From the law of conservation of energy, the potential energy is conserved into kinetic energy and vice versa.

That is, U = K

The potential energy of spring:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{k}}{{\mathbf{x}}}^{{\mathbf{2}}}}$, where k is the force constant and x is the displacement.

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

Force on the spring:

$\overline{){\mathbf{F}}{\mathbf{=}}{\mathbf{-}}{\mathbf{k}}{\mathbf{x}}}$

One type of BB gun uses a spring-driven plunger to blow the BB from its barrel.

A. Calculate the force constant of its plunger's spring if you must compress it to 0.150 m to drive the 0.0500-kg plunger to a top speed of 20.0 m/s.

B. What force must be exerted to compress the spring?

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