I know this question might sound silly, but I just started learning physics and struggling to understand when energy is conserved.

The statement "When there are only conservative forces on (or in?) the specific system" is just not satisfying enough for me I guess. Given these two problems how would I know whether or not energy is conserved?

  1. I have been asked to answer what is the maximum height $H$ a $30\ \text{kg}$ child can be lifted up given that the swing's ropes can only lift $50\ \text{kg}$.

I wanted to think of $\frac{1}{2}mv^2=mgH$ to find the speed and so the radial acceleration but then I asked my self: Isn't the tension of the rope is a non-conservative force? What is my system here? If it's just the swing or swing+ropes? And if it's the latter wouldn't the ceiling will produce external force?

  1. In this situation I was asked to say if there is conservation of energy and momentum in the system of weights+table+spring given the floor is frictionless (can't see in pic) and there is friction between weights and table.

Again I'm certain that the potential energy here is wasted on work of friction inside the system, but why here there's no conservation unlike the first problem? Looking on this whole system as one body isn't there only gravitational force (Because floor is frictionless)?

enter image description here

I tried looking on the web but still couldn't fully understand the terms. How would I know if there is conservation of energy? In what cases even if there's an non conservative force does energy conserve? Does it matter what system I choose?


  • $\begingroup$ In the 2nd problem you first state that there is friction between the weights and table, then you say that there is only a gravitational force. Which is correct? $\endgroup$ – sammy gerbil Jul 5 '18 at 8:11
  • $\begingroup$ Thanks for you comment, I meant that between weights and table there is friction, between table (in blue) and floor under it (not in picture) there is not friction. $\endgroup$ – Evy Jul 5 '18 at 8:21
  • $\begingroup$ If there is sliding friction then there is work being done against friction, so these forces are non-conservative. It does not make any difference if the forces and the work being done are internal or external. $\endgroup$ – sammy gerbil Jul 5 '18 at 14:32

Energy is always conserved. It is transformed into other forms like heat and sound which are not useful or cannot be recovered. What you are asking about is the conservation of mechanical energy - ie the sum of potential and kinetic energies.

Generally mechanical energy is conserved unless energy is being dissipated due to friction. This means that rough surfaces are sliding against each other. It also includes air resistance (drag) and internal friction, such as an elastic band getting hot when stretched and relaxed many times.

External forces which do no work on the system do not alter its mechanical energy, so they are conservative.

See The Conservation of Mechanical Energy.

  • $\begingroup$ Do you mean that in the first problem the tension does no work on the swing so the swing by itself is affected only by gravitational force? If so then why tension does no work? $\endgroup$ – Evy Jul 5 '18 at 8:25
  • $\begingroup$ That is correct. The tension does no work because is there is no motion in the direction of the force at either end of the string. $\endgroup$ – sammy gerbil Jul 5 '18 at 14:29

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.