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 :
[tex]\dfrac{1}{2}mv^2=\dfrac{1}{2}kx^2[/tex]
[tex]v=\sqrt{\dfrac{kx^2}{m}} \\\\v=\sqrt{\dfrac{1560\times (0.04)^2}{0.05}} \\\\v=7.06\ m/s[/tex]
So, the maximum velocity of the dart after the spring has transferred all its energy to it is 7.06 m/s.
