Imagine your trying to slide your textbooks to your freind who is sitting at the other end of table . How would knowing coefficient of friction impact how you would slide the book

a) x = 0.0175 m  and b) v = 1.178 m/s

Explanation:

a) Let's analyze the exercise gives us a compressed spring, which would have elastic energy and a glider that is initially at rest and then released acquiring kinetic and potential energy, as there is no friction, the energy is conserved

Initial

      Emo = Ue = ½ k x²

Final

      Emf = K + U = ½ m v² + mg y

      Emo = Emf

       ½ k x² = ½ m v² + mg y

At the highest point the speed is zero (v = 0). Let's calculate height trigonometry

      sin 44 = y / L

      y = L sin44

     ½ k x² = 0 + m g y

     x² = 2m g L sin44 / k

     x = √ (2 8.00 10⁻² 1.6 sin44 / 580)

     x = 0.0175 m

b) When the glider is 0.60m it is no longer in contact with the spring that contracted only 0.0175m

Let's write the mechanical energy at this point

       Em2 = K + U

       Em2 = ½ m v² + mg y₂

       L2 = 0.60 m

       y₂ = L2 sin44

      Emo = Em2

      ½ k x² = ½ mv² + mgh

      v² = (½ k x² -mgh) 2 / m

      v = √ [(½ k x² - mg L₂ sin44) 2 / m]

Let's calculate

      v = √ [(½ 580 0.0175² - 8 10⁻² 0.6 sin44) 2/8 10⁻²]

      v = √[ (0.08881 – 0.0333) 25]

      v = 1.178 m/s