# Conservation of energy conditions

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)?

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?

Thanks.

• 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? – sammy gerbil Jul 5 '18 at 8:11
• 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. – Evy Jul 5 '18 at 8:21
• 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. – sammy gerbil Jul 5 '18 at 14:32