A block of mass 0.490 kg is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x. The force constant of the spring is 450 N/m. When it is released, the block travels along a frictionless, horizontal surface to point circled A, the bottom of a vertical circular track of radius R = 1.00 m, and continues to move up the track. The speed of the block at the bottom of the track is vA = 13.4 m/s, and the block experiences an average frictional force of 7.00 N while sliding up the track. What is x? and what is the speed of the block if it reaches the top?

The value of x is  

The value of the velocity at the top is  

Explanation:

The diagram of this process is on the first uploaded image

From the question we are told that

     The mass of the block is

      The distance of compression is

      The force constant is

      The radius of the circular track is

       The speed at the bottom of the track is

        The frictional force experienced is

Now looking at this process we see that the potential energy of the spring is been transformed into the kinetic energy  of the block . So,

mathematically i.e

Making x the subject of the formula

The average workdone by friction is  

Here

The kinetic energy at the bottom is

The potential energy gained at the top of the circle is

Here h  is the height which is equal to d(diameter)  = 2r = 2 × 1 = 2 m and

g is acceleration due to gravity

Now substituting values

Since energy is can not be created nor destroyed but transformed  according to first law of thermodynamics

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