An 80.0-cm, uniform, 48.0-N shelf is supported horizontally by two vertical wire

Question

An 80.0-cm, uniform, 48.0-N shelf is supported horizontally by two vertical wires attached to the sloping ceiling. A very small 23.0-N tool is placed on the shelf midway between the points where the wires are attached to it. The left wire is 25 cm long at the very left end of the shelf, while the right wire is 75 cm and is 20 cm away from the right end of the shelf.

Find the tension in the left wire and the tension in the right wire.

Thank you!

(I'm having problems with this because I cannot calculate total tension. T1+T2-Wtool-Wshelf=0

Is T= ((Wtool x 0.3m) + (Wshelf x 0.4m)) / 0.6m? If so, I get T= 43.5 N. But how do I now find T1 and T2?

Explanation / Answer

You'll have to deal with torque. Remember that the shelf will want to rotate around it's center of mass, then have each of the tensions and the tool put a torque on the shelf. Also sum up the forces like you did:

Fy = T1 + T2 - mshelf*g - mtool*g = 0

The center of mass is at .4 meters from left end (L = .8 m)

The tool is located .3 meters from left end (draw a picture)

shelf gravity is excluded from torque as it will act through the axis of rotation.

T = - T1*(L/2) + T2*(L/2 - .2) + mtoolg(.1) =0

solve for T1, plug into second equation.

T1 = msg + mtg - T2

-.4(msg + mtg - T2) + .2*T2 = -mtoolg(.1)

.4T2 + .2T2 = -.1mtg + .4msg + .4mtg

.6T2 = .3mtg + .4msg

T2 = 1/2mtg + 2/3msg = 43.5

T1 = msg + mtg - T2

T1 = msg + mtg - 1/2mtg - 2/3msg

T1 = 1/3msg + 1/2mtg = 27.5

T1 + T2 = 71

Fgt + Fgs = 23 + 48 = 71 N

T1 = 27.5, T2 = 43.5 N

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.