Question

A flexible chain weighing 43.0 N hangs between two hooks located at the same height. At each hook, the tangent to the chain makes an angle of 42.0° with the horizontal. What is the tension in the chain?

Answer 1

The tension in a chain hanging between two supports can be found using the formula T = W / (2 sin ϴ). In this case, with a chain weight of 43.0 N and an angle of 42.0°, the tension is calculated by dividing the weight by two times the sine of the angle converted to radians.

Step-by-step explanation:

When a flexible chain hangs between two supports at the same height, forming an angle with the horizontal at each end, the tension in the chain can be determined using concepts from Physics, specifically static equilibrium and tension in a chain. In this question, the chain makes an angle of 42.0° with the horizontal, and it has a weight (W) of 43.0 N. Tension (T) in the chain at the points of support can be found using the formula T = W / (2 sin ϴ), where ϴ is the angle between the tangent to the chain at the point of attachment and the horizontal direction.

To solve for the tension, we first need to convert the angle into radians: 42.0° = 42.0 * (π/180) radians. Using the formula, the tension T in the chain can be found as follows:

T = 43.0 N / (2 * sin(42.0 * (π/180)))

By calculating the sine of the angle in radians and dividing the weight of the chain by twice this value, we can find the tension in each section of the chain at the supports.