Question

A 20 newton stone falls accidentally from a height of 4m on to a spring of stiffness constant 1960N/m. Write down the equation to find out the maximum compression of the spring

Answer 1

We apply law of conservation of Mechanical energy.
The idea is that when the stone falls through the given height all the Potential energy possessed by it(by virtue of 4m height ) converts into its kinetic energy and this is the energy with which it falls on the spring causing it to compress until the whole kinetic energy of the stone converts into Elastic potential energy of the spring .
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Potential energy at 4m height from spring = mgh = 20×4 = 80 J
so Kinetic energy at the instant when it reaches the spring = 80J
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Elastic potential energy(U) of the spring is given by :
U = ½×k×x²
where k is stiffness constant and x is compression (in our case ).
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Now all the KE of stone changes into U of the spring (maximum compression)
then,
80= ½× 1960×x²
solving it we get ;
x (max compression ) = 0.08163265 m .
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hope it helps !

Answer 2

Hope it helps!

In this problem simply use conservation of mechanical energy theorem.