A crane is being used to lift a container onto a cargo ship. You need to program

Question

A crane is being used to lift a container onto a cargo ship. You need to program the crane so that it lifts the container with a constant positive acceleration, a, during the first half of the lift and with a constant negative acceleration of the same magnitude, -a, during the second half of the lift. You want to do this so that the maximum speed of the crane is 1.5 m/s. The containers are initially at rest on the dock. The container has a mass of 1150 kg and the total distance the container is lifted is 2.5 m. What force must you have the crane lift the container during the first half (accelerating upwards) part of the lift? Give you answer in Newtons to four digits. Do not include units in your answer.

Explanation / Answer

So if I understand the problem correctly, one needs to lift the container 1.5 m and achieve 4 m/s in doing so. for constant acceleration from rest y = ½at² and v = at so substituting in y = ½vt t = 2y/v so the first half of the lift takes t = 2(1.5)/4 t = 0.75 s as v = at a = v/t a = 4/ 0.75 a = 5? m/s² from Newton F = ma F = m(g + a) F = 1450(9.81 + 5?) F = 22 kN is the upward force needed on the container to meet the required profile in the first half of the lift.

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