Whether the spring force is conservative or non-conservative ?

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The potential energy of a long spring when stretched by $2\,cm$ is $U$. If the spring is stretched by $8\,cm$, potential energy stored in it will be $.......\,U$

  • [AIPMT 2006]

An elastic string of unstretched length $L$ and force constant $k$ is stretched by a small length $x$. It is further stretched by another small length $y$. The work done in the second stretching is

Show that the law of conservation of mechanical energy is obeyed by pulling or compressing the block tied at the end of a spring.

A toy gun fires a plastic pellet with a mass of $0.5\  g$. The pellet is propelled by a spring with a spring constant of $1.25\  N/cm$, which is compressed $2.0\  cm$ before firing. The plastic pellet travels horizontally $10\  cm$ down the barrel (from its compressed position) with a constant friction force of $0.0475\  N$. What is the speed (in $SI\  units$) of the bullet as it emerges from the barrel?

slowing down of neutrons: In a nuclear reactor a neutron of high speed (typically $10^{7}\; m s ^{-1}$ ) must be slowed to $10^{3}\; m s ^{-1}$ so that it can have a high probability of interacting with isotope $^{235} _{92} U$ and causing it to fission. Show that a neutron can lose most of its kinetic energy In an elastic collision with a light nuclel like deuterlum or carbon which has a mass of only a few times the neutron mass. The material making up the light nuclel, usually heavy water $\left( D _{2} O \right)$ or graphite, is called a moderator.