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Phy 121
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Help with Lab
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You could easily and quickly repeat these calculations for the remaining 11 trials, and may do so if you wish. However, first click again on the 'Experiment-Specific Calculations' button, select 2, and enter when prompted the distance the ball moved down the ramp (10, 20 or 30 cm as required), the velocity reported previously for the trial, and the program will indicate the associated acceleration.
Using whatever means you believe will be most efficient, calculate the remaining accelerations.
Report the resulting accelerations below, three accelerations for each setup, in the same order and the same format used in the preceding box. Report three accelerations per line, separated by commas. You will report 4 lines, including one you can report as 'skipped'
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I am not sure what I am supposed to do to find experiment specific calculation. I do not have access to the data program.
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You can calculate accelerations based on the average velocities you calculated for the projectile motion. That will give you the final velocity on the ramp. The initial velocity is zero, and you know the distance on the ramp, so you will be able to reason out the acceleration.
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phy121
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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The complete analysis of the motion of the ball follows.
This analysis neglects the effects of air resistance, which at the level of precision attained in this experiment are insignificant. It also neglects edge effects at the end of the ramp (the ball does remain in contact with the ramp for a short time after it begins its fall; at the speeds encountered here that time will be very short and the effects are likely negligible).
General College Physics and University Physics students will be expected to understand the analysis; Principles of Physics students should understand the general scheme and are encouraged, but not required to understand all the details of this analysis.
You can skim (skim, not skip) this analysis now and come back to it after completing the experiment.
The ball leaves the ramp with an unknown velocity, which we will call v, at an angle theta below horizontal. We can easily determine theta from the slope of the ramp (tan(theta) = ramp slope).
The ball therefore has an initial downward vertical velocity v0_y = v sin(theta) and initial horizontal velocity v0_x = v cos(theta).
Let clock time be t = 0 at the instant the ball leaves the ramp. The horizontal velocity is constant so at a later clock time t the x position of the ball will be
x = v0_x * t.
Let the downward direction be positive. Then the initial vertical velocity is in the positive direction, as is the acceleration of gravity, so the vertical position at clock time t will be
y = v0_y * t + 1/2 g t^2.
v0_x and v0_y can both be expressed in terms of the unknown initial velocity v and the known angle theta.
At the instant of impact, x will be equal to the horizontal range of the projectile, and y will be equal to its distance of fall. Using x_range and y_fall for these distances we have the two equations
x_range = v0_x * t and
y_fall = v0_y * t + 1/2 g t^2.
Writing v cos(theta) and v sin(theta) for v0_x and v0_y the equations become
x_range = v cos(theta) * t and
y_fall = v sin(theta) * t + 1/2 g t^2.
All quantities in these equations are known, except t and v. So we have a system of two simultaneous equations which can be solved for v and t. (note that though we haven't yet solved for theta, we could do so at any time, given the information we have for the slope)
The solution is fairly straightforward. We solve the first equation for t, obtaining t = x_range / (v cos(theta) ). Then we plug this into the second equation to obtain
y_fall = v sin(theta) * (x_range / (v cos(theta)) + 1/2 g ( x_range / (v cos(theta))^2
which simplifies to
y_fall = x_range * tan(theta) + 1/2 g x_range^2 / (v^2 cos^2(theta))
You should be able to write this equation in standard mathematical notation, and when working through this analysis for yourself you should do so. For easy reference the equation looks like this:
It is straightforward to solve this equation for v. We obtain
v = +- sqrt( 1/2 g x_range^2 / (y_fall - x_range * tan(theta) ) / cos(theta).
Since we are only interested in the speed of the ball, we use the positive solution.
In standard simplified form the positive solution would be represented as follows::
We still haven't figured out theta.
We could figure out theta (theta = arcTan(ramp slope); use the calculator to get theta and then cos(theta) and sin(theta)) but we probably won't.
We can more easily use the sides of our ramp-slope triangle to find sin(theta) and cos(theta)
Alternatively we can use the fact that tan(theta) = ramp slope to figure out that
sin(theta) = ramp slope / sqrt(1 + ramp slope^2) and
cos(theta) = 1 / (1 + ramp slope)^2.
Once we have this information we can plug g, x_range, y_fall and our theta-related information into the equation to get v.
This formula will probably fairly meaningless to most students at this point, though most should have a fair idea of how it was obtained. The calculation has been built into the data analysis program. Just click on the Experiment-Specific Calculations button and choose the Ball and Ramp Projectile Experiment. Enter the following upon request:
the change in the ball's vertical position from the end of the ramp to the piece of plywood on the floor as the height of the drop (i.e., y_fall),
the difference between your mean straight-drop and projectile-landing positions as the horizontal range (i.e., x_range), and
the number of dominoes in the stack (from which the program will calculate slope, theta, etc).
Your information and the velocity of the ball, in cm/sec, will appear in the data window.
&#&# The program works, if you enter the data as indicated. If you get an error message, then give it another try, being careful to enter the data using the required syntax. If it doesn't work, copy the contents of each text box used at each step, as it appears just before you click the button, and also specify which button you clicked. Use one line for each textbox entry.
If it worked, you can leave the space below blank.&#&#
-------->>>>>>>> details, in case the program doesn't appear to have worked
Your answer (start in the next line):
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Not sure what I should do here, since this data program does not work on my Mac computer
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This part of the experiment analyzes the projectile behavior of the ball, giving you its average horizontal velocity.
You can ignore the slope of the ramp and assume that the ball's velocity as it leaves the ramp is horizontal. With that assumption you can find its average (and unchanging) horizontal velocity as it drops to the floor.
This is the velocity you will use as a basis for calculating the acceleration, per your previous question.
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phy 121
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Analysis of Angular Velocity Strap
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I am completely confused on the lab, I do not know where to even start. The first question: Report in the first line below the data you previously obtained for the trial with the least average velocity.
I am sorry, I just do not understand this at all.
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Your work on the Angular Velocity of a Strap lab was posted at your access site as
10-10-2013_____angular_velocity_of_a_strap
In the lab you calculated average angular velocities. You also reported your data as
45, 0.950, 1.242, 1.10
90, 0.729, 1.072, 1.799, 1.847
130, 1.278, 1. 644, 2.422
60, 1.057, 2.137, 2.392
110, 1.084, 1.714, 2.126
50, 1.187, 1.377, 2.579
30, 0.748, 0.758, 0.962, 1.243, 2.320, 0.888
135, 1.19, 1.774, 3.353
On each of those trials you calculated average angular velocity. One of those trials therefore had the least average angular velocity, and that is the data that you need to report in the present lab.
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Phy 121
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Experiment 7. Measuring Masses
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I am not sure where I am supposed to get the weight set. I watched the video and I can only find in my lab kit a sharp edge knife, and paper clips. I do not understand how I am supposed to weigh the the differences in weights for each different weight, if that makes sense. thank you for answering all of my questions. For some reason I am really having trouble understanding some of the experiments.
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The instructions for that experiment are
Experiment 7, Measuring masses: view only (on DVD)
'View only' means that you are just to watch the video. You aren't expected to perform the experiment. However it is possible that questions related to this experiment could appear on a test.
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