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Chapter 6: Q.32 (page 155)

You and your friend Peter are putting new shingles on a roof pitched at 25掳. You鈥檙e sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.0 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 0.55, with what speed should you push the box to have it gently come to rest right at the edge of the roof?

Short Answer

Expert verified

The speed that we should use to put the box at the edge of the roof is2.72m/s

Step by step solution

01

Content Introduction

The friction force is proportional to the normal force N exerted by the wall against the block in which the roof inclined at胃.

02

Content Explanation

The frictional force is given by Nwhere N=渭smgcos胃

From the force equation F=mamgsin胃-渭smgcos胃=maa=g(sin胃-渭scos胃)

The above equation is the key to solving the acceleration of the box

We are given:

渭s=0.55g=9.81m/s2s=5.0m

Use the equation where

vf2=vi2+2asvi2=0-2脳9.81(sin25-0.55脳cos25)脳5vi=2.72m/s

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