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 = 20.0 kg and the larger bottom crate has a mass of m2 = 88.0 kg. There is NO friction between the crate and the floor, but the coefficient of static friction between the two crates is ?s = 0.8 and the coefficient of kinetic friction between the two crates is ?k = 0.61. 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).
1) The rope is pulled with a tension T = 364.0 N (which is small enough that the top crate will not slide). What is the acceleration of the small crate?
m/s2
2) In the previous situation, what is the frictional force the lower crate exerts on the upper crate?
N
3) What is the maximum tension that the lower crate can be pulled at before the upper crate begins to slide?

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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