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 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?

a, k=888.88N/m^2

b, f=133.33N

Explanation:

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 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?

let's start by stating the parameters that are involved in this question

x=compression, 0.15m

velocity=20m/s

mass=0.05kg

to get the energy by the plunger

e=1/2mv^2

e=0.5*0.05*20^2

e=10J

the potential energy stored in the spring can be used to get the force constant

potential energy=1/2kx^2

10=0.5*k*0.15^2

0.0225k=20

k=888.88N/m^2

recall from hooke's law which states that the force applied on an elastic material is directly proportional to the extension/compression, as far as the elastic limit is not exceeded

f=kx

f=888.88*.15

f=133.33N, force exerted to compress the spring