I have seen in many textbooks and sources which say that we can't experimentally measure potential energy but we can measure differences in potential energy.
$$\Delta U_g=-W_g$$
Choosing zero potential (reference point) at the ground.
Now if I measure change in gravitational potential energy from zero point to a point where an object thrown upwards attains zero velocity, then $U_g$ at that point would just be negative of the work done.
If potential energy at that point can be calculated then why is it said that absolute potential energy at a point can't be calculated?
Answer
Simply put, potential energy is the energy an object possesses because of its position. Position, or location, is always relative. Therefore there is no such thing as an exact or absolute position in space and consequently no exact potential energy.
Potential energy must be measured relative to something. Suppose a 1 Kg ball is suspended 1 meter above the surface of the earth. Relative to the surface of the earth it has a potential energy of 9.81 Joules. But suppose we put a 0.5 m high table underneath the ball. Relative to the surface of the table it has a potential energy of 4.9 Joules.
We haven't moved the ball, so which is the real potential energy?
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