Question

You and your friend peter are putting new shingles on a roof pitched at 25 degrees. you are sitting on the very top of the roof when Peter who is at the edge of the roof directly below you, 5.0m away, asks you for a box of nails. Rather than carry the 2.5kg 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 the 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?

Answer 1

Answer:2.72 m/s

Explanation:

Given

Inclination of shingles$\theta =25^{\circ}$

Length of inclined Plane $s=5 m$

coefficient of kinetic friction $\mu _k=0.55$

Let u be the initial velocity

$F_{net}=mg\sin \theta -f_r$

$F_{net}=mg\sin \theta -\mu mg\cos \theta$

$a_{net}=\frac{F_{net}}{m}$

$a_{net}=g\sin \theta -\mu g\cos \theta$

$a_{net}=4.141-4.884$

$a_{net}=-0.744 m/s^2$ i.e. deceleration

$v^2-u^2=2a_{net}s$

$0-u^2=2\times (-0.744)\cdot 5$

$u=\sqrt{7.439}$

$u=2.72 m/s$