- #1
honlin
- 19
- 1
Homework Statement
A chain of mass M and length L is suspended vertically with its lowest end touching a scale. The chain is released and falls onto the scale. What is the reading of the scale when a length of chain, x , has fallen? (Neglect the size of individual links.)
Homework Equations
Weight = mg, Resultant force = ma, Newton third law.
The Attempt at a Solution
When the chain is suspended, by drawing the free body diagram of the chain, it should experienced three forces, upward tension, normal reaction by the scale, and its own weight.
When the chain falls onto the scale, it experience 3 forces too, upward tension, normal reaction and the weight of the the fallen chain.The weight of the fallen chain, W1 = (x/L)Mg. The upward tension has a reaction pair too, which is pointing downwards and has a magnitude of the weight of the chain which is still suspended. Therefore N2 = W2 = (L-x/L)Mg.
There are a total of 2 forces acting downward on the scale, the reaction of the tension, and the weight of the fallen chain. Therefore, the scale should read N2+W1=W1+W2 = W, the weight of the chain itself.
I do not have the answer for this question. Can someone please help me to check if my solution is correct because I am not confident with this answer. Thank you so much !