Grade 11Mechanics
All contacts are smooth, find maximum compression in spring
All contacts are smooth, find maximum compression in spring
1 Answer
Samyak Jain
Since all contacts are smooth, energy of the spring-mass system is not lost.
We can use principle of energy conservation here.
Initial speed of mass m is v0 , then initial kinetic energy of the mass is (1/2)mv02. ...(1)
Finally, kinetic energy of the mass reduces to zero and converts into spring potential energy when the spring has maximum compression.
Potential energy in the spring = (1/2)kx2 ...(2), x is the maximum compression in the string.
Equating (1) & (2), we get
(1/2)mv02 = (1/2)kx2 i.e. x2 = mv02 / k
x = v0
, which is the required maximum compression in the spring.
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