Question

A spring is compressed 1.5 meters and has a spring constant of 65 N/m.

a) How much force is involved in compressing the spring?
b) How much energy does the spring store?
c) How high could it potentially launch a 0.10 kg projectile?

Answer 1

a). Force = (spring constant) x (length of stretch or compression)

Force = (65 Newton/meter) x (1.5 meter)

Force = 97.5 Newtons

b). Energy = (1/2) (spring constant) x (length of stretch or compress)²

Energy = (1/2) (65 N/m) (1.5 m)²

Energy = (0.5 · 65 · 2.25) (N-m²/m)

Energy = 48.75 Joule

c). If all of the energy stored in the spring can be completely transferred to lifting the projectile, then the projectile's potential energy at the peak of the lift ... (mass) (gravity) (height) ... will be 48.75 Joule.

(0.1 kg) (9.8 m/s) (height) = 48.75 Joule

48.75 Newton-meter = (0.98) (kg-m/s²) (height)

48.75 (kg-m/s²)-m = (0.98) (kg-m/s²) (height)

Divide each side by (0.98 kg-m/s²) :

Height = (48.75 / 0.98) meter

Height = 49.74 meters