Problem 7-65 Energy cons. with friction - Part 5 - A

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.

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

Correct!

\(mgh = mgd \sin\theta\)

Therefore \(mgd \sin \theta = E_K + 2.0\times 10^2\)

\(E_K = (22\; kg)(9.8 \;m/s^2)(2.5\; m) \ \sin 44 - 2.0 \times 10^2 J = 1.8 \times 10^2 \;J \text{(answer to part (b))}\)

The energy lost due to friction is transformed largely into thermal energy \(= 2.0\times10^2\; J\) (answer to part (c))


You have completed this problem.