hello, please include the work. it\'s just question #5::: Two wooden crates rest

Question

hello, please include the work. it's just question #5:::

Two wooden crates rest on top of one another. The smaller top crate has a mass of m1 = 24.0 kg and the larger bottom crate has a mass of m2 = 86.0 kg. There is NO friction between the crate and the floor, but the coefficient of static friction between the two crates is ?s = 0.82 and the coefficient of kinetic friction between the two crates is ?k = 0.64. A massless rope is attached to the lower crate to pull it horizontally to the right (which should be considered the positive direction for this problem).

The rope is pulled with a tension T = 416.0 N (which is small enough that the top crate will not slide). the acceleration of the small crate==3.78 m/s2

In the previous situation, the frictional force the lower crate exerts on the upper crate? 90.76 N the maximum tension that the lower crate can be pulled at before the upper crate begins to slide= 884.86 N

The tension is increased in the rope to 1168.0 N causing the boxes to accelerate faster and the top box to begin sliding. the acceleration of the upper crate== 6.278

QUESTION:: 5) As the upper crate slides, what is the acceleration of the lower crate?

Explanation / Answer

24.0 * 6.278 = 150.672 N

a2 = (1168.0 - 150.672)/86.0 = 11.8 m/s2

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