File: POWER.DOC

**Background**

Here we are not considering the kind of power that a "President for Life" has over a country, but the power as defined in your physics text as the rate of doing work. A review of work and power in your text will show that there are several useful relations between these quantities. In a simple mechanical system

Work = change in the total energy

or if the velocity of the object is unchanged

Work = m g h

where m is the mass of the object, g is the acceleration due to gravity, and h is the vertical distance through which the object moved. Your book will show that power is the rate of doing work. That is, average power is the work done divided by the time it took to do that work.

In this experiment you are going to do some work by running up a set of stairs, and then you will calculate the average power you produced in order to do it.

References

1. Hewitt, P.G. *Conceptual
Physics*, 7^{th} Ed., (Harper Collins College Publishers, 1993) pp
98-100.

2. Crummet, W. P. and Western, A. B., *University Physics (Modes and applications)*, advanced copy, (Wn. C.
Brown, Publishers, Dubuque, IA, 1994) pp 174-175.

3. Ostdick, V. S. and Bord, D. J., *Inquiry Into Physics*, 2^{nd} Ed., (West Publishing Company,
St. Paul, MN, 1991) pp 104-111, 129, 133.

4. Serway, R., *Principles
of Physics*, (Saunders College Publishing NY, 1992) pp 179-181,190-192.

5. Tipler, P.A., Physics, (Worth Publishers Inc., NY, 1976) pp 184, 188-189.

6. Young, H.D., Physics, 8th Ed., (Addison Wesly, NY, 1992) pp 159-160, 172.

**Materials**

1 Stop watch

1 Ruler

**Instructions**

Find yourself a long set of steps. Ideally there should be at least 20 steps with no turns. There is a long flight of stairs inside the Business Complex just to the east of the physics building. For the truely ambitious there is always the football stadium or the Pan American Center.

Measure the height of one of these steps. With this measurement you will be able to calculate the total distance you raise your body when you run up these steps. Because the work you have done against the gravitational attraction of the earth is just your mass times the height to which you moved it (times g) , it will be easy to measure the work done. Your stop watch will tell you how long it took. The power you produced is just the quotient of these two numbers

**Report**

Your final report need not contain more than a brief description of where you did the experiment, the data that you took, and the final result. If you do any of the extensions suggested below, you should report a little more fully on your experience.

**Extensions**

There are three extensions to this experiment that you can easily do.

The first is to answer the question, "Did I produce as much power during the second half of the run as I did during the first half?" You can find the answer to that question by using the lap timer feature of your stop watch to record the time it took for you to get halfway up the stairs. Thus you have times for the first and second halves of the run as well as the time to go all the way up.

The second extension has to do with a more subtle point. The work you did went into more than just raising your body. Because you started from rest and were moving when you got to the top of the stairs, you also did work by increasing your kinetic energy. Estimate your velocity at the top of the stairs and calculate your kinetic energy at the end of your climb.

Remember that average velocity is
distance traveled divided by the time of travel. In this case the distance is
not the height h but is the slant distance along the stairs. You may need the
Pathagoren theorem to calculate it or you

can measure it. Your text will tell you that

KE
= 1/2 m v^{2}

where m is your mass and v is your velocity as calculated above.

Is your kinetic energy a significant fraction of your change in potential energy? You need to do the third extension before you can confidently answer this question.

The third extension suggests that you carefully consider the precision of the answer to the original question of what your power output was. Three measurements went into getting that result, your mass, the height to which you raised your body, and the time it took you to do so. Each of these measurements is to some extent uncertain. Estimate by how much each could be uncertain. The best way to consider uncertainties is to establish a percent uncertainty for each quantity. For example, measure the first step in several places. The variation in measurement (or the smallest difference that you could detect during the measurement) divided by the step size (times 100) will give you the percent uncertainty for one step (and hence for the total height.). The uncertainties for the other measurements can be determined in a similar fashion. The percent uncertainty for your final answer will probably be about the same as the largest percent uncertainty for the three measurements that went into the final result. Now you can answer the question in extension two.

You
might want to consider the effect of any landing in the stairway you used on
your final result.