- #1
zorro
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Suppose an object of mass 'm' is attached to a vertical spring of spring constant 'k' and slowly lowered to the equilibrium position. We have to find the extension in the spring.
I have two approaches-
1) At the equilibrium position,
force due to tension in the spring and weight of the object balance each other
i.e. kx = mg (x = extension produced in the spring)
or x = mg/k
2) Consider the object-spring-earth system.
When the block is lowered by a distance x, its potential energy decreases by mgx (taking the equilibrium position as reference level).
The elastic energy of the spring increases by 1/2 kx2.
Energy is conserved as no other external force on the system does work.
so mgx = 1/2 kx2
or x = 2mg/k
I'm curious to find out which one is correct.
Please provide convincing answers to both approaches.
I have two approaches-
1) At the equilibrium position,
force due to tension in the spring and weight of the object balance each other
i.e. kx = mg (x = extension produced in the spring)
or x = mg/k
2) Consider the object-spring-earth system.
When the block is lowered by a distance x, its potential energy decreases by mgx (taking the equilibrium position as reference level).
The elastic energy of the spring increases by 1/2 kx2.
Energy is conserved as no other external force on the system does work.
so mgx = 1/2 kx2
or x = 2mg/k
I'm curious to find out which one is correct.
Please provide convincing answers to both approaches.