Answer :
Complete Question
The image for this question is shown on the first uploaded image
Answer:
[tex]v = 3.4 \ m/s[/tex]
Explanation:
From the question we are told that
The mass of the collar is [tex]m = 2 \ kg[/tex]
The original length is [tex]L = 3.0 \ m[/tex]
The spring constant is [tex]k = 3.0 \ N/m[/tex]
Generally the extension of the spring is mathematically evaluated as
[tex]e = 4 -3 = 1 \ m[/tex]
Now with Pythagoras theorem we can obtain the length from A to B as
[tex]AB = \sqrt{5 ^2 + 4^2}[/tex]
[tex]AB = 6.4 \ m[/tex]
The extension of the spring at B is
[tex]e_b = 6.4 - 3 = 3.4 \ m[/tex]
According to the law of energy conservation
The energy stored in the spring at point A + the kinetic energy of the spring = The energy stored on the spring at B
So
[tex]\frac{1}{2} * k * e + \frac{1}{2} * m* v^2 = \frac{1}{2} * k * e_b[/tex]
substituting values
[tex]\frac{1}{2} * 3 * 1^2 + \frac{1}{2} * 2* v^2 = \frac{1}{2} * 3 * 3.4^2[/tex]
=> [tex]v = 3.4 \ m/s[/tex]
