# Energy conservation A block of mass m is able to slide on an inclined surface. At the bottom of the incline is a spring of stiffness k. It is our goal here to investigate how the total energy (kinetic + potential) changes as the block slides along the incline:  E = T + Vsp + Vgr.

Smooth incline
Suppose we consider the incline to be smooth. In this case, there is no work done on the system by non-conservative forces. Consider the simulation results below of the block sliding on a smooth incline. These results show that there is a complicated exchange in energy among the spring potential, the gravitational potential and the kinetic energy - however, the sum of these three remain a constant, as expected. Rough incline
Now we consider the incline to be rough. In this case, friction does work on the system. As we have discussed in class, the friction force on the block always opposes the motion of the block, therefore the work is always NEGATIVE. With this, we conclude that the energy decreases monotonically as the block slides along the incline, until the block comes to permanent rest. Consider the simulation results below of the block sliding on a smooth incline. These results show that there is still a complicated exchange in energy among the spring potential, the gravitational potential and the kinetic energy - here, however, the sum of these three  monotonically decreases with the motion, as expected. 