Problem 7-65 Energy cons. with friction - Part 3 - B

A box of apples (mass \(22\; kg\)) slides down a ramp inclined at \(44^\circ\) to the horizontal. The fiction force on the box has a magnitude of \(79\; N\). If the box starts from rest and slides \(2.5\; m\) along the ramp, determine:

(a) the work done by friction
(b) the box's final kinetic energy (using conservation of energy)
(c) the thermal energy produced.

[Ans. (a) \(-2.0\times 10^2 \;J\)   (b) \(1.8\times 10^2\; J\)   (c) \(2.0\times 10^2\; J\) ]

Accumulated Solution

FBD with all angles and forces indicated.

\(W_f = fd\\ W_f = (-79 \;N)(2.4 \;m) = -2.0\times 10^2\; J\; \text{ (answer to part (a))}\)

Correct! The force f and the distance moved d are in opposite directions, so the work done must be negative.

If \(E_K\) is Kinetic Energy, \(E_P\) is gravitational Potential Energy and \(E_f\) is energy lost due to friction then:

(A)  \(E_P + E_f = E_K\)

(B)  \(E_P = E_f + E_K\)

(C)  \(E_P = E_K - E_f\)

(D)  \(E_f = E_P + E_K\)