Purpose: To use present knowledge of projectile motion to predict where a ball will hit on an inclined plane.
Apparatus: We used the lab station table as a starting point. We then placed a tall ring stand on top of the table, with a clamp on it. This was the starting point. Then we used two aluminum v-channels; one was inclined and held up by the clamp. The lower side of the channel was then taped to a horizontal channel that met the edge of the table. The level channel was held up by two wooden blocks. We then let a metal ball roll from the top of the channel all the way off the table, and recorded where it landed with respect to the edge of the table by taping a blank piece of paper and placing a sheet of carbon paper on top of it so that it leaves a mark.
Monday, September 26, 2016
25 Sep 2016 - Modeling Air Resistance - Lab 4
Purpose: The purpose of this lab is to come up with a model for air resistance, which acting on a falling object, opposes the force of gravity.
Theory: Air resistance is a type of frictional force. It opposes motion in any direction. In this lab however, we will only focus on the effect it has on falling objects. Using coffee filters due to their ability to reach terminal velocity in freefall fairly easily, we can figure out the force that they are applying against gravity by using their velocities and masses.
Apparatus: Our apparatus was fairly simple; there was a long black drape that was used as a backdrop for a meter stick that was taped, and hanged off of a second-story balcony. Then coffee filters were dropped from the same balcony, and videos were recorded on our class laptops using logger pro. The meter stick was used to create a scale on logger pro, and the filters' motion was tracked and plotted on a graph by the software. The coffee filters were dropped 5 different times; they were stacked on top of each other in increments of 1,2,3,4, and5 coffee filters. After the motions were plotted by logger pro, we recorded the terminal velocities, given by the slope of the linear fit line. We then calculated the masses of the coffee filters using the fact that 150 filters had a mass of 134.2g.
The first three graphs below show the velocities of the filters in freefall. There was an error when the videos were recorded and we did not have data for 4 filters. The other graph is missing because I must have accidentally erased it. After we got all of the terminal velocities, we then plotted the velocities on a new sheet on the x-axis, with their respective masses on the y-axis and then we did a power fit line to generate a function, which was our model for air resistance. Air resistance was =k*v^n
k=constant=0.0003911+/-0.0001674
v=velocity=variable
n=power=3.299+/-0.6374
Conclusion: I do not think that this model works very well for air resistance as a whole. This is because this model is only for anything that is shaped like a coffee filter. Since air resistance is very dependent on the shape of the object moving through the fluid, something as simple as inverting the filter will cause this model to be inaccurate.
25 Sep 2016 - Non Constant Acceleration - Lab 3
Purpose:The purpose of this lab was to figure out how to use excel to help us calculate and interpret data using a computer, rather than doing it by hand.
Apparatus: Apple laptop.
Theory: We had a problem with an elephant on roller skates with a rocket strapped on its back, that came down a hill and then had the rocket ignite in direction opposite of its path. The information that we were looking for was the total distance that the elephant traveled before the rocket stopped it completely and changed its direction. We then took all of the given data and came up with a formula for the elephants acceleration. We could have then integrated the formula two times in order to come up with a position formula in order to find the total distance traveled by the elephant before its direction was reversed, but instead we used Microsoft Excel to find the information that we needed. We plugged in all of our numbers into the appropriate spaces and figured out out that between 19 and 20 seconds after the rocket firing is where the velocity will be zero. The total distance was then calculated to be 248m, which is in line with what the accepted value for this problem was. Each column at the top had formulas(that I cannot remember due to this lab being completed late, which is why I will stay on top of my labs from now on) that were filled down the columns.
Conclusion:
1) The results that we achieved numerically were exactly the same results that came from handling the problem analytically.
2) You could tell that the time interval chosen was small enough because when you plug in numbers you would get a number that is almost zero.
3) (do this with spreadsheet in class computer)
Lab Partners were Cesar and Elliot
Apparatus: Apple laptop.
Theory: We had a problem with an elephant on roller skates with a rocket strapped on its back, that came down a hill and then had the rocket ignite in direction opposite of its path. The information that we were looking for was the total distance that the elephant traveled before the rocket stopped it completely and changed its direction. We then took all of the given data and came up with a formula for the elephants acceleration. We could have then integrated the formula two times in order to come up with a position formula in order to find the total distance traveled by the elephant before its direction was reversed, but instead we used Microsoft Excel to find the information that we needed. We plugged in all of our numbers into the appropriate spaces and figured out out that between 19 and 20 seconds after the rocket firing is where the velocity will be zero. The total distance was then calculated to be 248m, which is in line with what the accepted value for this problem was. Each column at the top had formulas(that I cannot remember due to this lab being completed late, which is why I will stay on top of my labs from now on) that were filled down the columns.
1) The results that we achieved numerically were exactly the same results that came from handling the problem analytically.
2) You could tell that the time interval chosen was small enough because when you plug in numbers you would get a number that is almost zero.
3) (do this with spreadsheet in class computer)
Lab Partners were Cesar and Elliot
Sunday, September 25, 2016
25 Sep 2016 - Freefall Lab - Lab 2
Purpose: To test whether or not gravity on Earth accelerates objects at 9.8 m/s^2.
Apparatus: A 1.5m tall stand with a wire running along the entire height. There is a long, thin strip of paper that has marks "burned" on the from the wire at 60hz. at the top of the apparatus, there is a metal weight that is held up by an electromagnet. This metal weight is what causes the marks to be made at the paper. The position of the weight over the 1.5m drop is recorded at 60hz(1/60th of a second).
Theory: We are trying to measure the value of acceleration due to gravity on a falling object. The position of a falling object is recorded in exact time intervals of 1/60th of a second, and then was measured because it was imprinted on a 1.5m long strip of tape. We then plotted our points on a graph with the time on the x-axis and the change in distance on the y-axis. After this we then created a linear trendline and found the slope. The slope of the line gave us our value of gravity, as calculated using our measurements. The slope of a the line gives us our value of gravity because it shows acceleration. We know that the graph shows acceleration because if it was a constant speed with no acceleration, the line would have a slope of 0 and be flat.
Conclusions: Our value of gravity ended up being 9.2618 m/s^2, which was significantly off from the accepted value of gravity.
(9.81-9.2618/9.81)x100%=5.6% error
This error could have came from many sources, such as uncertainty as to the exact position of the falling object, because the marks on the paper were not perfect. Another source of error was human error in measuring the distances between the marks on the paper. One other source of possible error is that air resistance was not accounted for.
Questions:
1)if at t=0seconds v=1m/s; t=1 v=2; and t=2 v=3
the mid velocity is 2m/s
however, the average over the entire 2 second interval, is (3+1)/2=2m/s.
the mid-interval and average velocities are the same for constant acceleration.
2)
3)(already done above)
Part 2
1. The pattern of all the values from the class is that they are all very off from the accepted value.
2. The average value of the class is much lower than what is accepted.
3.All of the class values, except for one, are lower than the accepted value of g. This is due to systematic error. Either the experiment used to test the value of g was not a very good one, or the apparatus could have been a source of error. Another likely reason for consistent lower values of g is that air resistance has not been accounted for. Air resistance opposes the force of gravity in this situation and could have been great enough to affect our values enough to effectively lower the values for the entire class.
Lab Partners were Elliot and Cesar.
Apparatus: A 1.5m tall stand with a wire running along the entire height. There is a long, thin strip of paper that has marks "burned" on the from the wire at 60hz. at the top of the apparatus, there is a metal weight that is held up by an electromagnet. This metal weight is what causes the marks to be made at the paper. The position of the weight over the 1.5m drop is recorded at 60hz(1/60th of a second).
Theory: We are trying to measure the value of acceleration due to gravity on a falling object. The position of a falling object is recorded in exact time intervals of 1/60th of a second, and then was measured because it was imprinted on a 1.5m long strip of tape. We then plotted our points on a graph with the time on the x-axis and the change in distance on the y-axis. After this we then created a linear trendline and found the slope. The slope of the line gave us our value of gravity, as calculated using our measurements. The slope of a the line gives us our value of gravity because it shows acceleration. We know that the graph shows acceleration because if it was a constant speed with no acceleration, the line would have a slope of 0 and be flat.
(9.81-9.2618/9.81)x100%=5.6% error
This error could have came from many sources, such as uncertainty as to the exact position of the falling object, because the marks on the paper were not perfect. Another source of error was human error in measuring the distances between the marks on the paper. One other source of possible error is that air resistance was not accounted for.
Questions:
1)if at t=0seconds v=1m/s; t=1 v=2; and t=2 v=3
the mid velocity is 2m/s
however, the average over the entire 2 second interval, is (3+1)/2=2m/s.
the mid-interval and average velocities are the same for constant acceleration.
2)
3)(already done above)
Part 2
2. The average value of the class is much lower than what is accepted.
3.All of the class values, except for one, are lower than the accepted value of g. This is due to systematic error. Either the experiment used to test the value of g was not a very good one, or the apparatus could have been a source of error. Another likely reason for consistent lower values of g is that air resistance has not been accounted for. Air resistance opposes the force of gravity in this situation and could have been great enough to affect our values enough to effectively lower the values for the entire class.
Wednesday, September 7, 2016
7 Sep 2016 - Inertial Pendulum - Lab 1
Purpose: To find relationship between Period + Mass for an inertial pendulum.
Apparatus: Tray held on by two sheets of metal of approximate dimension (each: 1"x10"x1/16"), that was clamped onto the edge of the lab table.There was a tape on the tray side,which was suspended in the air, that was used as a marker of position every time the tray would oscillate through a photogate. The photogate measured the period of the swinging tray. 0-800 g of mass were added to the tray in 100g increments, and period was measured each time.
Theory: T= A(mass+Mtray)^n
Using the data we inputted into the computer, we determined that the mass of the tray was between 320g and 420g.
Unknown 1 had a period of .3908s with a measured mass of 174 grams
Unknown 2 had a period of .3344s with a measured mass of 78 grams.
Lab Partners were Kyle and Cesar.
Apparatus: Tray held on by two sheets of metal of approximate dimension (each: 1"x10"x1/16"), that was clamped onto the edge of the lab table.There was a tape on the tray side,which was suspended in the air, that was used as a marker of position every time the tray would oscillate through a photogate. The photogate measured the period of the swinging tray. 0-800 g of mass were added to the tray in 100g increments, and period was measured each time.
Theory: T= A(mass+Mtray)^n
Using the data we inputted into the computer, we determined that the mass of the tray was between 320g and 420g.
Unknown 1 had a period of .3908s with a measured mass of 174 grams
Unknown 2 had a period of .3344s with a measured mass of 78 grams.
Lab Partners were Kyle and Cesar.
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