Lab 10: April 03, 2017: Work and Power

Lab 10: Work and Power

Amy, Chris, and John 

April 03, 2017 

Today's lab is about calculate the power output we have by performing physical activities.

Theory: Work is defined as a force done on a object during a displacement period. Where F dot delta x is defined using the dot product. But a quantity that just work does not account for is time. You could supply the same amount of force to move an object the same amount of distance but there is no indicator for how fast this task was carried out. This is where the concept of power comes in, the time rate at which a work in done: 

Power=Work/Time

Apparatus and Procedure: For the first part of the experiment we had to lift a backpack up the side of the building. The backpack had pre-measured weights and we had to time how long it took us to lift it up a height h. As for the second part, we had to time ourselves walking up the stairs and then run the same staircase and time it as well.

                       

For the first part of the experiment we lifted a backpack with a known mass and recorded the time to lift it up the building using a pulley system. The work done is the pull I give the backpack and it is greater than the weight of the backpack in order to lift the backpack up. After measuring the force of the pull multiplying that by the height of the building gives the work done. 

The power is calculated by dividing the work done by the recorded time it took to lift the backpack up. 

The second part of the experiment was a little more arduous because it involved physical activity. We had to do this experiment twice; one walking upstairs and record the time then run the same stairs and record the time as well. Beforehand we calculated the length of a stair and multiplied it by the amount of stairs in order to find the distance we traveled. The height of one stair was 0.169 meters and there were 26 stairs so height = 4.394 m.

To find the force we exert we needed to find the normal force of the stairs on us: 

Data: Using the formula for power we can calculate the power output: 

My mass is approximately 55. 79 kg

Conclusion:

A) Kinetic Energy that was neglected=.5mv^2= .5*55.73*1^2= 27.865 J

Work for gravitational= mgh= 55.73*9.8*4.394= 2399.8 W.

The ratio between these two provides an uncertainty of 1.16% which can be neglected due to its small size and interference with the experiment. 

B)A microwave oven typically has a power consumption of approximately 1100 Watts. How many of the flights of stair we used in this lab would you have to climb each second to equal the power output a microwave oven?

Assuming a flight of stairs is the 26 stairs we climbed, I generated 570.6 Watts running up one flight of stairs. 1100 Watts / 570.6 Watts gives us a ratio of 1.93 so I would need to climb 1.93 flights of stairs to equal the power output of a microwave oven. 

C) Suppose you are cooking two potatoes in the microwave oven for a total of 6 minutes. How many flights of steps total would you have to climb to be equivalent to the amount of work that it took to run the microwave?

1100 Watts is a Joules/sec measurement. If we multiply this quantity by the time given (6 minutes or 360 seconds) we would get 396000 Joules. The work done climbing 1 flight of stairs was 2738.7 Joules  so 396000/2738.7 gives us 144.6 flights of stairs.

D) A person in reasonably good shape can comfortably put out 100 watts continuously (say, by riding a stationary bicycle connected to a generator.) A 100% efficient water heater would require about 12.5 MJ (megajoules = 10^6 Joules) of energy to heat water for a 10-minute shower (flow rate of 10 liters per minute ~ 2.5 gallons per minute, water being heated from 20 C to 50 C.)

1) How much power is this?

Since power is work divided by time, 12.5 MJ divided by 10 minutes or 600 seconds gives us a value of 20833.3 Watts. 

2) If you gathered a group of people to ride bicycle-powered generators in order to heat the water for your shower in real time, and each one was putting out 100 watts, how many people would it require to heat the water for your shower?

20833.3 Watts obtained in (1) divided by 100 Watts per person gives us a value of 208.3 persons. 

3) If instead you were going to provide all of the energy yourself, how long would you have to ride on a bicycle powered generator in order to heat water for your 10-minute shower?

If you were to be the only one generating power, at a rate of 100 Watts, you'd have to cycle 208.3 seconds to heat water for a 10 minute shower.

The lab itself ignored a number of quantities such as kinetic energy and non constant forces. We assumed a constant pull for the first experiment, the actual pulling were multiple non-constant forces because the backpack was not pulled up smoothly. There were other factors that attributed to this such as friction between glove and rope because in some cases the rope kept slacking. 

For the climb up the stairs case, simply using body mass is probably not the most accurate calculation for work, There are probably different cases to consider such as center of mass, all the intricate workings within the body (tension of tendons and inner mechanical workings) that contribute to movement up the stairs. There is also static friction between shoe and staircase that propels us forward but for the sake of simplicity within this lab, we just used a simple model to calculate power output.