You and your friend Peter are putting new shingles on a roof pitched at 22 . You

Question

You and your friend Peter are putting new shingles on a roof pitched at 22 . You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.5 m away, asks you for the box of nails. Rather than carry the 2.5 kg box of nails down to Peter, you decide to give the box a push and have it slide down to him. If the coefficient of kinetic friction between the box and the roof is 0.54, with what speed should you push the box to have it gently come to rest right at the edge of the roof?

Explanation / Answer

m = 2.5 kg , uk =0.54, g =9.81 m/s^2, theta =22 degrees

The frictional force is given by µN where N = mgcos

The force equation F = ma

is: mgsin - µkmgcos = ma

a = g(sin - µcos)

Next we use the equation v² = u² + 2as

v = 0, s = 5.5 m

u² = - 2sg(sin - µcos)

= -2*9.81*5.5 (sin(22) - 0.54cos(22))

v^2= -19.6*5.5*(0.3746- 0.5)

u = 3.688 m/s

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