If five floors are 3.8 m apart, how much gravitational potential energy would a man have?

Question

A man decides to climb an office tower using the stairs. If the floors are 3.8 m apart, how much gravitational potential energy would the man have relative to the ground floor if he made it to the fifth floor?

The answer is 41 J, but how would you figure that out without knowing the mass?

Answer 1

Wouldn't.

PE = mgH = mgNh; where H = Nh and N = 5 floors [assuming N = 0 for the ground floor] at h = 3.8 m depth each floor. The potential energy PE is the amount of work energy the man puts in by climbing those stairs against the force of gravity = W = mg. So the WE = WH = mgNh = PE. Thus, by work, the man's total energy becomes TE = PE.

If the man is suicidal, then his TE just prior to impact with the concrete below is TE = KE = 1/2 mv^2 = mgH = PE. That is, work by gravity done on the falling man converts all that PE at H into KE at near H = 0. In which case, his impact velocity is just v = sqrt(2gH), a version of one of the SUVAT equations.

But, and this is a big BUT, we can't do any of the energies without knowing the mass (or weight) of the man.