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 container during the lift is 5.4 m/s. The containers are initially at rest on the dock.

The container has a mass of 1037 kg and the total distance the container is lifted is 9.7 m.

What is the tension force in the cable used to lift the container during the first half (accelerating upwards) part of the lift?

Give you answer in Newtons to at least four digits. Do not include units in your answer

Explanation / Answer

given data
container speed = 5.4 m/s.
container mass = 1037 kg
height = 9.7 m
for constant acceleration from rest

y = ½at²
and
v = at
y = ½vt
t = 2y/v
so the first half of the lift takes
t = 2(9.7/2)/5.4
t = 1.796 s

as
v = at
a = v/t

a = 5.4/ 1.796
a = 3 m/s²

from Newton
F = ma
F = m(g + a)
F = 1037(9.81 + 3) =13283 N

F = 13.283 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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