# [Math] Physics Conservation of Energy Problem

physics

In the figure below, a block is released from rest at height $d = 24 \; \text{cm}$ and slides down a frictionless ramp and onto a first plateau, which has length $d$ and where the coefficient of kinetic friction is $0.50$. If the block is still moving, it then slides down a second frictionless ramp through a height of $d/2$ and onto a lower plateau, which has length $d/2$ and where the coefficient of kinetic friction is again $0.50$. If the block is still moving, it then slides up a frictionless ramp until it (momentarily) stops.

(b) Give the stopping point of the block, either as a distance along the first or second plateau (this would be a final stop) or as a height on the ramp at the right (this would be a momentary stop because the block will slide back down the ramp).

Based on the title of your question I assume you know that energy conservation is going to play a role.

You've only described a situation and not an actual question so I don't know what you are trying to compute. But here is some general advice.

Look at the initial state of the block. What are its potential and kinetic energies? This should give you an initial value for the energy.

At each stage its hits a horizontal surface with friction. This means energy isn't conserved right? How does the friction change the energy. How do forces in general change energy? Hint: Read up on the work energy theorem.

This should be enough to get you started.

This might help: $\Delta E =$Work Done$= F \cdot d$