A 5.0g pellet is placed on the barrel of a toy gun and is propelled by a spring of force constant 50N/m that?

Question

has been compressed 20cm and then released. Calculate the maximum velocity of the pellet when shot horizontally.

The answer is 20m/s, but I don't know why I keep calculating it wrong. This is what I did:

m = 0.005

Fs = 50N/m

L = 20cm

trying to solve for v.

i used the formula k = 1/2mv^2

and I tried to solve for v like that but I got 141.42.

Can somebody please explain to me what I'm doing wrong, and how to get 20m/s? Thank you.

Answer 1

When the spring is compressed, it builds up potential energy. Upon release, the energy stored is transferred to the bullet as kinetic energy. Using that, solve for the velocity.

U = KE

½kx² = ½mv²

v = (kx² / m)^(1/2)

= ((50 N/m x (0.2 m)²) / 0.005 kg)^(1/2)

= (400 m²/s²)^(1/2)

= 20 m/s