Lifting a fuel assembly


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? fuel lifter


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*t2. In this situation h0 and v0 are zero and h=2.5 at t=1.5 so
2.5=1/2*a*1.52, 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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