Two wooden crates rest on top of one another. The smaller top crate has a mass o

Question

Two wooden crates rest on top of one another. The smaller top crate has a mass of m1 = 18.0 kg and the larger bottom crate has a mass of m2 = 85.0 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 = 0.66. 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 = 406.0 N


The tension is increased in the rope to 1177.0 N causing the boxes to accelerate faster and the top box to begin sliding. What is the acceleration of the upper crate?

As the upper crate slides, what is the acceleration of the lower crate?

Explanation / Answer

1) T = 445 = (18 + 95) * acc acc of system mass = 3.938m/s2 acceleration of the small crate answer static friction force between m1 & m2 = 18 * 9.81 * 0.82 = 144.8 N kinetic friction force between m1 & m2 = 18 * 9.81 * 0.66 = 116.54 N 2)frictional force the lower crate exerts on the upper crate = 18 * 3.938 =70.88 N answer since frictional force the lower crate exerts on the upper crate

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