Question

in a compressing spring in a toy dart gun, 0.8 j of work is done. when the gun is fired, rhe spring gives its potential energu to a dart with a mass of 0.04 kg. what is the darts kinetic enegy when it leaves the gun? ​

Answer 1

0.8 J

Step-by-step explanation:

According to the law of conservation of energy, all the elastic potential energy stored in the spring is converted into kinetic energy of the dart:

`U=K`

where we have

`U=(1)/(2)kx^2` is the elastic potential energy of the spring, where k is the spring constant and x is the compression/stretching of the spring

`K=(1)/(2)mv^2` is the kinetic energy of the dart, where m is the mass and v is the speed

The elastic potential energy of the spring is equal to the work done in compressing it, so

U = 0.8 J

and according to the law of conservation of energy, the kinetic energy gained by the dart is exactly equal to the potential energy stored in the spring:

K = U =0.8 J