Answer:
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
