Question

A 50 g dart rests up against a spring that has been compressed 0.04 meters. It has a spring constant of 1560 N/m.What is the maximum velocity of the dart after the spring has transferred all its energy to it.

Answer 1

Answer:

The maximum velocity of the dart after the spring has transferred all its energy to it is 7.06 m/s.  

Explanation:

Given that,

Mass of the dart, m = 50 g = 0.05 kg

Compression in the spring, x = 0.04 m

Spring constant, k = 1560 N/m

We need to find the maximum velocity of the dart after the spring has transferred all its energy to it. The kinetic energy is converted to elastic potential energy as :

$\dfrac{1}{2}mv^2=\dfrac{1}{2}kx^2$

$v=\sqrt{\dfrac{kx^2}{m}} \\\\v=\sqrt{\dfrac{1560\times (0.04)^2}{0.05}} \\\\v=7.06\ m/s$

So, the maximum velocity of the dart after the spring has transferred all its energy to it is 7.06 m/s.