Human Power Lab

Purpose:

To determine the power output of a person.

Equipment:

2 two-meter sticks, stopwatch, kilogram bathroom scale, a volunter and a victim!

Introduction:

we used 2 main equations for this lab. The first explained the change in potential energy.
change in PE=mgh where m is mass, g is gravity and h is height.
The second equation descibed power.
Power=change in PE/change in time where power is measured in watts.
we also used a conversion factor between watts and horsepower
1watt=0.00134102209HorsePower (HP)

Procedure:

1. Determine my mass by weighing on the kilogram bathroom scale 100.055kg
2. Measure the stairwell. This was acomplished by placing the 2 meter measuring sticks end to end from the first floor landing up to the second floor landing. See the red line on the diagram. Measured to be 4.26m

3. Measure time for two trials accending the stairs. Trial One 6.30 seconds Trial Two 6.78 seconds
4. Calculate personal power output in watts.
Change in PE=mgh
m=100.155kg
g=9.8m/s^2
h=4.26m
Change in PE=4181.271 using significant figures 4200(kgm^2)/s^2
Power=change in PE/Change in Time
Trial one
Change in PE=4200
Change in time=6.30sec
Power=670watts
Trial 2
Change in PE=4200
Change in tme=6.78sec
Power=620watts
Average of Trial 1 and Trial 2
(670+620)/2=645watts average
Conversion to HorsePower
645watts*(0.00134102209HP/1watt)=0.865HP average

Questions:

1. Is is ok to use your hands on the handrailing to assist you in your climb ut the stairs? Explain? Answer: Yes! There is nothing in our equations that dictate you must only use your hands the only variable are mass, height, time and gravity. One could climb up the stairs on all four and still have the same change in PE.
2. Discuss some of the  problems with accuracy of this experiment. The primary problem was measuring the change in time while accending the stairs. the timer stood at the top unable to see the "victim" as they accended. the signal to start was from the timer who communicated with an assistant on the halfway landing. this individual then signaled the victim to begin. There was also some error in measuring of the stairwell hight. the meter sticks had to be placed end to end. Also the kickstop on the guardrail interfered with the measuring. This probably contributed to an error of plus or minus 1cm.

Human Power follow up Questions:

1. Two people of the same mass climb the same flight of stairs person A does it in 25s with person B compleating it in 35sec Which does the most work? Answer: They both do the same amount of work since work is not dependant upon the change in time Work=mgh. Since they have the same weight, live on the same planet and are climbing the same stairs, the work is the same. Which person expends the most power? Person A does Power=change in PE/change in time. The smaller the change in time the larger the power.
2. A box that weighs 1000 Newtons is lifted up 20.0meters is 10.0sec. What is the power in watts and kilowatts? Answer: 2000watts or 2kilowatts
3. A 64kg woman clims a 5.0m ladder. What work does she do? Answer: 3100Nm of work. What is the increase of gravitational potential energy at this hight? Answer: 3100NM increase. Where does this energy come from? Answer: Food! (energy stored in the human body from food).
4. which requires more work

Acceleration of Gravity on an Inclined Plane (09-04-12)

Purpose:

The purpose of this lab was to find the acceleration of gravity by studying the motion of a cart on an incline while gaining further experience using the Computer for data collection and analysis.
This lab can be found at http://www.hartnell.edu/physics/labs/4a/4accelerationofgravityinclined.pdf

Experiment

Data Collected from a cart on an inclined plane using 2 different angles
Equation for acceleration (gravity) along inclined plane:
gsinѲ=(a1+a2)/2
Scenario 1	sinѲ=5.9/210		Ѳ=1.61°
measured values	a1	a2	gexp	% difference
take 1	0.304	0.251	9.877	0.787
take 2	0.316	0.217	9.486	3.208
take 3	0.322	0.232	9.859	0.605
Average	na	na	9.741	0.605
Scenario 2	sinѲ=20.9/210		Ѳ=5.71°
measured values	a1	a2	gexp
take 1	0.988	0.929	9.631	1.726
take 2	0.981	0.908	9.490	3.161
take 3	0.985	0.926	9.601	2.033
Average	na	na	9.574	2.307

Below are 2 views of the same velocity vs time graph showing the slope (acceleration) for the trip up the ramp and then down the ramp respectively. Note: our measurement unit (sonar detector) is calibrated such that movement towards it is given a  negative value while movement away a positive one. Our unit was placed at the top of the inclined ramp and the cart was slid up before traveling back down. In both graphs below the line is the important feature (the dip before represents velocity changing due to external thrust by my hand, the dips and bounces after wards represent the effect of my hand stopping the cart).

Measuring velocity as cart rises up track

Measuring velocity as cart rolls back down track

Below is our graph of position vs time. the entire parabola is important the shaded grey area was not important in this lab

position vs time graph

Below is a crude drawing of our set up

Conclusions:

The graphs of velocity and graphs of position are consistent with what should be expected. The velocity graph should be a straight line, while position graph a parabola. In this experiment gravity was able to be measured at 9.7 meters per second per second. With numerous sources of error the error percentage was .6 of a percent from the actual value of gravity (9.8 meters per second per second). One interesting source of error was the meter stick, with millimeter marks on it it is better for larger measurements that smaller ones. More accuracy should be expected on the larger angle experiment, however this one had the largest percent difference of error. This may be because in fact while the side next to the motion detector was higher the side behind the cart was actually lower. Other sources of error came from the push on the cart. When a human hand is involved it is impossible to slide it up with the same forces every time. The hand and person tossing the cart can also get picked up by the motion detector interfering with the accuracy. For increased accuracy further experiments could use some mechanical way of launching the cart up the track. Also permanently attaching the motion detector instead of just letting it rest on the track might also increase accuracy. Finally by using a perfectly level table as a starting spot and with a more accurate way of measuring the angle of the track, perhaps a surveyor's theodolite the percent difference could be improved.

Lab 2 Acceleration of Gravity 08-28-12

The lab is found here
http://www.hartnell.edu/physics/labs/4a/2accelerationofgravityrubberballv2.pdf

#4 Why should the graph of position over time be a porabola for a ball tossed up and allowed to fall?
An observer of the ball would notice how smothly the ball transitions from movement to stop to movement in the oposite direction. A porabola decribes the motion of the ball over time. first moving (up) rapidly, slowing down, freezing (stopping), then slowly (falling down) finally picking up speed (falling) before reaching it original position. A porabola is merily the mathmatical way of descibing the balls motion.

#5 Table computed using experimented measurements and percent error equation
percent error=((measured-actual)/actual)*100%
actual for this experiment was 9.80m/s^2

Results from Falling Body Experiments
Trial	gexp (2A) (m/s2)	% Difference	gexp (m) (m/s2)	% Difference
1	-9.7	1.0	-9.9	1.0
2	-9.6	2.0	-10.1	3.0
3	-9.5	3.0	-9.9	1.0
4	-9.4	4.0	-9.0	8.0
5	-9.7	1.0	-9.6	2.0

There was some confusion as to significant figures steming from not reading the instuctions acurately enough leading to assuming that gravity was 9.8m/s^2; that is the reason for only 2 decimal places in the answers.

#6

Above is the graphs of position vs. time and velocity vs. time
The velocity graph for all 5 cases where velocity is positive; the ball is moving up. Where velocity reaces the y axis (y=0) the ball has reached the maximum hight and stopped moving. When velocity is negative the ball is falling down. The curve or line rather is negatively sloped because during that time is is being acted upon by gravity in the oposite direction of being thrown up. Hence it is slowing down after being tossed up and speeding up as it falls This graph represents how gravity is affecting the velocity of the ball.

Conclusions:
For balls tossed up and allowed to fall back down the graph position vs. time will be a porabola, the graph velocity vs. time will be a sloped line in the negative direction.
Significant digits are significant.

Graphical Analysis

In this lab I familiarized my self with the computer, Graphical Analysis software, Lab Pro interface, and the Logger Pro software. It was a team effort on the part of our table.

In the first part of the lab we made an equation (-16x^2+110t) as shown in the above graph. We gave it a title, y &x axis labels, and units.

In the second part of the lab. We used a sonar motion detector attached to the Lab Pro

 

Motion Detector (left)                          Lab Pro (right) 

We threw a ball up and let it drop while measuring time elasped and distance traveled. All this was graphed using our software. The graph appears below.

 The important part is the porabola shape that appears in red and is highlighted over in black. This equation was shown to be -4.968t^2+8.162t-0.714 where t was time in seconds and numerical values represented distance in meters.

Part II #2
From the equation of our measurements specifically the part (-4.968t^2) n was found to be 2.
Part II #3
Dimentional analysis conferms this [L]=[L]/[T^2]*[T]^n
solving will give you [T]=2
Unit analysis concurs m=m/s^2*s^n
solving yeilds n=2

Conclusions:
While it can be difficult to understand motion all at once, breaking it up it to small peices can be of immense benifit. In these experiments the objects were thrown straight up and gravity pulled them back down. Looking at the graphs one might think they had been kicked or thrown in an arch patern. This patern comes from the fact that as time elapess it adds a dimention to the graph. Acceleration was negative due to the fact that the motion detector is calibrated to sense velocities/accelerations heading away from it as positive and towards it as negative. It was laying on the ground pointing at the ceiling during our measurements. Therefore it measured acceleration due to gravity as a negative value.