 # Gravitational potential energy can be +ve , -ve or zero. Can anyone explain me this sentence with eg.? Also potential energy of a spring is always +ve. Is it right i mean we can stretch as well as can compress a sprinp.

11 years ago

Dear  RAjAT ,

The important point to understand is that potential energy is always relative to some point. What the potential energy is at a point really doesn't matter- it is the change between to points that is important. We can always choose a reference point at which the potential energy is 0. It happens that to be simplest, for gravitational problems, to take potential energy to be 0 "at infinity". Since potential energy increases as you move away from the center of a gravitating system, the potential energy is negative at any finite distance.

it should be pointed out that "gravitational potential energy is negative" is only true for problems with distances large enough to require the inverse square law. Consider the problem, "A 1 kg mass is dropped from the top of a 100 m cliff. What is its speed just before it hits the ground?"

A fairly standard way to do that is to say that the potential energy is mgh= 1(9.8)(100)= 980 Joules (positive!) while the kinetic energy is 0 so the total energy is 980 Joules at the top of the building. At the bottom of the building the potential energy is 0 while the kinetic energy is (1/2)v2 and so the total energy is (1/2)v2. Neglecting air resistance, by "conservation of energy" we have (1/2)mv2= 980 so v2= 1960 and v= 44.2 m/s. We have, implicitely, taken the "reference" point, for 0 potential energy, to be at the bottom of the building.

But we could just as easily take the "reference" point to be at the top of the building. Then, initially, we have both kinetic and potential energy to be 0: the total energy is 0 Joules. At the base of the building, the potential energy is -mgh= -980 Joules. Conservation of energy now give (1/2)mv2- 980= 0 giving exactly the same answer.

All the best.

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