phys4as17dggo: 05-April-2017: Work and Power

Lab 10: Work and Power
05-April-2017
Idea: Demonstrate the work-energy theorem and power in motion by determining the change in kinetic energy and the work required to move up a certain height, by a) running up a flight of stairs and b) lifting a mass to the same height.
Summary:

1) As seen, the first thing we did was to lift a bag of varying masses in a mass-pulley system, and time how long it took for us to pull it to the top. To obtain the height of the pull, we measured the height of a single step, and multiplied it by the number of individual steps it took to reach the balcony.

2) Then, we timed ourselves a) walking up the full length of the stairs and b) running up the same length of stairs

3) Using these, we could model the work-energy theorem and subsequently calculate the power it took to achieve these actions.

Data Analysis/Calculations:
In calculating the power it took to lift masses up a height H, I first found the height I was lifting to as previously mentioned, found the force due to gravity on each mass. From that I could find the Work it took to do this, and then by timing the entire process, find the power I'd exerted.
Calculating this, my data would reflect this: The more work I did in a short time, the more power I output, the more work I do in a far longer time, the less power I output, i.e. as power depends entirely upon the amount of work done over time.

In calculating the work it took to walk and run up the stairs (change in kinetic energy) plus potential energy at the top of the stairs, I needed to obtain my speed, which in order to do, I assumed that the stairs took the form of a triangle with an angle 40 degrees, and second, assumed that my velocity up the stairs was constant. I then also said my starting speed was zero. Using simple kinematics, I obtained a relationship for the vertical component of my velocity using my recorded time and the sine of 40 degrees. I then used that in order to solve for my velocity V along the hypotenuse, again assumed to be the stairs.
Finally, plugging in these values to my power equation gave me a result that I thought was very reasonable for when I walked up the stairs versus when I ran up the stairs. I expended about 61% less power when I walked up the stairs, even though I had a constant mass of 52kg.

Conclusion:
As I would expect, the faster I was able to get the same mass up the height, the more power I output. Logically, the same was true for the mass: the more mass I had to lift, the more work I did, therefore the more power I had to output. Therefore I could reasonably believe that power depended on both the work done and the time it took to do that work. Thus Power was demonstrated to be equal to the quotient of work and time.
1) In neglecting the kinetic energy in the work I did to lift the masses a height H, based on the fact that I, with a mass 52kg was able to exert 2,213 Joules of work to walk up the stairs in case 2 (WITH a Kinetic Energy and Potential Energy), I can calculate a reasonable percent error by using for the second value only my potential energy up the height H, as shown:

2) If a microwave oven has a power consumption of 100 Watts, in order to equal this power by climbing the stairs, I would need to climb the following steps per second.

3)If I am cooking in the microwave for a total of 6 minutes, I would have to climb the total flight of steps over 6 minutes to generate enough power to run the microwave.