Question

A 2 kg block is pushed by an external force against a spring with spring constant 131 N/m until the spring is compressed by 2.1 m from its uncompressed length ( 0).
The block rests on a horizontal plane that has a coefficient of kinetic friction of 0.74 but is NOT attached to the sprinr 2 kg 2.1 m 2 kg 131 N/m μ 0.74

After all the external forces are removed (so the compressed spring releases the mass) how far D along the plane will the block move before coming to a stop?
The acceleration due to gravity is 9.8 m/s .
Answer in units of m.

Answer 1

Answer:

   d = 19.92 m

Explanation:

As in this exercise there is friction we must use the relationship between work and energy

          W = ΔEm

Look for energy in two points

Initial. Fully compressed spring

          Em₀ = $K_{e}$ = ½ k x²

Final. When the block stopped

      $Em_{f}$ = 0

Let's look for the work of the rubbing force

       W = fr d cos θ

Since rubbing is always contrary to movement, θ = 180

      W = - fr d

Let's use Newton's second Law, to find the force of friction

Y Axis

          N- w = 0

          N = mg

The equation for the force of friction is

         fr = μ N

         fr = μ mg

We substitute in the work equation

          W = - μ m g d

We write the relationship of work and energy

     -μ m g d = 0 - ½ k x²

     d = ½ k x² / μ m g

Let's calculate

     d = ½ 131 2.1 2 / (0.74 2 9.8)

     d = 19.92 m