To practice Problem-Solving Strategy 5.1 for equilibrium problems. A pair of stu

Question

To practice Problem-Solving Strategy 5.1 for equilibrium problems.

A pair of students are lifting a heavy trunk on move-in day (Figure 1) . Using two ropes tied to a small ring at the center of the top of the trunk, they pull the trunk straight up at a constant velocity v? . Each rope makes an angle ? with respect to the vertical. The magnitude of the weight of the trunk is w.

Intuitively, what should the value of T be if the students stand close together so that the ropes are virtually vertical?

Explanation / Answer

Since the trunk moves up with constant velocity, By Newton's first law, net force on trunk is zero.

which means vertical component of tension balances weight w and meanwhile horizontal component cancel each other.

2T cos = w

T = w/2cos

Hence the value of T is w/2cos and if is very small(as the students stand close togather) , T = w/2

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