Question

Obtain expression for Potential energy of a spring attached to a mass m moving on a frictionless horizontal surface by graphical method​

Answer 1

Explanation:

We know that, total mechanical energy remains constant, if conservative forces act on the system only.

∴ K.E+ P.E= E (Constant)

ΔK+ΔU=0

ΔK=−ΔU

If the initial velocity is v, then kinetic energy is

½ mv

Final potential energy due to spring is=

2

1

kx

2

From conservation of energy, K.E=P.E

2

1

mv

2

=

2

1

kx

2

v=(

m

k

)x, where x= compression= L

Therefore, v=L

m

k

Hence, maximum momentum, P= mv

=L

Mk