
Concept explainers
A chain of length I and mass m falls through a small hole in a plate. Initially, wheny is very small, the chain is at rest. In each case shown, determine (a) the acceleration of the first link A as a function of y, (b) the velocity of the chain as the last link passes through the hole. In case 1, assume that the individual links are at rest until they fall through the hole. In case 2, assume that at any instant all links have the same speed. Ignore the effect of friction.

The acceleration of the first link A as a function of y.
Answer to Problem 14.116RP
The value of acceleration of the first link A as a function of Y is
Explanation of Solution
Given information:
Mass per cent length =
The value of length of the chain
Velocity is
Consider the case 1
And here we have to apply the principle of impulse and momentum
So, we must take:
So, we have to multiply both sides with yv, we get:
Applying integration on both sides, we get:
And then differentiating both sides, we get:
Here
So, the acceleration is:

The velocity of the chain as the last link passes through the hole.
Answer to Problem 14.116RP
The value of velocity of the chain as the last link passes through the hole is
Explanation of Solution
We must put y=l in first equation.
Again, consider the second case.
Here initial kinetic energy is
Initial potential energy is
Final kinetic energy is
Final potential energy is
We must differentiate the equation 2 with respect to Y.
We have a relation
And the acceleration is
Put y=l in equation 2, we get:
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Chapter 14 Solutions
Vector Mechanics For Engineers
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