- #1

kurt

- 8

- 0

_{n}. Each run up a given slope of height h in times t

_{n}. Gravitational accelartion, g, is constant.

Now there are 2 ways to calculate the average power of this group of people with 2 different results. The question is which way of calculating the average power (hence which result) is correct.

1st way: I calculate the power of each individual: P

_{n}=m

_{n}g h/t

_{n}and take the average of these P

_{n}. This is the average power of the group calculated using the first way: P

_{avg.1}= (P1 + P2 + P3 +…….+ Pn ) /n

2nd way: I take the average of n masses, m

_{avg}and the average of n times, t

_{avg}, then use the power formula and obtain the average power of the group using the second way: P

_{avg.2}=m

_{avg}g h/t

_{avg }.

When I do the two ways on the Excel I get slightly different results. Here is an example:

g (m/s2) h(m) m (kg) t (s) P=mgh/t (W)

9,81 2,24 51 7 7844,861

9,81 2,24 48 7 7383,398

9,81 2,24 46 4 4043,290

9,81 2,24 47 8 8262,374

9,81 2,24 51 5 5603,472

9,81 2,24 49 4 4306,982

9,81 2,24 50 6 6592,320

9,81 2,24 52 4 4570,675

9,81 2,24 54 7 8306,323

9,81 2,24 48 5 5273,856

9,81 2,24 47 8 8262,374

9,81 2,24 51 4 4482,778

6244,392 ←average of the individual powers

9,81 2,24 49,5 5,75 6254,464

average m average t power ↑ of averages

So which way (result) would be correct? By the way, plotting t against m and using the slope of the best fit line to calculate power is not appropriate here, as the slope comes out to be negative (-0.087) and the correlation is very weak (R2 = 0.017). I greatly appreciate your comments.