Question

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

(a) Calculate the force constant (in N/m) of its plunger's spring if you must compress it 0.100 m to drive the 0.0440 kg plunger to a top speed of 25.0 m/s.

_______ N/m

(b) What force (in N) must be exerted to compress the spring? (Enter the magnitude.) _______N

Answer 1

Given compression,x= 0.1m

mass of plunger = 0.044kg

speed of plunger, v =25m/s

(a)when the spring is released its potential energy is converted to kinetic energy of plunger

$PE=KE$

$\frac{1}{2}kx^{2}=\frac{1}{2}mv^{2}$

$kx^{2}=mv^{2}$

$k=\frac{mv^{2}}{x^{2}}$

$k=\frac{0.044kg*(25m/s)^{2}}{(0.1m)^{2}}$

$k=\frac{0.044*25^{2}}{0.1^{2}}$

ANSWER: ${\color{Red} k=2750N/m}$

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(b)Use the Hooke's Law

Force, $F=kx$

$F=2750N/m*0.1m$

ANSWER: ${\color{Red} F=275N}$

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