Question

A small ring is situated at the center of a hexagon and is supported by six strings drawn tight, all in the same plane and radiating from the center of the ring, and each fastened to a different angular point of the hexagon. The tensions in four consecutive strings are 1 N, 3.5 N, 4.5 N, and 3 N respectively. Find the tensions in the two remaining strings.

Answer 1

The tensions in the two remaining strings are 0 N.

Step-by-step explanation:

To find the tensions in the two remaining strings, we can use the principle of static equilibrium. Since the ring is at the center of the hexagon, the tension in all the strings will be equal.

Let's denote the tensions in the two remaining strings as T1 and T2. We are given the tensions in four consecutive strings as 1 N, 3.5 N, 4.5 N, and 3 N. Since the tensions are equal, we can set up the following equation:

Tension in string 1 + Tension in string 2 + Tension in string 3 + Tension in string 4 + Tension in string 5 + Tension in string 6 = 1 N + 3.5 N + 4.5 N + 3 N + T1 + T2

Simplifying the equation, we get:

T1 + T2 = 12 N - (1 N + 3.5 N + 4.5 N + 3 N)

T1 + T2 = 12 N - 12 N

T1 + T2 = 0 N

So the tensions in the two remaining strings are 0 N.