Potential energy reasoning  |  ProblemYour favorite glass vase, of mass m, sits on the first shelf of a bookshelf, a distance h above the ground.  If instead it were on the third shelf—a distance 3h above the floor—how much more gravitational potential energy would the Earth + vase system have? Group of answer choices0 (no difference)2mgh3mgh6mgh9mgh

The gravitational potential energy of an object is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the ground.

When the vase is on the first shelf, its potential energy is mgh.

When the vase is on the third shelf, its potential energy is mg(3h) = 3mgh.

The difference in potential energy between the third shelf and the first shelf is 3mgh - mgh = 2mgh.

So, the vase would have 2mgh more gravitational potential energy if it were on the third shelf compared to the first shelf.

The gravitational potential energy of an object is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the ground.

In the first scenario, the vase is a distance h above the ground, so its potential energy is mgh.

In the second scenario, the vase is a distance 3h above the ground, so its potential energy is mg(3h) = 3mgh.

The difference in potential energy between the two scenarios is 3mgh - mgh = 2mgh.

So, the Earth + vase system would have 2mgh more gravitational potential energy if the vase were on the third shelf instead of the first.