# Why does potential energy at point 1 = 0J?

Hi guys,

we went through this question in class and the answer to this question is 0J, but when I worked it out I got 3.94J.. Im very confused about how this can be 0J when there is clearly potential energy in the rubber ball. Can somebody explain this to me please?

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A rubber ball with a mass of 300 g is projected vertically upwards by a spring with a stiffness k = 350 N/m. The rubber ball has been pressed down beforehand, seen on the left in the figure, compressing the spring by 15 cm. This configuration is shown schematically in the figure below.

a) In the initial state, the potential energy of the spring is stored both in the spring and the rubber ball, What is the initial potential energy (PE)1 of the ball at point 1? Assume that the initial height of the ball (point 1) is the reference height.

### 1 Answer

- NCSLv 71 month agoFavourite answer
The GRAVITATIONAL potential energy can be zeroed anywhere. If you want to find how high it gets from position 1, it is easiest to set GPE = 0 J there.

"In the initial state, the potential energy of the spring is stored both in the spring and the rubber ball"

I hate that wording. Of course there is ELASTIC potential energy in the spring, but I don't know that I agree that any of it is stored in the ball. That energy would be stored in the spring whether the ball was resting on it or not.

"Assume that the initial height of the ball (point 1) is the reference height."

That basically sets the GPE there to 0 J.

So the EPE in the spring becomes GPE in the ball:

½kx² = mgh

½*350N/m*(0.15m)² = 0.300kg*9.8m/s²*h

h = 1.3 m

where the GPE is, as you say, 3.94 J

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