A 4.00-kg box sits atop a 10.0-kg box on a horizontal table. The coefficient of

Question

A 4.00-kg box sits atop a 10.0-kg box on a horizontal table. The coefficient of kinetic friction between the two boxes and between the lower box and the table is 0.600, while the coefficient of static friction between these same surfaces is 0.800. A horizontal pull to the right is exerted on the lower box, as shown in the figure, and the boxes move together. What is the friction force on the UPPER box? A 4.00-kg box sits atop a 10.0-kg box on a horizontal table. The coefficient of kinetic friction between the two boxes and between the lower box and the table is 0.600, while the coefficient of static friction between these same surfaces is 0.800. A horizontal pull to the right is exerted on the lower box, as shown in the figure, and the boxes move together. What is the friction force on the UPPER box?

Explanation / Answer

The first question to ask is: does anything move at all? Is 150 N enough to get things sliding? Let's find out.
The combined mass of the boxes is 14 kg, so the normal force is 14* 9.8 = 137.2 N. Therefore, the STATIC frictional force is 137.2 * 0.8 = 109.76 N, which is less than 150 N. So, theseboxes are definitely going to slide.
..
The kinetic friction can be found using the normal force as well:Fk = μk * FN = 0.6 * 137.2 =82.32 N.
Therefore, the net force on this system is 150 - 82.32 = 67.68N. Now we can find the acceleration of the whole thing:
F = ma
67.68 = 14 * a
a = 4.83 m/s2
So, since both boxes undergo this acceleration, the top box musthave its force provided via friction in order to achieve thisacceleration. We can find that frictional force using F = maagain:
F = ma
F = 4 * 4.83
F = 19.32 N
Since the problem statement says the upper box stays on top of thelower box, we can claim that this is indeed the frictional forcegiven to the upper box.

http://www.chegg.com/homework-help/questions-and-answers/400kg-box-sit-atop-10kg-box-horizontal-table-thecoefficient-kinetic-friction-boxes-between-q798103

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