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

Question

You and your friend Peter are putting new shingles on a roof pitched at 22 degree. You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.4 m away, asks you for the box of nails. Rather than carry the 2.1 kg box of nails down to Peter, you decide to give the box a push and have it slid down to him. If the coefficient of kinetic friction between the box and the roof is 0.50, with what speed should you push the box to have it gently come to rest right at the edge of the roof?

Explanation / Answer

here,

uk = 0.5

theta = 22 degree

r = 5.4 m, mass , m = 2.1 kg

A)

let the speed gained be v

work done by frictional force = potential energy lost - kinetic energy gained

uk * m * g * cos(theta) * (r/cos(theta)) = m * g * ( r * tan(theta)) - 0.5 * m * v^2

0.5 * 2.1 * 9.8 * cos(22) * (5.4/cos(22)) = 2.1 * 9.8 * ( 5.4 * tan(22)) - 0.5 * 2.1 * v^2

v = 3.19 m/s

the speed gained is 3.19 m/s

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