Question

to improve the acoustics in an auditorium, a sound reflector with a mass of 170kg is suspended by a chain from the ceiling. what is the tension in the chain? assume that the mass of the chain itself is 8.0kg.

Answer 1

Mass of the sound reflector is given as

$m_1 = 170 kg$

mass of the chain itself is

$m_2 = 8 kg$

now here since this system is suspended at rest and no acceleration is given for the system so in order to find the tension in the chain we will just use force balance equation

As per force balance we can say that weight of the chain and reflector downwards will be counter balanced by tension in the string

Now here we will have

$T = m_1g + m_2g$

since chain is given with some mass so tension at the top end of the chain will be

$T = 170* 9.8 + 8 * 9.8$

$T = 1744.4 N$

So here tension in the chain will be 1744.4 N at the top end and this tension will decrease as we move down along the length of the chain.