Friction Over a Curved Path

MediumPhysElo Quiz #8

48.Friction Over a Curved Path

+10

A fixed, solid hemisphere of radius

R

rests with its flat base on a horizontal floor. A small block of mass

m

is initially placed on the hemisphere such that the radius from the center of the hemisphere to the block makes an angle of

60^\circ

with the vertical. A person slowly drags the block to the highest point of the hemisphere by applying a pulling force that is always tangent to the surface. The coefficient of kinetic friction between the block and the hemisphere is

\mu_k

. What is the total work done by the person on the block?

\frac{1}{2}mgR(1 + \mu_k)

\frac{1}{2}mgR(1 + \sqrt{3}\mu_k)

\frac{1}{2}mgR\left(1 + \frac{2\pi}{3}\mu_k\right)

\frac{1}{2}mgR(\sqrt{3} + \mu_k)

\frac{1}{2}mgR(2 + \sqrt{3}\mu_k)

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