Home » Physics » How to apply law of conservation of energy in mechanics

How to apply law of conservation of energy in mechanics

We often comes across the problems in mechanics where we need to apply the law of conservation of energy where gravitational potential energy or gravity is involved . For solving such problems you can consider the following problem solving strategy,

  1. First of all define the system which includes all the interacting bodies . Now choose a zero point for gravitational potential energy according to your convenience.
  2. Select the body of interest and identify the point about which information is given in the question. Also identify the point where you want to find out asked quantity about the body of interest.
  3. Check for the possibility of the presence of non-conservative forces. If there are no non-conservative forces present then write down the energy conservation equation for the system and identify the unknown quantity asked in the question.
  4. Solve the equation for the unknown quantities asked in the question by substituting the given quantities in the equation obtained.

If only conservative forces involved like Gravity

Total Energy at point A = Total Energy at point B

If non-conservative forces like Friction are involved, we need to write the energy loss in overcoming Friction

Total Energy at Point A – Total Energy at point B = Workdone to overcome friction forces


$\Delta U + $\Delta K.E$ = work done by friction

Solved Examples


An object of mass M slides downward along a plane inclined at angle $\theta$.
The coefficient of friction is k
Find d(U + KE)/dt
(a) $kmg^2cos \theta (sin \theta – kcos \theta)$
(b) $kmg^2sin \theta (sin \theta – kcos \theta)$
(c) $kmg^2 (sin \theta – kcos \theta)$
(d) none of the above
$ma = mgsin \theta – kmgcos \theta$
$a = gsin \theta – kgcos \theta$
So v = u + at
$v = g (sin \theta – kcos \theta)t$
now $\Delta U + \Delta K.E$ = work done by friction
d(U + E)/dt = friction force. velocity
$= kmg cos \theta \times g (sin \theta – kcos \theta)$
$=kmg^2cos \theta (sin \theta – kcos \theta)$

Related Articles

How to Solve Equilibrium and Potential energy Questions Effectively for JEE Examination
Energy facts
How to find the force if you know the potential energy
How to solve Work And Energy/kinetic energy problems
Download Class 10 Physics formulas and summary pdf
How to find workdone by several forces acting on a object

Leave a Comment

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.