Can a sudden blow truly change potential energy?

[Lil123]

Homework Statement

A 2-kg mass on a frictionless table is attached to one end of a
massless spring. The other end of the spring is held by a frictionless
pivot. The spring produces a force of magnitude 3r newtons
on the mass, where r is the distance in meters from the pivot to the
mass. The mass moves in a circle and has a total energy of 12 J.The mass is struck by a sudden sharp blow, giving it
instantaneous velocity of 1 m/s radially outward.

Relevant Equations

E =kinetic energy +potential energy

Why there will be no change in potential energy due to this sharp blow ? Potential energy is a function of position , so won't this position get changed due to this sharp blow?Please help!

 

[kuruman]

Why there will be no change in potential energy due to this sharp blow ? Potential energy is a function of position , so won't this position get changed due to this sharp blow?

What is your reasoning for saying that "there will be no change in potential energy"?

 

[haruspex]

There is no instantaneous change in its PE, since its distance from the pivot does does not change instantly; only its speed from the pivot does.

 

[Lil123]

@haruspex So, is it correct to say that mass doesn't have enough time to change its potential energy due to this sudden blow

 

[haruspex]

@haruspex So, is it correct to say that mass doesn't have enough time to change its potential energy due to this sudden blow

Yes. The intent of "sudden" is that the duration is negligible. If it lasts $\Delta t$ and produces a velocity $v$ then the displacement during the blow is, roughly, $v\Delta t$. If $\Delta t$ is negligible then so is the displacement.