A 50.0- c m , uniform, 54.0- N shelf is supported horizontally by two vertical w

Question

A 50.0-cm, uniform, 54.0-N shelf is supported horizontally by two vertical wires attached to the sloping ceiling (the figure (Figure 1) ). A very small 16.0-N tool is placed on the shelf midway between the points where the wires are attached to it.

A)  Find the tension in left wire.

B) Find the tension in right wire.  

A 50.0-cm, uniform, 54.0-N shelf is supported horizontally by two vertical wires attached to the sloping ceiling (the figure (Figure 1) ). A very small 16.0-N tool is placed on the shelf midway between the points where the wires are attached to it. Find the tension in left wire Find the tension in right wire.

Explanation / Answer

T1 = left wire's tension force
T2 = right wire's tension force

small tool's weight = 16 N {acts 15 cm from left hand end of shelf}
shelf weight = 54 N (acts 25 cm from left hand end of shelf}
Submation F = 0 {vertical direction}
T1 + T2 = 16 + 54 = 70 N
T1 = 70 - T2

Now apply Static Equilibrium to all Torques (moments) acting on shelf,
take LEFT-END (or UR choice) of shelf location as PIVOT point for Submation torques:
let CW torque be positive

Submation torques = 0 = (16)(0.15) +(54)(0.25) - (0.3)T2
0.3T2 = 2.4 + 13.5 = 15.9

T2 = 15.9/0.3

    = 53 N

T1 = 70 - 53 = 17 N

(a) The tension in left wire is 17 N

(b) The tension in right wire is 53 N

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