The speed is 2.5 m/s
Explanation:
The total (mechanical) energy of the mass-spring system at any point during the motion is the sum of the kinetic energy (KE) and the potential energy (PE):
[tex]E=KE+PE=3.24 J[/tex]
and it is constant.
The kinetic energy can be written as
[tex]KE=\frac{1}{2}mv^2[/tex]
where
m = 0.500 kg is the mass
v is the speed
While the potential energy is
[tex]PE=\frac{1}{2}kx^2[/tex]
where
k = 330 N/m is the spring constant
x is the elongation
So the first equation becomes
[tex]E=\frac{1}{2}mv^2 + \frac{1}{2}kx^2[/tex]
Therefore, if we substitute
x = 0.100 m
We can find the speed when the elongation is x = 0.100 m:
[tex]v=\sqrt{\frac{2E-kx^2}{m}}=\sqrt{\frac{2(3.24)-(330)(0.100)^2}{0.500}}=2.5 m/s[/tex]
Learn more about kinetic and potential energy:
brainly.com/question/6536722
brainly.com/question/1198647
brainly.com/question/10770261
#LearnwithBrainly
