Question

3. 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?

Please include all of your steps.

Answer 1

• Mass=0.0500kg=m
• Speed=20m/s=v

$\\ \rm\rightarrowtail KE=\dfrac{1}{2}mv^2$

$\\ \rm\rightarrowtail PE=\dfrac{1}{2}kx^2$

• Both are equal

$\\ \rm\rightarrowtail \dfrac{1}{2}mv^2=\dfrac{1}{2}kx^2$

$\\ \rm\rightarrowtail mv^2=kx^2$

$\\ \rm\rightarrowtail 0.0500(20)^2=k(0.150)^2$

$\\ \rm\rightarrowtail 0.0500(400)=k(0.0225)$

$\\ \rm\rightarrowtail 20=0.0225k$

$\\ \rm\rightarrowtail k=888.89N/m$

Now

#b

$\\ \rm\rightarrowtail F=-kx$

$\\ \rm\rightarrowtail F=-888.89(0.150)$

$\\ \rm\rightarrowtail F=133.34N$