Strings with restitution

Classical Mechanics Level 4

Two blocks A and B of mass m a = 1 kg m_{a}=1\text{ kg} , m b = 2 kg m_{b}=2\text{ kg} placed on a frictionless horizontal floor are connected by a very light cord. The block A is given a velocity u = 3 m/s u= 3\text{ m/s} towards right. If the coefficient of restitution defined for the cord is e = 0.6 e=0.6 , find velocity with which block B begins to move.


The answer is 1.6.

S.Shri Hari by S.Shri Hari , 21, India

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1 solution

Aniket Sanghi
Aug 16, 2016

I guess , the meaning of restitution of string is , like when 2 bodies collide their normal forces give impulse and hence the motion , here Tension gives impulse . Rest all is same .

Let velocity of B be v2 and A be v1

Momentum Conservation equation

2 v 2 + v 1 = 3 2v2 + v1 = 3

Coefficient of restitution's equation

v 2 − v 1 = 0.6 × 3 v2 - v1 = 0.6 × 3

On solving we get v 2 = 1.6 m / s \boxed{ v2 = 1.6 m/s }

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Just curious. Can someone clarify the concept of the Coefficient of Restitution for a string? Does this get covered in the general definition?

PS: I guessed the same too when I read the question :P

S.Shri Hari - 4 years, 9 months ago

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yes , it just means that it is not an ideal string( if it had been ideal it would not act like a slack string but rather like a rod which just transfers energy) , it's somewhat we find in real lives , the string builds up tension very fast and gives a impulse to both the blocks ( to stop the moving block and to give motion in the stationary block) that impulse is defined by c.o.r. .

A Former Brilliant Member - 4 years, 9 months ago

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