Question

A 0.89 kg ball is connected by means of two ideal strings to a vertical, rotating rod. The strings are tied to the rod and are taut. The upper string is 28.0 cm long and has a tension of 31.1 N, and it makes an angle θ2 = 62.0° with the rod, while the lower string makes an angle θ1 = 51.0° with the rod. (a) What is the tension in the lower string?

Answer 1

The diagram for this scenario is:

Determining the tension of the bottom string in the y-direction using Newton's second law. We'll make ''down'' the positive y-direction.

ΣF_y = ma_y

ΣF_y = 0

mg+T_y - 31.1cos62 = 0

T_y = 31.1cos62 - (0.89)(9.8)= 5.9 N

Using the angle the bottom string makes with the pole and the y-tension in the string gives us the tension in the bottom string.

T = 9.38 N is the tension in the lower string.