Question

While a roofer is working on a roof that slants at 36° above the horizontal, he accidentally nudges his 85.0-N toolbox, causing it to start sliding downward from rest. If it starts 4.25 m from the lower edge of the roof, how fast will the toolbox be mov- ing just as it reaches the edge of the roof if the kinetic friction force on it is 22.0 N?

Answer 1

Answer:

$v = 5.23 m/s$

Explanation:

As the tool box start slipping from the roof we can say that work done by all forces on it will be equal to change in its kinetic energy

so we have

$W_f + W_g = \frac{1}{2}mv^2 - 0$

here we know that

$W_f = - F_f .d$

so we will have

$W_f = - 22(4.25) = -93.5 J$

now work done by gravity is given as

$W_g = mgsin\theta(d)$

$W_g = 85 sin36(4.25)$

$W_g = 212.33 J$

now we have

$212.33 - 93.5 = \frac{1}{2}(\frac{85}{9.8})v^2$

$v = 5.23 m/s$