Hydrostatic Water
In our second group lab we studied hydrostatic water. What we wanted o figure out was how long it would take for the water to flow through different sized holes at the bottom of a cylindrical container.
What We Need to Figure Out
Velocity
Volumetric flow rate
Materials
A bucket
Two stable surfaces (notebooks) for containers to balance on
3 Cylindrical containers (empty soups cans with lids removed), label as 1, 2, and 3
Drill with 3 different sized drill bits
Ruler
Stopwatch
Marker
Steps
(The containers were pre-drilled and marked for us)
1. Measure and record diameter of the bottom of the can
2. Drill a hole through the center of the bottom of the can
3. Mark the inside of each can with a line, 3 inches from the bottom
4. Place the soup cans next to each other on the bucket leaving a gap for water flow through
5. Cover the hold of your 1st can with your finger and fill to the marked line
6. Remove finger as you place can on notebooks on buckets, with the hole above the gap
7. Measure the time it takes for the water in the can to deplete.
8. Record data and repeat steps with rest of cans
Results
Here is a chart of our collected data
Here is a chart for out analyzed data
What we observed was that as the size of the hole in each can increases so does the average velocity of the water flow as listed in the chart. Can 3, which had the largets hole, hda the greatest avergae velocity followed by 2 then 1.
(L to R: Donny Barnas, Erik Storer, Nancy Afonso, Nixandra McGuffie)
Purpose of the Experiment
Our objective is to examine the relationship between energy and a moving object
Objective
Determine the effect of releasing a ball from different heights on a ramp affects the potential and kinetic energy of the ball. Find how manipulating height affects potential energy and ball’s ability to break through obstacles. Furthermore, we want to find how many joules of energy tissue and foil can withstand before ripping.
Questions
1. At which angle of the ramp in relations to the ground will produce the greatest level of velocity?
2. What is the maximum amount of gates each ball is capable of penetrating?
3. How does the size/weight of the four different balls affect their end results?
4. Does changing the height or starting distance of the balls significantly affect the end result of broken gates, if so how?
Materials
1 weighted ball (60g)
Adjustable, metal curtain rod (used as ramp). We cut off one curved end of the rod to make our ramp linear
Tape Measure
Tin foil and tissue paper (used as gate sfor ball to break through)
Stop Watch
Weighted Sphere/Ball
Curtain Rod used as ramp
Principles
The main principles tested in our experiment are potential energy, kinetic energy, and velocity.
Potential Energy: The energy possessed by a body as a result of its position or condition rather than its motion. In our experiment, potential energy is the energy of the ball before it is released down the ramp. As the height of the ramp increases so does the gravitational potential energy of the ball allowing the ball to covert more potential energy to convert to kinetic energy as it rolls down
Potential Energy = Mass x Gravitational Acceleration x Height
Kinetic Energy: The energy possessed by a system or object as a result of its motion. Kinetic energy is dependent on two variables: mass and velocity of the object. As the ball rolls down the ramp potential energy will be converted to kinetic energy.
Kinetic Energy = ½ x Mass x Velocity^2
Velocity: The rate and direction of the change of an object or simply speed in a given direction. The distance traveled by the ball from the top of the ramp to its destination point over the time spent to reach that point.
Velocity = Distance / Time
Procedure
1. Measure length and height of rod
2. Calculate Potential Energy
3. Place tissue/foil at end of rod
4. Hold ball in starting position and release
5. Calculate Velocity and Kinetic Energy
6. Document other findings (i.e. did ball break through tissue paper/foil)
Results
From years of nose blows ripping through our tissues, our group reasoned that with tissue’s minimal density, the ball would have a better chance of rolling through the paper. This is because its lesser density would require less energy of the ball.
Our results proved us right. The ball was able to rip through the tissue when potential energy was at 0.104 Joules whereas the ball did not break through the foil until potential energy reached 0.224 Joules.
Here is a chart and graph of our data:
As shown in the above graph and chart, the “gates” broke when potential was at its highest. This is because height is a major component of potential energy. As height increases so does potential energy needed for the ball to break through.
Kinetic energy remained constant during all trials because the mass of the ball was unchanging (.06kg or 60g) and it traveled the same distance in the same amount of time, velocity (1.38m/s). This means that the ball’s potential energy in this experiment is the most determining factor of the ball breaking through the tissue/foil.
Questions Answered
Q: What was the lowest height that will cause a break in the tissue and tinfoil?
A: For our 60g ball test the minimum height was 0.17m for tissue and 0.38m for foil
Q: How many joules did each of these heights equate to for potential energy?
A: For the tissue 0.104J and for the foil 0.224J was required.
Q: How does the size/weight of the four different balls affect their end results?
A: Discuss after class activity.
Q: Did you notice the potential energy increased or decreased in relation to height?
A: As height increased the P.E. also increased
Q: Does changing the height or starting distance of the ball significantly affect the end result of breaking the gate, if so how?
A: The higher the ball the more joules are present providing enough velocity to eventually penetrate the gate subjective to starting height.
From our experiment we could rewrite the age old saying to the higher they are the harder they fall.
After watching each installment of Michael Bay’s box office hit, I found the true origins of America’s favorite robots. No the Transformers aren’t from Cybertron but from the bottom of a box of Legos and constructed by students like me and my classmates. Well not really, but the drama of that is so much more exciting.
Anyhow, this is the first of our activities and in it we set out to study the motion of our newly constructed robots as well as the measurements of distance and power. We calculated our results using a few key formulas. The set of formulas we used formed a Jenga tower. Each piece supported another and if you miscalculated one thing the whole came crashing down and you had to start all over.
First we started with measuring diameter of the robot’s tires in order to calculate circumference. We measured using a standard and converted from inches to centimeters to meters.
Here’s the conversion equations:
cm = in • 2.54
m = cm/100
The diameter of the tires equaled 0.0508 m. From this we calculated circumference using this equation: circumference = π • diameter or C = πd. From this we calculated that C=0.1596. This is the number we input into the computer program for Lego Mindstorm.
We powered on our robots to begin and the math still wasn’t over. With the circumference we needed to figure out number the of wheel turns. For this we had another equation:
Number of Wheel Turns = (rotation°) / (360°/1 Turn)
Then both wheel turns and circumference were used to calculate the distance our robot travelled:
Distance (meters) = Number of Wheel Turns • Circumference
Distance was entered into yet another equation to find velocity:
Velocity = Distance (meters) / Time (seconds)
It all seems very mathematical, and it is, but most of the information could be inputted into the program and was automatically calculated; we recorded the given information.
To begin the actual experiment, we cleared a pathway for the robot to travel without any obstructions (like its power cord which kept getting in the way) and adjusted the power so that the distance would not exceed the measurement of our ruler, 12 inches or 30.48 centimeters or 0.3048 meters.
We conducted a trial of one power level (75) and three sets of testing for increased accuracy. We found that our measurements of distance we never the same and always greater than those measured by the computer. This could be due to eyeballing exact distances when they fell between the marked lines of the ruler. I’ll list our measurements or distance (D) and velocity*(V) compared to those of the computer in addition to number of wheel turns (WT).
*Because in our tests we set time (seconds) = 1, velocity and distance are equivalent in number
Test 1
Students Computer
D = 0.27305 D = 0.227873
V = 0.27305 V = 0.227873
WT = 1.42778
Test 2
Students Computer
D = 0.2795 D = 0.24605
V = 0.2795 V = 0.24605
WT = 1.54167
Test 3
Students Computer
D = 0.27432 D = 0.246493
V = 0.27432 V = 0.246493
WT = 1.54444
At the end of our trial set we were to calculate our margin of error in order to measure how applicable our results would be on the grand scale. A high margin of error means results are less accurate/applicable and a low margin of error means results are more accurate/applicable. To measure this we used this equation:
% Error = ( (Distance measured – Distance calculated by computer) / ((Distance measured + Distance calculated by computer) / (2) ) •100%
The margin of error for each test is detailed below.
Test 1
% Error = ( (0.27305 – 0.227873) / ( (0.27305 + 0.227873) / 2) ) •100%
% Error = ( (0.045177) / ( (0.0500923 / 2) ) • 100%
% Error = ( (0.045177) / (0.2504615) ) • 100%
% Error = 0.18037503 • 100% = 18.04%
Test 2
% Error = ( (0.2795 – 0.24605) / ( (0.2795 + 0.24605) / 2) ) • 100%
% Error = ( (0.03345) / ( (0.52555 / 2) ) • 100%
% Error = ( (0.03345) / (0.262775) ) •100%
% Error = 0.12729521 •100% = 12.73%
Test 3
% Error = ( (0.27432 – 0.246493) / ( (0.27432 + 0.246493) / 2) ) •100%
% Error = ( (0.027827) / ( (0.520813) / 2) ) • 100%
% Error = ( (0.027827) / (0.2604065) ) • 100%
% Error = 0.10685985 •100% = 10.69%
The average for the % error for all three tests is as follows:
Average % Error = (% Error Test 1 + % Error Test 2 + % Error Test 3) / (Total Number of Tests)
Average % Error = (18.04% + 12.73% + 10.69%) / 3
Average % Error = (41.46%) / 3 = 13.82%
Given the small sample size of our testing, I think our margin of error is reasonable though next time we can do more to improve our measuring accuracy.
That’s all for this Lego Mindstorm experiment. Until next time!
