***the two questions relate, I believe you would use the formula found in 1 to s

Question

***the two questions relate, I believe you would use the formula found in 1 to solve 2 but that also could be wrong.

1. Give the standard friction model formula for kinetic friction and, starting from energy considerations, deduce a formula relating final speed of the falling weight when it hits the floor to the initial height, the masses, g and the coefficient of friction. Then, relate the distance fallen and the time to the coefficient of friction. Show the steps including algebra.

2. If the sliding block has mass 500 gm and the falling weight has mass 200 gm, how fast would the falling weight be going when it hit the floor if it started from 1.00 meters up and if the coefficient of sliding friction happened to be .25?

Explanation / Answer

initial energy = potential energy

potential energy = m1gh

m1 = mass of falling block

final energy = 0.5 * m1*v^2 + work done by friction

work done by friction = k * m2 * g * h

k = coefficient of friction

m2 = mass of sliding block

by conservation of energy

initial energy = final energy

m1 * gh = 0.5 * m1 * v^2 + k * m2 * g * h

v = sqrt(2 * gh(m1 - k * m2) / m1)

putting the values we'll get

0.2 * 9.8 * 1 = 0.5 * 0.2 * v^2 + 0.25 * 0.5 * 9.8 * 1

v = 2.71 m/s

velocity when it hit the floor = 2.71 m/s

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