5-April-2017: Work and Power

When talking about work and power, the first thing came to my mind is driving. When we step deeper on the gas pedal, the engine gives a larger power for the car. Then, as a result, the car receives some more work to transfer into kinetic energy and goes faster. Today, we did three activities outside the classroom to find out the power we do daily and compare them with other machines.

Purpose

Calculate the power of daily action, and by the function see how much work do we do on daily. Then, compare it with the power of some heating objects.

Plan

1. Do some "workout" outside the classroom. Calculate the work through the change of the height, the weight, and g. Then, divide the work by time to get the power.
2. First "workout" is lifting a known mass up by a measured distance. Use a stopwatch to time for lifting the backpack from the ground to the bottom of the backpack being level with the top of the balcony. Then, use a ruler to measure the height of one level of stair. Multiply the measurement with the number of stairs to get the height of one floor.
3. Second "workout" is walking up the stairs. Use a stopwatch to time. Detect the angle of stair with phone.
4. Third "workout is running up the stairs. Use a stopwatch to time.
5. Use the function

to calculate our work done on the progress of "workout", and then divide it by time to get our power. 6. Notice that when we walk/run up the stairs, there will be a kinetic energy in our body. So using the functions

to add kinetic energy.

To do

We got out of classroom to the balcony to set up the pulling machine as following.

We wore a pair of gloves to protect our hands. Then, with help from the other student, we measure the time we pull up.
The result came out that I spent 10.2s to pull up a 6 kg bag. And there are 26 17-centermeters stairs.
As walking up, I can time myself with phone.
I spent 15.5s to walk up. And the angle is around 45º.
Then, in similar step, I measure I need 4.5s to run up stair.

Analyze

The height of stairs is 26*0.17m=4.42m
For the first part, I calculated my power is 6*9.8*4.42≈260J.
Then we power is 260/10.2≈25.5 W.

For the second part, because my weight is 95 kg, my work done for gravity will be 95*9.8*4.42≈4115 J. Because my velocity is 4.42/(cos45º*15.5)≈0.40m/s. Then, kinetic energy will be 0.5*95*0.4^2≈7.7J. Total work is 4123 J.
Then my power is 4123/15.5≈266 W.

In the third part, using the same function as last part, and I get my total work is 4207J, and my power is 4207/4.5≈939 W.

Uncertainty

The base uncertainties are ∆h = 0.01m, ∆t = 0.1s, ∆θ = 1º

By the function

We can get

Then, for the first part, the uncertainty will be ±0.256 W

For the second and third part, by the functions

Then, the uncertainty will be 

Then, the uncertainty for those part will be ±2.08 W and ±24.3 W. 

Compare

A typically microwave has 1100W. 

Then I need to climb 1100/939≈1.17 times of stairs. 

If I cook two potatoes for 6 minutes (360 seconds), the total work is 360*1100 = 396000 J. 

Then, I need to complete 396000/939≈422 times stairs. 

For a 100% water heater (require 10 minutes and 12.5 MJ energy to heat 10-minutes shower's water), the power is 12.5 * 10^6 / 600 ≈ 20800 W. Then it needs 20800/100 = 208 men to heat the water. (A normal man can produce 100 W constantly.) If I am the only one to produce the energy, it will take 12.5 * 10^6 / 100 = 125000 s to produce the energy.

Conclusion

Because my weight is pretty large, the work I done everyday is  more than normal people. However when comparing with the heater, I am just doing a small part of work.