Question

A toy "spring gun" has a spring with a spring constant of 30,000 N/m and is depressed 4 cm. It shoots a plastic dart with a mass of 45 grams. How fast will the dart travel if there is no friction?

Answer 1

Answer:

 32.66 m/s

Explanation:

$k=30000N/m\\x=4 cm=0.04 m\\m=45g=0.045kg$

The potential energy stored in the spring will impart kinetic energy into the dart:

$\frac{1}{2}kx^2=\frac{1}{2}mv^2\\v=\sqrt{\frac{k}{m}}x$

substitute the values:

$v=\sqrt{\frac{30000}{0.045}}\times0.0=32.66m/s$