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course Phy 121
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See also conservation of energy on an incline, short version, which is appropriate for all Principles of Physics students, and for General College Physics students whose lab goal is to just pass the required lab portion of the course.
Note that the data program is in a continual state of revision and should be downloaded with every lab.
Hypothesis: The total of the potential and kinetic energies is nearly constant as a ball rolls down a grooved track, except for a small friction loss.
In this experiment we test the hypothesis that, for a ball rolling without slipping on a constant incline, the increase in the kinetic energy of the ball is very nearly equal to the decrease in its potential energy, and that the difference is within experimental error equal to the work done against friction.
See CD EPS01 for Lab Kit Experiment 16. The video file shows a toy car rolling down an incline; in this experiment we will use a ball on an incline.
The kinetic energy in this experiment includes both the translational kinetic energy, which is the kinetic energy 1/2 m v^2 associated with the motion at velocity v of the center of mass, and the rotational kinetic energy, the kinetic energy associated with the 'spinning' motion of the ball about its center of mass.
As in previous experiments, we will determine the velocity of the ball by using its projectile behavior as it rolls down then off of the end of the incline before falling to the floor. You will be able to use the data analysis program to determine the translational velocity attained by the ball.
Once the translational velocity and hence the translational kinetic energy is determined, the dimensions of the ball and the ramp will determine the ratio of rotational to translational kinetic energy.
Using a 'constant-velocity ramp' you will determine the slope necessary to overcome friction, which provide a good indication of the energy lost to friction.
Once you know the translational and rotational kinetic energies gained by rolling down the incline, and the energy required to overcome friction, you will be able to compare the total of these energies with the potential energy loss of the ball as it rolls down the incline.
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Begin by setting up the ramp and determining the slope at which the frictional force and the component of the gravitational force directed down the plane are in equilibrium. From this we will determine the frictional force for small slopes.
The key is to use a ramp that is just barely steep enough that the ball will travel up then 'turn around'.
Note: If you have only the 15 cm ramp and a large marble, rather than the 30 cm ramp and steel ball, it is still possible to get good results for this experiment. Use dimes instead of quarters in order to get a ramp just barely steep enough to allow the marble to turn around and come back down (other combinations of coins may also be useful; for example a quarter on one end and a dime on the other will make the ramp even less steep). It isn't hard to get a 15-cm ramp on which the ball takes at least a couple of seconds to travel up, and a couple more seconds to travel back down.
Use the larger of the steel balls provided with your lab kit; if you don't have the steel balls use the larger marble..
• Place the incline on a reasonably level tabletop or countertop. Place a quarter under the right end of the incline. Place the ball at the 'bottom' of the incline and give it a nudge, sufficient to carry it at least halfway up the incline. If the ball rolls up the incline, then turns around and rolls back down, then the quarter 'works' for right end.
• Then place the quarter under the left end of the incline, and repeat the trial. If the ball rolls up the incline, then without any interference reverses direction and rolls back down, then the quarter 'works' for the left end and you can proceed.
• If the quarter didn't 'work' both ways, then try again using two quarters. Keep increasing the number of quarters one at a time, until the system 'works' both ways.
• Make a note of the number of quarters you end up using.
• Place your quarter(s) under the right edge of the incline, place the ball a couple of centimeters above the other end and give the ball a quick nudge. Time the ball as it travels up the incline, then as it travels back down. Also note the point at which the ball turns around (this can be done by placing a marker at the 'highest' point of the ball's path).
• Record the distance up and the distance down, as well as the time up and the time down.
• Repeat until you have 5 trials. The distances don't have to be the same every time, but the times up and the time back down should in each case (each) be at least 2 seconds.
In the box below report in the first line the distance up, the time required to travel up, the distance down and the time to travel down the incline on the first trial. In the second thru the fifth lines, report the same information for your subsequent trials. Starting in the next line, indicate the meanings of the numbers you have reported.
----->>>> dist and `dt up, dist and `dt down each of 5 trials
Your answer (start in the next line):
18.55 cm, 2.13 sec, 18.55 cm, 2.77 sec
18.33 cm, 2.14 sec, 18.33 cm, 2.79 sec
18.47 cm, 2.11 sec, 18.47 cm, 2.58 sec
18.65 cm, 1.9 sec, 18.65 cm, 2.33 sec
18.85 cm, 2.14 sec, 18.85 cm, 2.88 sec
The first number and the third number is the distance traveled by the ball. Second numbers are the times for going up/down ramp.
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In the space below report, one trial to a line in comma-delimited format, the acceleration up and the acceleration down the incline, and the difference in these accelerations. Beginning in the sixth line explain how you determined your accelerations from the given data. Be sure your explanation connects your determination of acceleration result to the initial data, and be sure to include an explanation of the algebra of the units, and include a sample calculation for one of your trials.
----->>>> accel up, down 5 trials
Your answer (start in the next line):
8.17cm/s/s, 4.84 cm/s/s, 3.33 cm/s/s
8.005 cm/s/s, 4.71 cm/s/s, 3.295 cm/s/s
8.30 cm/s/s, 5.55 cm/s/s, 2.75 cm/s/s
10.33 cm/s/s, 6.87 cm/s/s, 3.46 cm/s/s
8.23 cm/s/s, 4.55 cm/s/s, 3.68 cm/s/s
I found this (for example using the first one) 18.55 cm/ 2.13 sec=
8.71 * 2= 17.42= 17.42/2.13= 8.17 cm/s/s (first number)
18.55/ 2.77 sec= 6.70= 6.70 *2= 13.39/ 2.77= 4.84 (second number)
8.17 cm/s/s- 4.84 cm/s/s= 3.3 cm/s/s (third number)
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Now place the quarters under the other end and repeat to obtain at least 5 trials.
• For each trial determine the acceleration of the ball as it travels up the incline, and as it travels back down.
In the space below report in the first line the distance up, the time required to travel up, the distance down and the time to travel down the incline on the first trial. In the second thru the fifth lines, report the same information for your subsequent trials.
----->>>> repeat with quarters
Your answer (start in the next line):
18.75 cm, 1.99 sec, 18.75 cm, 2.33 sec
17.88 cm, 1.77 sec, 17.88 cm, 2.18 sec
18.11 cm, 2.01 sec, 18.11 cm, 2.24 sec
18.99 cm, 2.22 sec, 18.99 cm, 2.77 sec
18.85 cm, 2.13 sec, 18.85 cm, 2.35 sec
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In the space below report, one trial to a line in comma-delimited format, the acceleration up and the acceleration down the incline, and the difference in these accelerations. Beginning in the sixth line explain how you determined your accelerations.
----->>>> accel 5 trials
Your answer (start in the next line):
9.47 cm/s/s, 6.91 cm/s/s, 2.56 cm/s/s
11.41 cm/s/s, 7.52 cm/s/s, 3.80 cm/s/s
8.97 cm/s/s, 7.22 cm/s/s, 1.75 cm/s/s
7.71 cm/s/s, 4.95 cm/s/s, 2.76 cm/s/s
8.31 cm/s/s, 6.83 cm/s/s, 1.48 cm/s/s
You may if you wish do the remainder of this experiment using your data from the experiment 'Uniformity of Acceleration for a Ball on a Ramp' (that experiment is in turn a continuation of the experiment Ball and Ramp Projectile Behavior, which preceded it). In those experiments you set up '2-, 3- and 4-domino ramps' and carefully observed the range of the ball as it rolls down and off the ramp. Based on the ranges and the vertical drop, you used the data analysis program to determine the speed of the ball at the end of the ramp.
• If you have only the 15-cm ramp then you would have used half the specified number of dominoes (i.e., 1 domino instead of the specified 2, and 2 dominoes instead of the specified 4), and your 10, 20 and 30 cm rolls were probably 5, 10 and 15 cm).
• The data program requests the number of dominoes, from which it calculates a slope based on a 30-cm ramp. A 15-cm ramp has only half the 'run' of a 30-cm ramp, so if you used a 15-cm ramp you would enter double the number of dominoes you actually used. That is, if you use 1 domino on a 15-cm ramp, tell the program you used 2; if you used 2 dominoes tell the program you used 4. If you happened to use 3 or 4 dominoes, you would tell the program you used 6 or 8, respectively.
If not, you should review the instructions for those experiments, set up ramps with 2 and 4 dominoes (1 and 2 dominoes if using a 15-cm ramp). Using 5 trials you should obtain horizontal ranges for the ball rolling distances of 15 cm and 30 cm along each ramp (use 7.5 and 15 cm if you have only the 15-cm ramp), and calculate the mean and standard deviation of ranges for each set of 5 trials. You will have a total of 4 five-trial means and standard deviations to report.
If you use the data from the experiments you will have information for 10, 20 and 30 cm rolls on 2- and 4-domino ramps, for a total of 6 five-trial means and standard deviations, which you will have reported once already (you should report once more).
In the space below report in the first line the number of dominoes, the distance of the roll down the ramp, and the mean and standard deviation of the horizontal range for your first setup. In the second line report the same information for your second setup, etc., until you have reported your results for all of your setups (4 setups if you obtained new data for the experiment, 6 setups if you used your old data). In the first subsequent line, give the distance the ball fell after leaving the end of the ramp.
-------->>>> 10, 20, 30 cm rolls 2 and 4 dom; report # dom, dist, mean and std dev of horiz range first ramp; same reversed ramp; then 2d, then if present 3d; also vert dist of fall
Your answer (start in the next line):
2 Dominoes, 10 cm, 7.99 cm, +-.2881 cm
2 Dominoes, 20 cm, 8.04 cm, +-.4944 cm
2 Dominoes, 30 cm, 8.19 cm, +-.487 cm
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You might already have your data and your results from the previous experiment. However if you are using data obtained specifically for this experiment, you will need to use your mean horizontal ranges to find the corresponding velocities. The instructions for doing so were given in the previous experiments, and are repeated here for easy access:
Using the 'Experiment-Specific Calculations' button, select 1, as you did in the preceding experiment, and respond with the information necessary to calculate the speed of the ball at the end of the ramp, based on the mean distance observed for your first set of 5 trials.
The program is the simplest way to get your results, and the majority of students follow instructions and use it successfully. If you can't get that program to give you reasonable results, you can follow the alternative procedure below. This will take a little longer but the process is the same for every trial, and should quickly become routine.
• Using the acceleration of gravity and the distance to the floor, figure out the time `dt it takes the ball to fall from rest from the end of the ramp. For typical distances to the floor the time of fall will be in the neighborhood of .4 seconds.
• Using your value of `dt and the horizontal displacement of the ball after leaving the end of the ramp, calculate the resulting average horizontal velocity. This is a fairly good approximation of the velocity at the end of the ramp.
• Multiply your horizontal velocity by the slope of the ramp. This gives you a pretty good approximation of the vertical component of the ball's speed as it leaves the end of the ramp. Note that the slope of your ramp (its rise / run) will probably be between .05 and .12.
• Using the ball's vertical velocity when it leaves the end of the ramp, and the acceleration of gravity, find the corrected time of fall, which we will call `dt_corr. Be sure you are careful about the signs of your quantities.
• Using `dt_corr and your horizontal displacement, find the corrected horizontal velocity.
• Your corrected horizontal velocity still won't be exactly right (you would have to continue the above process and infinite number of times to refine it to an exact value), but the difference is unlikely exceed experimental uncertainty.
• The difference between the horizontal component of the ball's and the magnitude of its velocity at the end of the ramp will also be insignificant.
In the space below, report in the first line the number of dominoes, the distance of the roll and the final velocity on the ramp for the first trial. In subsequent lines report the same information for subsequent trials: If you got your results by calculating rather than by using the program, include a sample calculation for one of the trials.
------>>>>> # dom, dist of roll, final vel 1st trial; then subsequent trials
Your answer (start in the next line):
2 Dominoes, 10 cm, 20.5 cm/s
2 Dominoes, 20 cm, 20.7 cm/s
2 Dominoes, 30 cm, 20.9 cm/s
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Measure the height of a stack of 4 dominoes, as accurately as you can. In the space below give in the first line the height per domino. In the second line describe how you made your measurement and how you then determined the height per domino.
------>>>>> height per domino
Your answer (start in the next line):
3.85 cm
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For the 2-domino ramp, the ramp descends through a distance equal to the height of two dominoes while rolling a distance of about 30 cm. In the space below, give in the first line the total descent of the ball for the entire 30 cm of roll. In the second line give the amount of descent per cm of roll. Starting in the third line explain how you obtained your two results.
Note that the word 'descent' is clearly defined in the above paragraph being equal to the height of two dominoes; 'descent' refers to the vertical distance through which the ball descends. If the ball rolls 30 cm, it does not descend 30 cm. 30 cm would be the distance of roll for the trial in which the domino rolled the entire length of the ramp. Its descent for the entire 30-cm roll will in this case be about equal to the height of the two dominoes (perhaps a little more, depending on exactly where the dominoes were positioned).
------>>>>> dist of descent, descent per cm, 2 dom
Your answer (start in the next line):
1.67 cm
.059 cm
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For the 2-domino ramp, use the preceding results to determine the amount of descent that would correspond to rolls of 10 cm, 15 cm, 20 cm and 30 cm. Give these results as 4 numbers in the first line, delimited by commas. In the second line explain how you obtained your results.
To check whether your results make sense, note that the more centimeters the ball rolls, the further it will descend. You just got done calculating the amount of descent per cm of roll, which provides a basis for the present calculation.
------->>>>>>> descent for 10, 15, 20 and 30 cm on 2 dom ramp
Your answer (start in the next line):
For 10 cm: .55, for 15 cm: .84, for 20 cm: 1.11, for 30 cm: 1.67
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For your remaining calculations, assume that the mass of the ball is 100 grams. This isn't completely accurate, but the mass of the ball isn't critical and if necessary results could later be adjusted very easily for the accurate mass.
Determine how much work it would take to raise the mass of the ball, against the downward gravitational pull, through each of the distances of descent you have calculated. In the space below indicate in the first line the first distance of descent, then the work. In subsequent lines give the remaining distances of descent and corresponding amounts of work. In the first line following your data lines, specify the units of the quantities you have given, and explain how you obtained your results. Include a set of sample calculations for one of your lines.
----->>>> work to raise 100 g thru each dist of descent, each line dist of descent and work to raise
Your answer (start in the next line):
2 Dominoes, 10 cm, .55 cm of descent, .00539 J
2 Dominoes, 15 cm, .84 cm of descent, .00823 J
2 Dominoes, 20 cm, 1.11 cm of descent, .0108 J
2 Dominoes, 30 cm, 1.67 cm of descent, .0164 J
F = 9.8 * .1 kg
= .98 N
W = .98 N * ( .55 cm/ 100 cm/ 1 m )
W = .00539 J ( N-m )
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The differences in acceleration observed at the beginning of this experiment, between the ball traveling up the ramp and the ball traveling down the ramp, are due to the change in the direction of the frictional force.
• At any point on the ramp, the gravitational force has a component along the ramp, which is the same whether the ball is moving up or down.
• However the frictional force is always in the direction opposite the motion, so when the ball is moving up the ramp the frictional force is in the same direction as the gravitational force component along the ramp, whereas when the ball is moving down the ramp the frictional force is in the opposite direction.
• It follows that the difference in net force while the ball is traveling up the ramp, and the net force while the ball is traveling down the ramp, is double the force of friction.
Based on the above:
• What was the average of the differences previously observed between the accelerations up the ramp and the acceleration down the ramp? Answer in the first line of the space below.
• On a 100-gram ball, how much difference in force would be required, to result in this much acceleration? Answer in the second line of the space below.
• What therefore is the force of friction on the ball? Answer in the third line of the space below.
• Starting in the fourth line, explain how you obtained your results. Include a set of sample calculuations.
------>>>>>> ave of differences between accel, force diff required, frictional force
Your answer (start in the next line):
7.22, 4.95
.00702 N, .0045 N
.00315 N, .0025 N
a = 7.22 cm/s/s
F = m * a
F = ( .1 kg * 7.22 cm/s/s / 100 cm/ 1 m )
F = .00702 N
F_friction = .5 * .00702 N
F_friction = .00315 N
.007 N is the force required, on one particular trial, to accelerate the ball at 7 cm/s^2.
However 7 cm/s^2 appears to be the acceleration of the ball on the incline, not the difference in the up and down accelerations, which typically was in the general vicinity of 3 cm/s^2.
Please reread this question and modify accordingly
We need to compare PE loss, work against friction, translational KE and rotational KE. Are your units for these quantities all the same?
----->>>>> are units compatible?
Your answer (start in the next line):
Yes in joules
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Standard units of work/energy are:
• Joules, which are the same as N * m, or kg * m^2 / s^2, and
• ergs, which are the same as dyne * cm, or g * cm^2 / s^2.
We expect that PE loss should be equal to total KE gain + work done against friction, where total KE gain is translational KE gain + rotational KE gain.
Your instructor is trying to gauge the typical time spent by students on these experiments. Please answer the following question as accurately as you can, understanding that your answer will be used only for the stated purpose and has no bearing on your grades:
• Approximately how long did it take you to complete this experiment?
Your answer (start in the next line):
3 hours
Standard units of work/energy are:
• Joules, which are the same as N * m, or kg * m^2 / s^2, and
• ergs, which are the same as dyne * cm, or g * cm^2 / s^2.
We expect that PE loss should be equal to total KE gain + work done against friction, where total KE gain is translational KE gain + rotational KE gain.
Your instructor is trying to gauge the typical time spent by students on these experiments. Please answer the following question as accurately as you can, understanding that your answer will be used only for the stated purpose and has no bearing on your grades:
• Approximately how long did it take you to complete this experiment?
Your answer (start in the next line):
3 hours
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Excellent data, and good analysis, but I'm not sure you answered that last question correctly.
&#Please see my notes and submit a copy of this document with revisions, comments and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes. &#
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