# The barrel of a toy gun is held parallel to the ground. The gun's spring has a force constant of...

## Question:

The barrel of a toy gun is held parallel to the ground. The gun's spring has a force constant of 3.7 x {eq}10^2 {/eq} N/m and it is compressed 3.0 x {eq}10^{-2} {/eq} m as a ball of mass 5.0 x {eq}10^{-3} {/eq} kg is held against it. An average retarding force of magnitude 6.0 x {eq}10^{-1} {/eq} N acts on the ball as it moves through a distance of 1.5 x {eq}10^{-1} {/eq} m in the gun's barrel before leaving the gun.

a) Find the elastic potential energy stored in the spring.

b) Assuming that all the spring's energy is transferred to the ball, calculate:

i) the energy lost by the ball through friction.

ii) the speed with which the ball leaves the gun's barrel.

## Recoil in a Gun Using The Conservation of Spring Energy

When the spring inside a gun is compressed by a ball, it builds up elastic potential energy. When the spring is released, the potential energy stored in the spring gets transferred to the ball in the form of kinetic energy, which causes the ball to gain velocity and shoot out of the gun.

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We are given:

{eq}\text{ Spring Constant: } k = 3.7 \times 10^2 ~\rm N/m \\ \text{ compression in spring: } x = 3 \times 10^{-2} ~\rm m \\ \text{... Hooke's Law & the Spring Constant: Definition & Equation

from

Chapter 4 / Lesson 19
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After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.