

Guide 83. Effect of Changing the 0 level for Gravitational Potential Energy This guide will examine how changing the 0 or reference level for gravitational potential energy affects the solution of a conservation of energy problem. Consider a problem we've looked at before. This is a ball tossed upward in the absence of air friction. Open this animation and read the problem description. Play the animation and view the energy bars to see how they show energy changes as a function of time. Screen captures of the bars are shown below at three instants of time. In Figure 1, all the energy is kinetic, since the ball starts at the U_{g} = 0 level. In Figure 2, U_{g} has increased while K has decreased, but the sum, E_{sys}, remains constant, since no external forces do work on the system of ball, Earth, and gravity. In Figure 3, the ball is at the top of its path where the velocity and hence kinetic energy are zero. Hence, all the energy is gravitational potential.
Now open this animation. The physical situation modeled is the same one. However, the U_{g} = 0 level is selected to be the highest point of the path. Remember that this level is not a unique choice, but it's a choice one must make in doing a conservation of energy problem. The same three instants of time are shown in the screen captures below. Note that U_{g} is always negative due to our choice of the U_{g }= 0 level. However, kinetic energy always remains positive as a result of the fact that the terms in mv^{2}/2 cannot be negative. The system energy is constant at a value of 0.


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