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All spring string and pulley shown in figure are light initially when both the spring were in their natural lenght the system was released from rest the maximum displace ment of the block is x×5mg/k calculate x

All spring string and pulley shown in figure are light initially when both the spring were in their natural lenght the system was released from rest the maximum displace ment of the block is x×5mg/k calculate x

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Grade:11

1 Answers

Tanmay Sinha
13 Points
5 years ago
x1 be the displacement from spring attached to centre of pulley and x2 be the displacement from spring 2.  Net displacement of mass m will be 2x1+x2.
Now, T=kx2----(1)
and 2T=kx1. ----(2)
Now, from 1 and 2,
x1=2x2----(3)
Now from work energy conservation theorem,
(1/2)k(x1)2 +(1/2)k(x2)2= mg(2x1+ x2)
Using eq.(3),
x2=2mg/k
x1= 4mg/k
Net displacement=2x1+x2=8mg/k +2mg/k=10mg/k
On comparing we get x= 5
 
 
 

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