A spring has a constant of 500 N/m. The spring is compressed 15 cm and a 2 kg ball is placed on the spring in its compressed state.When the spring is released, what is the kinetic energy of the...

A spring has a constant of 500 N/m. The spring is compressed 15 cm and a 2 kg ball is placed on the spring in its compressed state.

When the spring is released, what is the kinetic energy of the ball as it leaves the spring? What is the potential energy of the spring it its compressed state? What is the potential energy of the spring as the ball leaves the spring? What is the total energy of the system (ball and spring) when the spring is compressed? As the ball leaves the spring?

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

At the initial stage the system has only the potential energy of the spring which is compressed.

As the spring is released and the ball leaves the spring whole energy stored in the spring is transferred to the ball as kinematic energy of the ball.

Initial potential energy of the ball = (1/2)k*x^2

                                              = 0.5*500*(15/100)^2

                                              =  5.625 J


When the ball leaves the spring, the spring is fully stretched and x=0.

So the energy in the spring = (1/2)*500*0^2

                                                = 0 J

 

So there is no energy remained in the spring. All the energy is as the kinematic energy of the ball.

Kinematic energy of the ball as it leaves = 5.625 J

 

Assumption

  • As the spring releases no losses of energy will occur as noise or vibration
  • No frictional forces acting on the spring and the ball
Sources:

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