A block is released from rest at the top of a quarter-circle curved frictionless surface. The radius of the curvature is r. When the block reaches the bottom of the curvature it slides for a distance x on a rough horizontal surface with coefficient of friction μ until it comes to rest. A. Derive an equation for the stopping distance of the block in terms of m, μ, r, and fundamental constants. b. On the graph below, make a sketch of the friction force as a function of distance along the rough surface. Label the graph with appropriate units. c. Describe how the graph could be used to calculate the work done by friction over an arbitrary distance x along the rough surface.

The radius of the curve is changed to 2r and the experiment is repeated.

d. A student reasons that the block will take twice the time to stop as it did with the curve with radius r. Is the
student’s reasoning correct?
___ Yes ___ No
e. In a clear, coherent paragraph-length response that may also contain diagrams and/or equations, explain your
reasoning.
f. Compare the energy ET of the block-path system when the block is at the top of the curve, to the energy EB
when the block is at the bottom of the curve before entering the rough horizontal surface.
ET EB ET = EB
g. Explain you reasoning.