Question

A spring-loaded gun has a spring for which

k =180N /m

and is initially compressed by

14cm

. It fires

a

0.024kg

projectile vertically. Find the maximum height above the initial position?​

Answer 1

7.5 m

Step-by-step explanation:

k = Spring constant = 180 N/m

x = Displacement of spring = 14 cm

m = Mass of projectile = 0.024 kg

a = g = Acceleration due to gravity =
`9.81\ \text{m/s}^2`

s = Displacement of projectile

v = Final velocity = 0

u = Initial velocity

The potential energy of the spring will be equal to the kinetic energy of the object

`(1)/(2)kx^2=(1)/(2)mu^2\\\Rightarrow u=\sqrt{(kx^2)/(m)}\\\Rightarrow u=\sqrt{(180* 0.14^2)/(0.024)}\\\Rightarrow u=12.12\ \text{m/s}`

`v^2-u^2=2as\\\Rightarrow s=(v^2-u^2)/(2a)\\\Rightarrow s=(0-12.12^2)/(2* -9.81)\\\Rightarrow s=7.5\ \text{m}`

The maximum height reached above the initial position is 7.5 m