A 60.0-cm, uniform, 46.0 -N shelf is supported horizontally by two vertical wire

Question

A 60.0-cm, uniform, 46.0-N shelf is supported horizontally by two vertical wires attached to the sloping ceiling (see figure). A very small 24.9-N tool is placed on the shelf midway between the points where the wires are attached to it. Find the tension in each wire. Begin by making a free-body diagram of the shelf. (Enter your answers from smallest to largest.)

T = N T = N A 60.0-cm, uniform, 46.0-N shelf is supported horizontally by two vertical wires attached to the sloping ceiling (see figure). A very small 24.9-N tool is placed on the shelf midway between the points where the wires are attached to it. Find the tension in each wire. Begin by making a free-body diagram of the shelf. (Enter your answers from smallest to largest.)

Explanation / Answer

he length of the wires and the slope of the ceiling are irrelevant to the tension since we're apparently letting them be massless and perfectly unyielding. Good problem design, though.

So, we have 2 weights on the wires. The one is the tool, which is midway between the wires. That will contribute equally to each: 11.5 N. Add that on at the end but forget about it until then.

For simplicity, we set the origin to be on the left wire. The torque from gravity and from the right wire need to balance. Both forces are perpendicular to their displacements from the origin, so that keeps things simple.

Torque from gravity = - Torque from right wire
40 cm * (- 48 N) = - 60 cm * F(right)

Well, - 40/60 = - 2/3 -> F(right) = 2/3 * 48 N = 32 N.

That leaves 16 N to achieve force balance on the left wire.

Add in the 11.5 N from the tool to each, and we get

27.5 N (left) and 43.5 N (right)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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