Potential energy negative, force & displacement co-linear?

AI Thread Summary
The discussion centers on the calculation of gravitational potential energy (V_g) at a specific point where it is found to be negative. The user questions why the gravitational potential energy is negative when both force and displacement are co-linear, which typically results in positive work. The confusion arises from the use of a negative height in the equation V_g = mgh_2, where h_2 is defined as negative due to the chosen reference point. This indicates that the object is below the reference height, leading to a negative potential energy value. The conversation highlights the importance of reference points in determining potential energy values in physics.
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Homework Statement


In the following question, in the solution, why is it that when they calculate the gravitational potential energy at point 2 (impact with spring), it is negative? I know that if both the force and displacement act in the same direction, then the work done should be positive. Why is it not the same thing here?
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I think they mean both answers could work when the equation is solved...however one answer would obviously make more sense in this case.
 
Oh sorry about that being un-clear. I mean for $$V_g = mgh_2 = (50)(9.81)(-x \sin 20)$$

why is it negative?
 
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