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 tens
27.2N and 39.2N
40.5N and 62.5N
30.4N and 53.7N
16.6N and 27.3N

Answer 1

Answer on Question #45338, Physics, Mechanics | Kinematics | Dynamics

Task: 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

27.2N and 39.2N

40.5N and 62.5N

30.4N and 53.7N

16.6N and 27.3N

Solution:

$$\begin{array}{l} \sum F_{x} = -F + T \cos \theta = 0 \\ \sum F_{y} = T \sin \theta - W = 0 \\ \Rightarrow T = \frac{F}{\cos \theta} = \frac{30}{\cos \theta} \\ W = T \tan \theta = 30 \tan \theta \\ \end{array}$$ $$\begin{array}{l} T^{2} = F^{2} + W^{2} \\ T^{2} = W^{2} = 900 \Rightarrow W = 30N \\ \end{array}$$

Answer: tension ≈ 53N, W = 30N.