The question
Name: ______________________ Date: ____________ A block sliding down a rough ramp (12 points)
Diagram
A block sliding down a rough ramp
A block of mass m is given a push and then slides down a straight ramp tilted at angle θ above the horizontal. The coefficient of kinetic friction between the block and the ramp is μk, and μk < tan θ. Air resistance is negligible.
(a) Draw a free-body diagram of the block while it slides down the ramp. Represent each force with a distinct arrow starting on the dot, and label each force with its type and the object that exerts it. [3 points]
(b) Derive an expression for the size of the block's acceleration in terms of θ, μk and physical constants. Begin your derivation by writing a fundamental physics principle or an equation from the reference information, and make sure it is consistent with your free-body diagram. [3 points]
(c) At t = 0 the block is already moving down the ramp at speed v0. On the axes, sketch a graph of the block's speed against time while it slides down the ramp. On the same axes, sketch with a dashed line the speed against time if the ramp were frictionless and the block started with the same v0. [3 points]
(d) A student repeats the experiment with a block of twice the mass, made of the same material and given the same initial speed v0. Explain how the free-body diagram, your expression in part (b), and the graph in part (c) together show how the new block's speed-time graph compares with the original one. [3 points]