Vectors Question (Calculus?)?

Question

The tension T at each end of the chain has magnitude 25 N. What is the weight of the chain?

Answer 1

The data presented in this problem are not complete. How is the chain configured? How many degrees do the ends of the chain make with either a horizontal or vertical reference?

Anyway, without making any further assumptions, the general working formula is

T1(sin A) + T2(sin B) = mg

where

T1 = T2 = tension at each end of the chain = 25 (given)

A = angle formed by one end of the chain with the horizontal

B = angle formed the the other end of the chain with the horizontal

m = mass of the chain

g = acceleration due to gravity = 9.8 m/sec^2 (constant)

Substituting values,

25(sin A) + 25(sin B) = 9.8(m)

25(sin A + sin B) = 9.8(m)

Solving for "m",

m = (25/9.8)(sin A + sin B)

As previously mentioned, if the values of "A" and "B" are known, then simply substitute them in the above derived formula to determine the value of "m".