6.3.P8a

The apparatus shown in the figure below uses a spring to launch a small block along a track. A latch holds the block of mass m in place against the compressed spring (spring constant k) as shown. When the ring is raised the block is launched along the track.  The part from B to C has significant friction (coefficient of sliding friction, µ). When it reaches D it slides up the ramp to point E. The parts of the track from A to B and from C to E can be considered frictionless for this problem and the size of the mass can be ignored compared to the distances along the ramp.

When the block is launched, it gets through the frictional part, rises up the ramp to point D, a height h above the straight part of the ramp. It then slides back down. On its return, it gets to point B and stops. The distances are shown on the figure and the angle of the ramp is θ as shown.

For the items below write an expression that represents the appropriate energy in terms of the parameters of the problem, k, m, μ, θ, and the distances d₁, d₂, L, h. (Do NOT use any other variables or symbols. Writing "total energy = E" or "KE = ½mv²" will get no credit.)  Use the horizontal part of the track as the "zero" for gravitational potential energy.

(a) The work done by the frictional force as the block passes from B to C.

(b) The potential energy of the block at the point E.

(c) The total work done by the friction force throughout the whole motion.

(d) The total mechanical energy just before the block is released.

Justify your answers.

(e) Presuming that you are given values for k, m, θ, and all the distances, could you find an expression that would allow you to calculate the coefficient of friction μ ? If so, write it and explain what physical principles you are using. If not, explain why not and what you would need to know in order to find μ.

Joe Redish 3/30/15