One end of a spring is fixed, while the other can be moved in such a way to stre

Question

One end of a spring is fixed, while the other can be moved in such a way to stretch or compress the spring. Suppose we choose the origin to be the position of the left end of the cart when the system is at equilibrium, and the direction such that a displacement that stretches the spring is positive, as seen in Fig. 11.6, (where a 0.75 kg cart has been attached to the free end of the spring).

3. If the cart is released from rest at the 2.0 cm mark, what will its kinetic energy be when it first passes through the spring's equilibrium point and what will it's velocity be when it first passes through the spring's equilibrium point?

Explanation / Answer

   spring constant of the spring is the slope of force Vs displacement graph given.

   k = spring constant = slope = 66.67 N/m.

  3. to find out the kinetic energy at equilibrium position we must use work energy theorem.

    work done by spring force on cart = change in kinetic energy of the cart

   kx2 /2 = mv2 /2

   here x = 0.02 m and k = 66.67 N/m.

   substituting the values we get K.E = 0.0133 J

   now mv2 /2 = 0.0133 and m= 0.75 kg.

   solving for v, we get v = 0.0355 m/sec.

   velocity at equilibrium position = 0.0355 m/sec

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