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A spring-mass system ( m1 + massless spr...

A spring-mass system ( `m_1` + massless spring + `m_2`) fall freely from a height `h` before `m_2` colliding inelastically with the ground. Find the maximum value of `h` so that block `m_2` will break off the surface. Assume k=stiffness of the spring.

Text Solution

Verified by Experts

`v_1=sqrt(2gh)`

For block `m_2` to be lifted up
`kx=m_2gimpliesx=(m_2g)/(k)`
Now,
`1/2m_1v_1^2=m_1gx+1/2kx^2`
Solve to get `h=(m_2(2m_1+m_2)g)/(2m_1k)`
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