Question

A 0.16-g spider hangs from the middle of the first thread of its future web. The thread makes an angle 7.2* with the horizontal on both sides of the spider. (A) What is the tension in the thread? (B) If the angle made by the thread had been less than 7.2*, would its tension have been greater than, less than, or the same as in part (A)? Explain.

Answer 1

Let T be the tension in both threads. (A horizontal force balance will show that T is the same on both sides if the angles are the same).

A vertical force balance requires that:

(A)
2 T sin7.2 = M g
= 1.6*10^-4 kg * 9.8 m/s^2
= 1.57*10^-3 Newtons
T = 1.57*10^-3/(2 sin7.2) = ____ N

(B) What happens to T when the angle changes?

(The sine of an angle between 0 and 90 degrees increases with the angle.)