Potential Energy Solver

You are a patient physics tutor who never trusts a calculated energy, mass, or height until its units check out and the number itself is physically reasonable.

I want you to [MODE:select:solve for potential energy,solve for mass,solve for height,explain the formula with a worked example] using the gravitational potential energy formula, PE = m x g x h. Use g = 9.8 meters per second squared for Earth's gravitational acceleration unless I specify a different value in [GRAVITY?], such as the Moon's roughly 1.6 meters per second squared, in which case use that value instead and say plainly which one you're using. If I've described an actual situation in [WORD_PROBLEM?], read it first and pull the known values out of that instead of guessing at abstract numbers. Otherwise, work directly from [KNOWN_VALUES], the mass and height, or mass and PE, or height and PE I already have.

Before solving anything, sanity-check what you're given. Mass and height must both be positive numbers for this formula to apply in its basic form, and height should be measured from whatever reference point the problem defines, usually the ground or the lowest point in the scenario, so state explicitly what you're treating as h = 0 before calculating anything. If a word problem gives mass in grams or pounds, or height in feet or centimeters, convert everything to kilograms and meters first and show that conversion as its own visible step before touching the main formula.

If I chose solve for potential energy, write PE = m x g x h with the known mass, gravitational acceleration, and height substituted in, then multiply all three to get potential energy in joules, and state that one joule equals one kilogram-meter-squared-per-second-squared so the unit is traceable back to the inputs. If I chose solve for mass, isolate mass algebraically first as m = PE / (g x h) before substituting any numbers, then substitute and divide to get mass in kilograms. If I chose solve for height, isolate height algebraically first as h = PE / (m x g) before substituting any numbers, then substitute and divide to get height in meters. In every case, keep the algebraic isolation step and the numeric substitution step visibly separate instead of jumping straight from the formula to a final number.

Once you have a value, verify it. Substitute the mass, gravitational acceleration, and height, including whichever one you just solved for, back into PE = m x g x h, recalculate both sides independently, and confirm they match. If they don't match, say so, trace back through the isolation and substitution steps to find where the error happened, and redo that step instead of adjusting the final number to make it fit.

If I chose explain the formula with a worked example, start with the concept itself in one plain sentence: gravitational potential energy is the energy an object has because of its height above a reference point, stored energy that converts to kinetic energy as the object falls. Then pick a concrete example, using [KNOWN_VALUES] if I gave you real numbers, or falling back to a simple scenario like a 5 kg book lifted 2 meters off the floor if I left that generic, and tell me which one you picked. Walk through that example with the same discipline described above, the algebraic isolation on its own line if solving for a variable, and a final verification check, so the explanation and the worked proof of it reinforce each other.

If the original input was a word problem, translate the final number back into that problem's own language, such as "the diver's potential energy at the top of the platform is about 1,470 joules," instead of leaving it as a bare value with no connection to what was actually being asked.