Thread: Tension Question

A crane is lifting a crate mass 600kg vertically.
i)If the crate is travelling at a constant speed, find the tension in the lifting cable.
ii)If instead the crate is accelerating upwards at 0.02m/s, find the tension in the lifting cable.

Cheers

part i)

when the mass is moving a t a constant speed the acceleration of the mass is 0 ms^-1.

Using newton's second law of motion:

resultant force, F = ma

F = T - mg
where T = tension in the cable

T - mg = ma →(1)
but a = 0

T - mg = 0
T = mg
T = 600(9.81)
T = 5886 N

part ii)
given now that the mass accelerates upwards with an acceleration of 0.02 ms^-1. To achieve this the tension in the cable must be larger than the weight of the mass

from (1)
T - mg = ma
T = m(a+g)
T = 600(0.02+9.81)
T = 5898 N