A crane is being used to lift a container onto a cargo ship. The crane initially

Question

A crane is being used to lift a container onto a cargo ship. The crane initially lifts the container up with a constant positive (upwards is positive) acceleration, a lift . The crane then reduces the tension in the cable so that the container slows to a stop with a constant negative (downward) acceleration, astop=-3alift. Assume the acceleration goes directly from upwards to downwards with no time between the two. The container has a mass of 592.8 kg, the total distance the container is lifted is 6.4 m, and the tension in the cable lifting the container is 6357 N while the container is accelerating upwards. What is the largest velocity of the container during the entire lift? Give you answer in m/s to at least three digits.

Explanation / Answer

From Newton's second law

ma = T - mg

a = (T - mg)/m

a = (6357 - 592.8 x 9.8)/592.8 = 0.92 m/s^2

we know from eqn of motion

v^2 = u^2 + 2 a S

u = 0 => s = v^2/2a

we have, S = s1 + s2 = 6.4 m

v^2/2a + v^2/2a' = 6.4

given that a' = 3 a

v^2/2a (1 + 1/3) = 6.4

v^2/2 x 0.92 (4/3) = 6.4 => v = sqrt [(6.4 x 3 x 2 x 0.92)/4] = 2.972 m/s

Hence, v = 2.972 m/s

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