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A particle of mass m slides down a fixed, frictionless sphere of radius R. starting from rest at the top.
a. In terms of m, g, R. and ?, determine each of the following for the particle while it is sliding on the sphere.
i. The kinetic energy of the particle
ii. The centripetal acceleration of the mass
C1985M2. An apparatus to determine coefficients of friction is shown above. At the angle ? shown with the
horizontal, the block of mass m just starts to slide. The box then continues to slide a distance d at which point it hits
the spring of force constant k, and compresses the spring a distance x before coming to rest. In terms of the given
quantities and fundamental constants, derive an expression for each of the following.
a. µs
b. ?E, the loss in total mechanical energy of the block-spring system from the start of the block down the incline
to the moment at which it comes to rest on the compressed spring.
the coefficient of static friction.
c. µk, the coefficient of kinetic friction.
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