Name: Conservation of Mechanical Energy
Uploaded: 2019-07-19
Duration: 5 min 12 s
Description: When a body falls from a height towards the ground, its potential energy decreases but not the total mechanical energy. Let us understand this using data.

Question

Explain 'potential energy'. Give its dimensions and SI unit. Give an example of potential energy other than that of gravitational

P E

.

Accepted Answer

The gravitational force on a ball of mass $m$ is $m g$ . The work done by the external agency against the gravitational force is $m g h$ . This work gets stored as potential energy. Gravitational $P E$ of an object, as a function of height $h$ , is denoted by $U (h)$ and it is the negative of work done by the gravitational force in raising the object to that height.
$U (h) = m g h$
Gravitational force $F = - \frac{d U (h)}{d h} = - m g$
The $- v e$ sign indicates that the gravitational force is downward.
Mathematically (for simplicity, in one dimension), the potential energy $U (x)$ is defined if the force $F (x)$ can be written as $F (x) = - \frac{d U}{d x}$ .

$\Rightarrow \int_{x_{i}}^{x_{1}} F (x) d x = - \int_{U_{i}}^{U_{t}} d U = U_{i} - U_{f}$
The work done by a conservative force such as gravity depends on the initial and final positions only. Its dimensions are $[{ML}^{2} T^{- 2}]$ .
SI unit is joule (J).
Example of $P E$ other than gravitational $P E$ .
(i) Energy associated with the state of compression or expansion of an elastic spring.
(ii) The energy associated with state of separation of charged particles is called electrical potential energy.

Explain 'potential energy'. Give its dimensions and SI unit. Give an example of potential energy other than that of gravitational $P E$ .

Important Questions on Work, Energy and Power

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Explain 'potential energy'. Give its dimensions and SI unit. Give an example of potential energy other than that of gravitational PE.

Important Questions on Work, Energy and Power

Learn and Prepare for any exam you want !

Explain 'potential energy'. Give its dimensions and SI unit. Give an example of potential energy other than that of gravitational $P E$ .