While a roofer is working on a roof that slants at = 36.0 degrees above the hori

Question

While a roofer is working on a roof that slants at = 36.0 degrees above the horizontal, he accidentally nudges his m = 8.50 kg toolbox, causing it to start sliding downward, starting from rest. A frictional force of magnitude fk = 22.0 N acts on the toolbox as it slides. If the box starts d = 4.25 m from the lower edge of the roof, how fast v will the toolbox be moving just as it reaches the edge of the roof? Assume that the acceleration due to gravity is g = 9.80 m/s2

Enter the initial speed and the height symbolically in terms of the variables given in the problem introduction (m,g,,fk,v and d), separated by a comma.

Explanation / Answer

Here,

theta = 36 degree

m = 8.5 Kg

fk = 22 N

d = 4.25 m

let the final speed of the is v

Using work energy theorum

0.5 *m * v^2 = m * g * d *sin(theta) - fk * d

0.5 * 8.5 * v^2 = 8.5 * 4.25 * sin(36) * 9.8 - 22 * 4.25

solving for v

v = 5.19 m/s

the final speed of the toolbox is 5.19 m/s

------------------------------------------

initail speed of toolbox = 0 m/s

for the height = d * sin(theta)

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