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A block of mass 11.8 kg slides from rest down a frictionless 35.6° incline and is stopped by a strong spring with k = 3.11 x 10^4 N/m. The block slides 2.17 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed?

Answer :

Answer:

 x = 6.58 m

Explanation:

For this exercise let's use the concept of conservation of mechanical energy. Let's look for energy at two points the highest and when the spring is compressed

Initial

    Em₀ = U = m g and

Final

    [tex]E_{mf}[/tex] = ke = ½ k x2

As there is no friction the mechanical energy is conserved

    Em₀ = [tex]E_{mf}[/tex]

     m g y = ½ k x²

Let's use trigonometry to face height

     sin θ = y / L

     y = L sin θ

     x = √ 2mg (L synth) / k

     x = √ (2 11.8 9.8 2.17 sin35.6 / 3.11 104)

      x = 6.58 m

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