A 20. kg suitcase at the baggage handling facility of an airport has an initial

Question

A 20. kg suitcase at the baggage handling facility of an airport has an initial speed of 8.0 m/s and slides to rest due to friction on a flat, horizontal surface. The coefficient of kinetic friction for the suitcase on the surface is 0.20. Use the following two methods to calculate the average power produced by friction as the suitcase comes to rest: (a) Use Newton’s 2nd Law to find the acceleration, use constant acceleration equations to find x and t, then calculate the work done by friction and finally the power. (b) Use the work-energy theorem to find the work (from the change in kinetic energy), and then find the power (using the t found in part (a)). Be sure to include the proper sign on the work done by friction.

Explanation / Answer

P = W / t
Fk = uk * N
Fk = 39.2 N

F = ma, W of suitcase = mg = 196N
N = W = mg
Force of Friction magnitude = umg
Since force of friction is the only horizontal force on the suitcase,
a = F / m = umg / m = ug
a = 0.20*9.80m/s² = 1.96m/s²

We now know vf, vi, a, we want time.
a = v / t
a*t = v
t = v / a
t = (0 - 8.0m/s) / (-1.96m/s²)
t = 4.08s

Now we want to find distance
v² = vi² + 2ad
(v² - vi²) / 2a = d
d = 64.0m²/s² / 3.92 m/s²
d = 16.32m

W = Fd
Ek = Fd
1/2mv² = 39.2N * 16.32m = 640 J = W / t = P = 640 J / 4.08s = 156.8 W
W = 640J
P = 156.8 W

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