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A metal block of mass m slides on a horizontal surface that has been lubricated with...

A metal block of mass m slides on a horizontal surface that has been lubricated with a heavy oil such that the block su?ers a viscous resistance that varies as the three-halves power of the speed, that is, F(v) = −cv3/2. If the block is given an initial speed v0, calculate (a) the velocity as a function of time v(t) and (b) the velocity as a function of position. (c) Use these results to show that the block cannot travel farther than 2mv01/2 / c.

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Answer #1

(a)

Velocity as a function of time

b)

c)

Block stops at distance , that is

distance traveled by metal block is

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