A unit of any physical quantity is a definite measurement of its magnitude. The term potential energy was first introduced by the 19th century Scottish engineer and physicist William Rankine.
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The energy possessed by a body virtue of its state or position is called potential energy. When a stone is lifted from the round to some height, work is done against the force of gravity. This amount of work is stored in the stone in the form of its potential energy. Due to this energy it acquires the capacity of doing work .For example - a stretched rubber, a compressed, a wound up string have potential energy.
How is the Unit of Potential Energy Measured?The potential energy of a body at a height above the ground is measured by the amount of work done in lifting it to this height against the force of gravity. Let a body of mass m be lifted from the ground or earth’s surface to a vertical height h the force F (vertically upwards) needed to lift the body must be just equal to the force of gravity (mg) on the body acting vertically downwards.
Then potential energy of the body at height h is equal to the work done on the body to lift it to a height h. Thus, potential energy is equal force (mg)*displacement (h) i.e. E="mgh," now we know that SI unti for force is newton(N). Height can be measured in length so its unit is metre(m). So the unit for potential energy will be newton-metre.Actually mgh is the gain in potential energy of the system of body and earth.
It has been assumed here that when the body is on the earth’s surface, the potential energy of the body is zero. Thus when a body is projected vertically upward, its potential energy increases. Similarly when a body is dropped, its potential energy decreases.Conclusion for the Unit of Potential EnergyWe can conclude that potential energy is that energy which is stored within a system. The SI units of Potential energy is Joule (J).When a body of mass m is taken from a height h1 to a height h2 above the ground , the gain in potential energy is equal to mg(h2-h1);if h2>h1.Potential energy is considered losses when potential energy is equal to mg (h1-h2); if h1>h2.Its unit will be Joule or newton-metre.