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You and your friend Peter are putting new shingles on a roof pitched at 24 degrees . You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.0m away, asks you for the box of nails. Rather than carry the 2.1kg box of nails down to Peter, you decide to give the box a push and have it slide down to him.

A) If the coefficient of kinetic friction between the box and the roof is 0.53, with what speed should you push the box to have it gently come to rest right at the edge of the roof?
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The frictional force is given by µN where N = mgcos theta

The force equation F = ma

is: mgsin theta - µmgcos theta = ma

m cancels so,

a = g(sin theta - µcos theta)

where ? = 20 deg, µ = 0.53 and g = 9.81 m/s^2

Next we use the equation v^2 = u^2 + 2as

v = 0, s = 5.0 m

Thus

u^2 = - 2sg(sin? - µcos?)
= -2*9.81*5.0 (sin20 - 0.53cos20)

u = 5.72 m/s
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