Question

I am suppose to do this by calculating data from people walking up the stairs. Person A who weighted 88.5kg took 12.46 seconds person b with 72kg took 8.07seconds person c with 56kg took 7.21 seconds and person d with 53 kg took 7.06 seconds however I do not know which one exerted more power from my dataHeight of stairs = 2 m

Answer 1

We are given the following data

Person A: mass = 88.5 kg and time = 12.46 seconds

Person B: mass = 72 kg and time = 8.07 seconds

Person C: mass = 56 kg and time = 7.21 seconds

Person D: mass = 53 kg and time = 7.06 seconds

We are given the following conclusion

"The person with the most mass did the most work and exerted the most power"

Recall that the work done in climbing the stairs is given by

`W=mgh`

Where m is the mass of the person, g is the acceleration due to gravity, and h is the height of the stairs.

Since g and h are constant for all people, the work done is directly proportional to the mass of the people.

`\begin{gathered} W_A=mgh=88.5\cdot9.81\cdot2=1736.37\; J \\ W_B=mgh=72\cdot9.81\cdot2=1412.64\; J \\ W_C=mgh=56\cdot9.81\cdot2=1098.72\; J \\ W_D=mgh=53\cdot9.81\cdot2=1039.86\; J \end{gathered}`

As you can see, the person with the most mass did the most work.

Recall that the power is the rate of doing work and is given by

`P=(W)/(t)`

Where W is the work done and t is the time.

`\begin{gathered} P_A=(W)/(t)=(1736.37)/(12.46)=139.36\; \; (j)/(s) \\ P_B=(W)/(t)=(1412.64)/(8.07)=175.05\; \; (j)/(s) \\ P_C=(W)/(t)=(1098.72)/(7.21)=152.39\; \; (j)/(s) \\ P_D=(W)/(t)=(1039.86)/(7.06)=147.29\; \; (j)/(s) \end{gathered}`

Notice that person B exerted the most power although he had done less work than person A.

Therefore, the second part of the conclusion is not correct.

This is due to the fact that power also depends on time, power will be greater if work is being done in a short period of time.