Launching cart on track without air

If we turn off the air flow we now have a cart with finite friction. The mechanical energy injected through the compression of the spring just causes a small displacement of the slide which then remains stationary with no visible sign of mechanical energy. The frictional force between slide and track have dissipated the mechanical energy. We can use the measured displacement to determine the coefficient of friction between slide and track. When we apply conservation laws it is important to prudently choose initial and final states and to be aware of his choice. In this case we are really un-interested in what the velocity of the brick was during its motion. We therefore choose

Initial State:

Brick at rest spring compressed

Final State:

Brick at rest spring decompressed

We write the Kinetic Energy Work theorem:

Where

denotes the work performed by the spring and

is the work performed by friction. Inserting these results and that and with our choice of initial and final states we get

We confirm that increases for smaller values of d as expected. Putting in numbers we get

If desired we can measure directly by measuring the force required to pull the loaded slide along the track. This experiment yields

in good agreement with the previous result.