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

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 .

Part A

The initial and final states of the toolbox are illustrated in the figure. Identify the initial speed viof the toolbox and the vertical distance h through which the toolbox moves.(Figure 1)

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.

Part B

Determine the initial and final kinetic energies, Ki and Kf.

Enter the initial and final kinetic energies of the toolbox symbolically in terms of the variables given in the problem introduction (m,g,?,fk,v and d), separated by a comma.

Part C

Determine the initial and final potential energies, Ui and Uf.

Enter the initial and final potential energies of the toolbox symbolically in terms of the variables given in the problem introduction (m,g,?,fk,v and d), separated by a comma. Do not use the variable h introduced in Part A.

Part D

Determine the work Wother done by any nonconservative forces acting on the toolbox.

Enter the work done by nonconservative forces symbolically in terms of the variables given in the problem introduction (m,g,?,fk,v and d).

Explanation / Answer

A) h = dsin@

initial speed = 0

B) initial KE = 0

final KE = mv^2 /2

C) Initial potential energy = mgdsin@

final potential energy = 0

D) Work done by friction = fk*d

Using work energy theorem,

work done by gravity + work done by friction = change in KE

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