Fortran Exercise # 2: Coefficient Of Restitution
Fortran Exercise #2: Coefficient Of Restitution
1. DEFINITION
In this lab, we shall be studying the coefficient of restitution of a superball. The coefficient of restitution, COR, is the ratio of the bounce-back velocity to the original velocity of an object undergoing impact (such as a ball impacting the ground after being dropped from an initial height). Using the principle of the conservation of energy, the COR can be used to relate the bounce-back height to the original height of a ball dropped from rest. In fact, this ratio is equal to the square of the COR. Mathematically, if a ball is dropped from a height h(0), and bounces back to a height h(1), then:
As the object hits the ground, it is compressed (like a spring) such that …show more content…
Your task will be to fill in the missing instructions and data. Specifically, you must: (1) enter the 5 measured bounce-back heights, (2) prompt for, read in, and echo an average (average over all five bounces), coefficient of restitution and the initial height of the ball, (3) calculate the bounce-back heights from the initial height and an average COR, and (4) after each calculation, print the bounce number, the calculated bounce-back height, and the measured bounce-back height on the same line. As you run the program, you will enter a guess for the COR and the initial height of the ball. The program will then compute and print out the calculated bounce-back heights. Compare the calculated heights to those measured at each bounce, and determine a better COR for the experiment. Keep running the program using different CORs until you obtain a "best" COR (to do this, you will have to keep running the program with different values of COR until you find one where the 5 calculated heights most closely match the measured bounce-back heights.)
Here, we define the variables for you, as follows - bounce number = i (integer)
2.1 Input quantities (to be …show more content…
the bounce number as follows:
4. CHECK RESULTS
Are the results intuitively correct? I.e., is the maximum 1.0? Is the minimum greater than zero? Does the height squared continually decrease with bounce number?
Do the COR squared and calculated bounce back heights match your hand calculation?
5. SUMMARY AND CONCLUSIONS
Discussion - answer the following questions and include your answers with the results you hand in:
Discuss why there is variability in the 5 measured heights at each bounce and whether our averaging process indeed did help us to obtain better values.
Discuss why the measured data do not agree perfectly with the calculated data. Be sure to note any systematic disagreement, i.e. any patterns - are the calculated values higher for lower bounces, and lower for higher bounces, or vice versa?
To aid in the previous discussion, tabulate and provide a separate file of COR(i) calculated from measured values vs. bounce number.
Discuss how the experiment could be improved and extended.
6. TO HAND IN:
After the program has been run to obtain the best value of COR, create a script file to hold the output.
%script cor.script
%whoami
%pwd
%ls -l
1. DEFINITION
In this lab, we shall be studying the coefficient of restitution of a superball. The coefficient of restitution, COR, is the ratio of the bounce-back velocity to the original velocity of an object undergoing impact (such as a ball impacting the ground after being dropped from an initial height). Using the principle of the conservation of energy, the COR can be used to relate the bounce-back height to the original height of a ball dropped from rest. In fact, this ratio is equal to the square of the COR. Mathematically, if a ball is dropped from a height h(0), and bounces back to a height h(1), then:
As the object hits the ground, it is compressed (like a spring) such that …show more content…
Your task will be to fill in the missing instructions and data. Specifically, you must: (1) enter the 5 measured bounce-back heights, (2) prompt for, read in, and echo an average (average over all five bounces), coefficient of restitution and the initial height of the ball, (3) calculate the bounce-back heights from the initial height and an average COR, and (4) after each calculation, print the bounce number, the calculated bounce-back height, and the measured bounce-back height on the same line. As you run the program, you will enter a guess for the COR and the initial height of the ball. The program will then compute and print out the calculated bounce-back heights. Compare the calculated heights to those measured at each bounce, and determine a better COR for the experiment. Keep running the program using different CORs until you obtain a "best" COR (to do this, you will have to keep running the program with different values of COR until you find one where the 5 calculated heights most closely match the measured bounce-back heights.)
Here, we define the variables for you, as follows - bounce number = i (integer)
2.1 Input quantities (to be …show more content…
the bounce number as follows:
4. CHECK RESULTS
Are the results intuitively correct? I.e., is the maximum 1.0? Is the minimum greater than zero? Does the height squared continually decrease with bounce number?
Do the COR squared and calculated bounce back heights match your hand calculation?
5. SUMMARY AND CONCLUSIONS
Discussion - answer the following questions and include your answers with the results you hand in:
Discuss why there is variability in the 5 measured heights at each bounce and whether our averaging process indeed did help us to obtain better values.
Discuss why the measured data do not agree perfectly with the calculated data. Be sure to note any systematic disagreement, i.e. any patterns - are the calculated values higher for lower bounces, and lower for higher bounces, or vice versa?
To aid in the previous discussion, tabulate and provide a separate file of COR(i) calculated from measured values vs. bounce number.
Discuss how the experiment could be improved and extended.
6. TO HAND IN:
After the program has been run to obtain the best value of COR, create a script file to hold the output.
%script cor.script
%whoami
%pwd
%ls -l