Question

A 30 kg child climbs 15 meters up a tree when he stops to have a look around. What is the child's potential energy in joules?
[Assume g=$10m/{s^2}$]
A. 1500
B. 3000
C. 4500
D. 6000

Answer 1

Hint: When we do any work against the conservative force then the work done by us will be stored in the form of potential energy in the system and potential energy increases. Along the direction of conservative force then potential energy of the system decreases.
Formula used:
$U = mgh$

Complete answer:
Let us assume there is an object. We are displacing that object up very slowly which means at every instant we can assume its velocity will be zero. When we are moving an object upwards which means that we are displacing the object against the gravitational force. That literally means we are doing some work and according to conservation of energy that work will not go in vain. It will get converted in some form and that is nothing but in the form of potential energy.
If we clearly observe the above case, as the object is moving against gravity i.e as the work done by gravity is negative, the potential energy of the system is increasing.
Hence from the above relation we have the formula ${F_c} = - \dfrac{{dU}}{{dx}}$
${F_c}$ is conservative force and ‘U’ is the potential energy and negative sign indicates that along the direction of conservative force, potential energy of the system decreases.
Here conservative force is its weight so ${F_c} = mg$
We get the expression of the potential energy of mass ‘m’ at height ‘h’ as
$U = mgh$
Here mass is 30kg and height is 15 meters. So gravitational potential energy will be
$\eqalign{
  & U = (30)(10)(15) \cr
  & \Rightarrow U = 4500J \cr} $

Hence option C will be the answer.

Note:
Potential energy is valid only if conservative forces are present. Gravity, spring force are the examples for conservative forces. Law of conservation of energy is valid everywhere but the law of conservation of mechanical energy is valid only when no non conservative force acts. Mechanical energy means the sum of potential and kinetic energies.