A crate of mass 11.5 kg is pulled up a rough incline with an initial speed of 1.

Question

A crate of mass 11.5 kg is pulled up a rough incline with an initial speed of 1.50 m/s. The pulling force is 100 N parallel to the incline, which makes an angle of 17.0° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 5.25 m.
(a) How much work is done by gravity?
J
(b) How much mechanical energy is lost due to friction?
J
(c) How much work is done by the 100 N force?
J
(d) What is the change in kinetic energy of the crate?
J
(e) What is the speed of the crate after being pulled 5.25 m?
m/s

Explanation / Answer

Mass m = 11.5 kg Initial speed u = 0 Pulling force F = 100 N Angle = 17 degrees The coefficient of kinetic friction = 0.400 Pulling distance S = 5.25 m (a) Work is done by gravity w = -mg sin x S                                                = -568.83 J (b) Mechanical energy is lost due to friction = -mg cos x S                                                              w' = -65.12 J Here negative sign indicates loss (c)Work is done by the 100 N force w " = F S                                                               = 525 J
(d)The change in kinetic energy of the crate K = Net work done                                                                       = w + w' + w"                                                                       = -108.95 J
(e) The speed of the crate after being pulled 5.25 m is v = ? From work energy theorem , K = ( 1/ 2) m[u 2 - v 2 ]                                       2K / m= u 2 - v 2                                      -18.94 = -v 2                                               v = 4.35 m / s
m/s

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