A 3-m-long heavy chain, mass of 30 kg, is lowered from a barn loft by a farmer. The downward acceleration of the chain is 3 m/s $2$ . What is the tension in the chain at its midpoint of 1.5 m from an end?
A) 0 N
B) 200 N
C) 150 N
D) 100 N

Question

Quizplus · Accepted Answer

The tension in the chain at its midpoint can be calculated by considering the weight of the half chain below the midpoint and the net acceleration. The mass of the half chain is $15 \, \text{kg}$ (since the total mass is $30 \, \text{kg}$ and it's being considered at the midpoint). The force due to gravity on this half is $15 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 147 \, \text{N}$. However, since the chain is accelerating downwards at $3 \, \text{m/s}^2$, the effective acceleration is $9.8 \, \text{m/s}^2 - 3 \, \text{m/s}^2 = 6.8 \, \text{m/s}^2$. Thus, the effective force is $15 \, \text{kg} \times 6.8 \, \text{m/s}^2 = 102 \, \text{N}$, which rounds to approximately $100 \, \text{N}$, indicating the tension at the midpoint.

A 3-M-Long Heavy Chain, Mass of 30 Kg, Is Lowered 222

A 3-M-Long Heavy Chain, Mass of 30 Kg, Is Lowered $2$