5-April-2017: Lab 10: Activity -- Work and power

Eric Chong

Lab 10: Activity -- Work and Power

Lab Partners: Harvey Thai and Lynel Ornedo

Purpose: For this activity, we will be calculating our power output for lifting a known object and our power output for running up the stairs.

Introduction/Theory: Power is how fast one does work over time. Work depends on the direction of the force applied and how far it is applied. For this activity, we will be using the gravitational force as as the force and how high we go in order to measure how much work we do against gravity. We will be lifting a backpack with a known mass by pulling it up with a rope and timing it. We will also be running up stairs to see how fast we can do the work to reach the top height.

Procedure: We performed the backpack part of the lab first. For this part, we had a backpack with a known mass and we lifted it up to a certain height as fast as we could. The height that the bag reached is the same as the height of the top of the stairs in the second part of the lab, which turns out to be 4.498 m, and we will explain how we measured it in the next part. We used our phones to time how fast the lifting process was. Fairly simple. The time to lift the bag was 11.26 seconds.

For the next part, we ran up a set of stairs and timed how fast it took for us to reach the top. Again, we used our phones to time, and we estimated the angle that the stairs made with the ground to be around 30 degrees. We measured the height of one of the stairs, which turned out to be 17.3 cm, and multiplied it by 26, since there are 26 stairs. This means that the height at the top of the stairs is 4.498 m, as mentioned previously. We also used Harvey's mass, as he was the one who ran up the stairs, which turns out to be about 72.56 kg. We also recorded the time it takes to get up the stairs by walking instead of running. The time it takes for running is 5.46 seconds, and the time for walking is 13.29 seconds.

From here, we can calculate the power of both parts. We can use W=mgh, where m is mass in kg, g is gravitational acceleration, and h is height, for the work against gravity. After calculating the work, we can divide the work by time in order to get power. Here is the data with the calculations in spreadsheet form:

The first picture depicts the work done and the power of lifting the bag up to the specified height. The second picture shows the power of walking and running. As expected, there is less power in walking than in running, since the time for walking is larger.

Conclusion: a) Here are the calculations for the kinetic energy for walking:

Based on the kinetic energy calculated, compared to the work done when moving up against gravity, the value for kinetic energy is negligible, and thus will not produce a significant error in our calculations.

b) Here is the calculation for how many flight of stairs we have to run in order to equal the power output of a microwave oven

According to the calculation, the approximate number of stairs to run per second in order to match the power output of a microwave oven is 9 stairs.

c) Here is the calculation for the number of stairs to run in order to equal the amount of work it took to run the microwave:

According to the calculation, the number of stairs to run in order to equal the amount of work to run the microwave is approximately 3214 stairs.

d) 1.) Since the amount of work to heat water for a 10-minute shower is 12.5 MJ, the power is approximately 20833 Watts (calculated from converting 12.5 MJ to Joules, and the time to seconds, and dividing Joules by seconds).

2.) If I gathered a group of people to heat up my shower by riding bicycle-powered generators, I would need about 209 people (calculated from dividing 20833 by 100, since each person exhibits about 100 Watts of power).

3.) If I were going to provide all of the energy myself, I would need to ride for about 35 hours (calculated from dividing 12500000 J by 100 J/s, and then converting the result to hours).

Overall, this activity showcased the mechanics of power in relation to work and time. Some sources of uncertainty could stem from the reading of the timer due to reaction time, and also the measuring of the angle and the height of the stairs.