Question

The 2-kg collar is attached to a spring that has an un-stretched length of 3.0 m. If the collar is drawn to point B and releases from rest, what is the speed when it arrives at point A. Note that k = 3.0 N/m and neglect friction.

Answer 1

Complete Question

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Answer:

$v = 3.4 \ m/s$

Explanation:

From the question we are told that

   The mass of the collar is  $m = 2 \ kg$

    The original length is  $L = 3.0 \ m$

     The spring constant is  $k = 3.0 \ N/m$

     

Generally the extension of the spring  is  mathematically evaluated as

        $e = 4 -3 = 1 \ m$

Now with Pythagoras theorem we can obtain the length from A to B as

        $AB = \sqrt{5 ^2 + 4^2}$

       $AB = 6.4 \ m$

The  extension of the spring at B is  

     $e_b = 6.4 - 3 = 3.4 \ m$

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

     $\frac{1}{2} * k * e + \frac{1}{2} * m* v^2 = \frac{1}{2} * k * e_b$

substituting values

    $\frac{1}{2} * 3 * 1^2 + \frac{1}{2} * 2* v^2 = \frac{1}{2} * 3 * 3.4^2$

=>   $v = 3.4 \ m/s$