A 80.0-cm, uniform, 45.0-N shelf is supported horizontally by two vertical wires

Question

A 80.0-cm, uniform, 45.0-N shelf is supported horizontally by two vertical wires attached to the sloping ceiling (the figure (Figure 1) ). A very small 28.0-N tool is placed on the shelf midway between the points where the wires are attached to it.

Part A

Find the tension in left wire.

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Part B

Find the tension in right wire.

A 80.0-cm, uniform, 45.0-N shelf is supported horizontally by two vertical wires attached to the sloping ceiling (the figure (Figure 1) ). A very small 28.0-N tool is placed on the shelf midway between the points where the wires are attached to it.

Part A

Find the tension in left wire.

TL =   N  

SubmitMy AnswersGive Up

Part B

Find the tension in right wire.

TR =   N  

SubmitMy AnswersGive Up

A 80.0-cm, uniform, 45.0-N shelf is supported horizontally by two vertical wires attached to the sloping ceiling (the figure (Figure 1) ). A very small 28.0-N tool is placed on the shelf midway between the points where the wires are attached to it. Part A Find the tension in left wire. TL = N SubmitMy AnswersGive Up Part B Find the tension in right wire. TR = N SubmitMy AnswersGive Up

Explanation / Answer

Together both wires must support 108.0 N The slope of the ceiling is not relevant.
We need to find the centre of mass.

Taking it from the left end, the shelf has a force of 80 N at a distance of 40 cm
And the tool has a force of 28 N at a distance of 30 cm

Total moment is 4040 Ncm
and distance is total moment/ total force = 4040/108 = 37.41 cm from the left end.

Now consider the plank. If there is any rotational moment at all around the left end, the plank must pivot and fall. The only upwards moment is provided by the right hand wire.
This must also produce a moment of 4040 N but in the opposite direction ( upwards)
So Fr * 40 = 4040
Fr = 101 N upwards

Fl + Fr =108 so Fl = 7 N Upwards.

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