Question

A rope suspended from a ceiling supports an object of weight W at its opposite end. Another rope tied to the first at the middle is pulled horizontally with a force of 30N. The junction P of the ropes is in equilibrium. calculate the weight W and the tension T in the upper part of the first rope.
a) 40.5N and 52.5N
b) 16.6N and 27.3N
c) 30.4N and 53.7N
d) 27.2N and 39.2N

Answer 1

Answer on Question #68396 – Physics – Mechanics | Relativity

A rope suspended from a ceiling supports an object of weight W at its opposite end. Another rope tied to the first at the middle is pulled horizontally with a force of 30N. The junction P of the ropes is in equilibrium. calculate the weight W and the tension T in the upper part of the first rope.

a) 40.5N and 52.5N

b) 16.6N and 27.3N

c) 30.4N and 53.7N

d) 27.2N and 39.2N

Solution.

Figure 1

The equilibrium condition for the point P is

$$\overrightarrow {T _ {1}} + \overrightarrow {T _ {2}} + \overrightarrow {W} = 0; \overrightarrow {T _ {1}} + \overrightarrow {T _ {2}} = - \overrightarrow {W} = \overrightarrow {P K};$$

We use the Pythagorean theorem for a right triangle $PKT_{1}$ (Fig. 1)

$$T _ {1} ^ {2} + W ^ {2} = T _ {2} ^ {2}; T _ {1} = 3 0 N; T _ {2} ^ {2} - W ^ {2} = 9 0 0;$$

We now verify each of the answers:

a) $52.5^{2} - 40.5^{2} = 2756.25 - 1640.25 = 1116$

b) $27.3^{2} - 16.6^{2} = 745.29 - 275.56 = 469.73$

c) $53.7^{2} - 30.4^{2} = 2883.69 - 924.16 = 1959.53$;

d) $39.2^{2} - 27.2^{2} = 1536.64 - 739.84 = 796.8$;

Thus, all the answers are incorrect.

**Answer:**

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