The main purpose of the lab is to calculate the power output one can generate walking up a set of stairs. Power is defined as the rate at which energy is converted from one form to another. To find the gravitational potential energy we measured the vertical height of the stairs and recorded our own mass in kilograms. With the formula △PE = mgh, (m - mass, g - gravity, h - height) we can calculate the potential energy. In order to find the power out put we used divided our potential energy by the average time it took to climb the stairs.
Materials:
- two meter sticks
- stopwatch
- kilogram scale
Procedure:
- Determine your own mass in kilograms.
- Measure the vertical height of the stairs.****Make a sketch for the method the height was found.
- After having a person recording the time, walk or run up the stairs to the second floor.
- Everyone will do two trials to climb up the second floor. Record both times.
- calculate the total power output by using the formulas from the introduction. Obtain the average power output from both trials.
- Put the average output power on the board and calculate the average power of the entire class.
- Determine your power output in terms of horsepower.
Sketch of the Stairs
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| Picture 1.1 The stair set leading to the second floor that has a height of 4.29 meters. |
Calculations
Table1
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| *Note: power is in watts |
Gravitational potential energy
F = mg △PE = mgh
F= (63.16 kg)(9.8m/s^2) △PE = (63.16kg)(9.8m/s^2)(4.29m)
F= 619 N △PE = 2655.37 J
Power:
Power1 = △PE / △t1 Power2 = △PE / △t2
P1 = 2655.37 J/ 4.25 s P2 = 2655.37 J / 5.07 s
P1 = 624.79 w P2 = 523.74 w
Horse Power: 1 HP = 745.699872 watts
HP1 = 624.79 w (1 HP/ 745.699872 w)
HP1 = 0.84 hp
HP2 = 523.74 w (1 HP/ 745.699872 w)
HP2 = 0.7 hp
Class Averages:
634.98 watts
.82 hp
Percent difference:
((measured class value - measured value) / class value) * 100
△PE
((634.98 w - 574.3 w) / 634.98 w) *100 = 9.55 %
HP
((0.82 hp - 0.77 hp) / 0.82 hp) *100 = 6.09 %
Questions:
1. Is it okay to use your hands and arms on the hand-railing to assist you in your climb up the stairs? Explain why or why not.
If one is trying to be consistent it would be more beneficial to not use the railing or if it was used, use it in both trials. This is because as you swing around the corner, you can feel a greater acceleration than a normal turn. The assist will have a greater influence on the time since the mass, height, and gravity are used as constants.Overall the gravitational potential energy will be the same for both scenarios.
2. Discuss some of the problems with the accuracy of this experiment.
Some of the problems that can occur during the lab are that the measurement of the height was inaccurate or the time could've been off by a few milliseconds due to different reaction times from the person walking and the record individual.
Follow up Questions:
1. Two people of the same mass climb the same flight of stairs. Hinrik climbs the stairs in 25 seconds. Valdis takes 35 seconds. Which person does the most work? Which person expands the most power? Explain your answers.
They both do the same amount of work. To calculate this we use △PE = mgh and the mass in this case are the same, giving the same value for the amount of work done. Hinrik is the one who expands more power since he had the ten seconds less than Valdis. The lab helps demonstrate a clearer picture. Table 1 shows that when my time climbing up the stairs was less, the more power I used and my slower time had less power.
2. A box that weights 1000 Newtons is lifted a distance of 20.0 meters straight up by a rope and pulley system. The work is done in 10.0 seconds. What is the power developed in watts and kilowatts.
h = 20.0 m Power = △PE / △t
t = 10 s = (1000 J * 20 m) / 10 s
w = 1000 N = 2000 watts or 2 kilowatts
3. Brynhildur climbs up a ladder to a height of 5.0 meters. If she is 64 kg:
a) What work does she do?
The work that she does is lift the 64 kg against gravity to the height of 5 meters.
b) What is the increase in the gravitational potential energy of the person at this height?
Work = mgh
= 64 kg * 9.8 m/s^2 * 5 m
= 3136 J
c) Where does the energy come from to cause this increase in P.E.?
The energy comes from her as she puts in work to climb up the ladder while the constant force of gravity pulls her down.
4. Which requires more work: lifting a 50 kg box vertically for distance of 2m , or lifting a 25kg box vertically for a distance of 4 meters?
50 kg box: 25 kg box:
△PE = mgh △PE = mgh
= 50 kg * 9.8 m/s^2 * 2 m = 25 kg * 9.8 m/s^2 * 4 m
= 980 J = 980 J
Both require the same amount of work.
Conclusion:
The lab helps give a greater understanding of gravitational potential energy. In order to climb the set of stairs, there's a need for work since the individual needs to fight against the downward force of gravity. In both trials the same mass and height are equal and g remains a constant 9.8 m/s^2 so the same amount of potential energy is the same but the faster one goes the more power is generated since the the work is cramped into a smaller time. The method to find power is to use the formula power = mgh / t.
The percent difference between the gravitational potential energy from the class and mine was a 9.55 %. While the horsepower difference was about 6.1%. This makes clear sense since when i observed the class do their trials i noticed that mostly everyone was rushing while i maintained a steady pace.
The most obvious sources of error are that we had a person telling us when to go and then another person running the time. This could be a conflict because the reaction times among the individuals might not be the same. Another factor is the way we measured the height of the stairs.
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