Question

A playground ball that is hollow within rolls down a ramp with an incline of 42 deg (relative to the x-axis).

1) What does the FBD look like with all forces acting on the sphere with arrows and conventional symbols? How does a titled xy look next to the diagram?

2) What is the static friction coefficient should the playground ball be on the verge of slipping? Use the x, y, and angular versions of N2L in order to find 3 eq in 2 unknown values, should we treat m (mass) and r (radius) as known givens. Get rid of 2 unknowns that provide no value, which will result in the coefficient of friction as it only depends on the incline angle.

Answer 1

μ is the coefficient of static friction and it is obtained as a function of angle alone.

The coefficient of friction in this case is 0.36.

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