A mass of 0.5 kg moving with a speed of 1.5 m/s on a horizontal smooth s...

Q. A mass of 0.5 kg moving with a speed of 1.5 m/s on a horizontal smooth surface, collides with a nearly weightless spring of force constant k = 50 N/m. The maximum compression of the spring would

Description : Aipmt Neet 2004 | WPE Q 2 | Let’s focus on some words given in qus like ‘smooth horizontal” which tells us that Mechanical energy will remain conserved here because only internal conservative force  ( sping force in spring – ball system)is present.

Note: Gravity is also present but ,since surface is horizontal there will be no change in G.P.E or no work will be done by gravity.

Conservation of Mechanical Energy

The work-energy theorem, shows that the change DKE in a body’s kinetic energy is equal to the net work done on it :
 DKE = Wnet
Consider separately the work Wc done by conservative force and the work Wnc done by nonconservative forces. Then
DKE = Wc+ Wnc
We’ve defined the change in potential energy DU as the negative of the work done by conservative forces. So we can write
DKE = – DU + Wnc
or DKE + DU = Wnc
We define the sum of the kinetic and potential energy as the mechanical energy. Then Equation shownthat the change in mechanical energy is equal to the work downe by non-conservative forces.
i.e. DE = Wnc
D \E = 0 if Wnc= 0
Thus if work done by non-conservative forces is zero the mechanical energy of the system is unchanged.
This called law of conservation of mechanical energy. It may also be written as
DU + DK E = 0
or DU = – DKE
or U + K E = constant

or Uin + K Ein = Uf + K Ef

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