying 1N for 1 second. During that 1 second, the ship travelled for 1000 m (again, ignoring the acceleration caused by the force applied). The work done now is 1N * 1000 meters, or 1000J.

Is this correct? How is it possible that the man, using the same “strength or force” gives a different amount of energy to the spaceship (100J when the spaceship goes at 100 m/s and 1000J when it goes at 1000 m/s)?

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[...] should be 1N times the space travelled in one second

Not quite. Both the man and the bag are moving equally, and you should think only of the relative motion (how much farther away the bag moves from the man).

This is because the coordinate system is moving with them. Seen from this system, they don't move at all.

When someone moves in an isolated space with no other object to compare with, then who says that they are moving? Who measures the 100 m/s? It must be 100 m/s faster than something else - but why isn't that something else instead moving backwards with 100 m/s and the spaceship being at rest?

Bottom line is that terms like these are relative. Otherwise you would do a tremendous amount of work by moving you book across the table, because the Earth is actually moving at an incredible speed around the Sun.

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