In the potential energy equation, the zero point for h can usually be chosen arb

Question

In the potential energy equation, the zero point for h can usually be chosen arbitrarily as makes the most sense in a problem. For example, we would measure the potential energy of a pole vaulter from the ground from which he or she takes off.
A 2 kg mass is on a lab table that is 1 m high. The ceiling of the lab is 4 m high. Using g = 10 m/s2, find its potential energy in joules measured from the:



a. floor
b. lab table
c. The ceiling of the lab
The mass is now moved so that it is 1 m above the table. Determine now the potential energy in joules measured from the:
d. floor
e. lab table
f. The ceiling of the lab
Find the change in potential, Uf - Ui
for each set of calculations:
g.
h.
i.

j. Does the value of potential energy depend on the zero point chosen?
k. Does the value of the change in potential energy depend on the zero point chosen?

Explanation / Answer

The formula for gravitational PE is always PE = mgh. The height (h) is the issue of concerns in this problem based on the chosen zero reference point for the height. For parts A, B, and C. The zero reference point is the table (1 m higher than the floor). a) PE = mgh = (2)(10)(1) = 20J b) PE = mgh = (2)(10)(0) = 0J c) PE = mgh = (2)(10)(-3) = -60J The negative is because the reference point is below the ceiling height. For parts D, E, and F the mass is now 1 m above the table, which is 2 m above the floor. d) PE = mgh = (2)(10)(2) = 40J e) PE = mgh = (2)(10)(1) = 20J f) PE = mgh = (2)(10)(-2) = -40J (same explanation for the negative) For parts G, H, and I we need to find change in PE or PEf - PEi. Parts d, e, and f are final PE's and parts a, b, c are initial PE's at the three separate locations g) Change in PE from floor = PEf - PEi = 40J - 20J = 20J h) Change in PE from lab table = PEf - PEi = 20J - 0J = 20J i) Change in PE from ceiling = PEf - PEi = -40J - -60 = 20J. Note the double negative So for part j, YES the PE depends on the zero point. All values when the reference point was changed. For part k, NO, the change is PE is indepent of initial zero point. All three changes in PE were 20J.

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