Problem 7-65 Energy cons. with friction - Part 4 - 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

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

Correct!

The initial \(PE \;(\text{initial} \;KE = 0)\) is converted to \(KE\) and energy lost via friction.

The initial \(PE\) is:

(A)   \(mgd\; \sin\theta\)

(B)   \(mgd\)

(C)   \(mgd\; \cos \theta\)

(D)   \(mgh \sin \theta\)