Lifting a fuel assembly

## Question:

A 500kg fuel assembly for a nuclear reactor is being lifted using
the pulley system shown below. It is hoisted upward with constant
acceleration such that h=0 at t=0 and h=2.5m at t=1.5s. What is
the tension in the cable at point A during the motion?
## Answer:

If we have a constant upward acceleration (a) then position (h)
is initial position (h0) plus initial velocity (v0) times time
(t) plus 1/2*a*t^{2}. In this situation h0 and v0 are
zero and h=2.5 at t=1.5 so

2.5=1/2*a*1.5^{2}, or 5=2.25*a, or
a=2.22m/s/s.

The tension in the line attached to the fuel assembly must be
sufficient to overcome a negative 9.8m/s/s gravitational
acceleration and accelerate it upwards at 2.22m/s/s. The total
acceleration provided by this line then is 12.02m/s/s. With a
mass of 500kg this results in a force of 6010N. The mechanical
advantage of a pulley arrangement is equal to the number of lines
lifting on the object, in this case 2. So the tension at A is
3005N or 3.01kN rounded up.
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