A block of mass m is released from rest at a height hi and slides down a frictio

Question

A block of mass m is released from rest at a height hi and slides down a frictionless curved ramp onto a table-top. The table top is of length l and the coefficient of kinetic friction between it and the block is u. The bock then slides back up a second frictionless ramp to a height hf.

a. Find an expression for hf in terms of the variables above.

b. What is the minimum initial height hi, required for the block to be able to climb to a final height hf that is greater than zero?

c. What is the value of hf for m=.5 kg, u=.3, l=.5, and hi=.5 m?

d. What values did you not n eed to find your solution?

Explanation / Answer

a)

iniital energy E1 = m*g*hi

work done by friction Wf = u*m*g*l

final energy E2 = m*g*hf

from energy relation

E1 - W = E2

m*g*hi - u*m*g*l = m*g*hf

hf = hi-u*l <<<_---answer

+++

b)

hi = hf + ul

(c)

hf = 0.5 - (0.3*0.5) = 0.35 m

(d)

mass m = 5 kg

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