Question

You and your friend Peter are putting new shingles on a roof pitched at 21∘. You're sitting on the very top of the roof when Peter, who is on the edge of the roof, 5.1 mm away, asks you for the box of nails. Rather than carry the 2.3 kgkg 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 0.53, with what speed should you push the box to have it gently come to rest right at the edge of the roof?

Answer 1

3.69 m/s

Step-by-step explanation:

Forces :

mgsin Θ - mumgcosΘ = ma

g x sinΘ - mu x g x cosΘ = a

9.8 x sin 21 - 0.53 x 9.8 x cos 21 = a

a = -1.337 m/s²

so you have final velocity = 0 m/s

initial velocity = ? m/s

Given d = 5.1 m

By kinematics

vf² = vo² + 2ad

0 = vo² + 2 x -1.337*5.1

vo = 3.69 m/s