Question

A stone weigh 200 pounds is suspended from a rope the stone is pulled aside comes to rest when a horizontal force of 130 pounds is applied. What is the tension in the rope? what angle does the rope makes with the horizontal?

Answer 1

By Newton's law, the body will be at rest if the sum of the projections of forces is equal. From here we get the angle of deviation from the vertical.

$$F_T*sin\alpha-F*cos\alpha=0$$ $$tg\alpha=F/F_T=130/200=0.65$$ $$\alpha=33°$$

but we need a tilt angle to the horizontal:

$$\beta=90°-\alpha$$ $$\beta=57°$$

The tension force of the thread is equal to the sum of the projections

$$T=F_t*cos\alpha+F*sin\alpha$$ $$T=239 pounds$$

Answer: 57°, 239 pounds