Question

A spring-loaded gun of spring constant k=575 N/m is compressed a distance 35 cm (.35) before firing a 45 g dart. Assuming the gun is pointed horizontally, at what speed does the dart leave the gun. Please show work, thanks!

Answer 1

ACCORDING to principle of conservation of energy, all the mechanical enegy will remain conserved and potential energy will be converted into kinetic energy of the dart.

potential energy stored in the spring = 0.5 kx²

U = 0.5*575*0.35²

U = 35.21 JOULE

Kinetic energy stored in the dart, K = 0.5 mv²

K = 0.5*0.045*v²

K = 0.0225 v²

0.0225 v² = 35.21

v² = 1564.88

v = 39.55 m/sec