Chap. 04 K6 of 10 Problem 6.32 You and your friend Peter are putting new shingle

Question

Chap. 04 K6 of 10 Problem 6.32 You and your friend Peter are putting new shingles on a roof pitched at 25 You're siting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.1 m away, asks you for the box of nails. Rather than carry the 2.3 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 0.53, with what speed should you push the box to have it gently come to rest right at the edge of the roof? Express your answer to two significant figures and include the appropriate units. m/s Provide Feedback Next >

Explanation / Answer

Given,

theta = 25 deg ; d = 5.1 m ; m = 2.3 kg ; uk = 0.53

The acceleration of the block will be:

a = g [sin(theta) - uk cos(theta)]

a = 9.81 (sin25 - 0.53 cos25) = 0.57 m/s^2

from eqn of motion

v^2 = u^2 + 2 a S

v = sqrt (2 a S) = sqrt (2 x 0.57 x 5.1) = 2.41 m/s

Hence, v = 2.41 m/s (upto two decimal places)

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