00:01
Five students compete to determine their power by running up the stairs from the foyer level of a certain building up to the rooftop where there's a garden okay so their mass and weight and the time that took them to reach the rooftop were recorded we are to determine the power of each student in watts and in horsepower and answer the question, who among them is the strongest and who among them is the weakest.
00:42
So the helpful equations that we have here are the equation for power, which is given as the ratio of work done to time.
00:55
And we also have here the associated gravitational potential energy given by mass times acceleration due to gravity times height so looking at looking back at our figure here we will let the reference of the gravitational potential energy to be at the level of the foyer or the entrance hall so we'll take it as point one in the rooftop as the last point.
01:30
By the way, the height of the building is 13 meters.
01:33
So with respect to the reference, each student here has no distance from the reference at the initial state and at the final state this would be their distance from the reference.
01:48
So the only force that does work here from point one to point two is their weight or the gravitational force.
01:56
Gravitational force is a conservative force so it does not the in calculating the work done by a conservative force the actual distance traveled by each student here as they went up the stair does not affect the work done by gravity because it's only the initial and the final points that are taken okay so we will start with our equation of power here.
02:31
So we are to determine the power.
02:33
As mentioned earlier, the work, the only force that does work here is gravity.
02:38
So we'll have the work done by gravity divided by the time it takes for each student to travel up the 13 -meter building.
02:52
So recalling what we know about work done by gravity.
02:56
Okay.
02:57
So we, that's equivalent to the negative change in the gravitational potential energy.
03:04
But this time we will only focus on the magnitude of this so that this becomes, we have gravitational potential energy in the final state minus the gravitational potential energy in the initial state.
03:20
Since y sub 1 is zero for all students.
03:23
Then they do not have any gravitational potential energy associated with them in the initial state.
03:30
So we're saying here that the work done by gravity is just equivalent to the final gravitational potential energy.
03:39
So this would be the mass of each student times acceleration due to gravity magnitude times their final height.
03:48
So it means that this becomes m, g.
03:53
Y sub 2 and then the time so this is our main working equation for each of the student in determining the individual power so let's start with student a so the power of student a we have the mass it has to be in kilograms so there's no conversion needed 55 kilograms times 9 .8 times 13 meters divided by travel time is 16 seconds.
04:25
So this gives us 438 watts and then we'll just convert this.
04:33
Let's recall that one horsepower is equivalent to 746 watts.
04:40
So we can do the conversion here.
04:44
We have 746 watts here in every horsepower.
04:49
So the horse, the watts is out here...