A mass of 0.5 kg hangs motionless from a vertical spring whose length is 1.10 m and whose unstretched length is 0.50 m. Next the mass is pulled down to where the spring has a length of 1.30 m and given an initial speed upwards of 1.3 m/s. What is the maximum length of the spring during the motion that follows?

The maximum length during the motion is

Explanation:

From the question we are told that

           The mass  is  

            The vertical spring  length is  

            The unstretched  length is  

          The initial speed is

          The new length of the spring

The spring constant k is mathematically represented as

Where F is the force applied  

           y is the difference in weight which is  

The negative sign is because the displacement of the spring (i.e its extension occurs against the force F)

    Now  substituting values accordingly

The  elastic potential energy is given as

  where D is this the is the displacement  

Since Energy is conserved the total elastic potential energy would be

Substituting value accordingly

So to obtain total length we would add the unstretched length

 So we have

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