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Phy 121
Your 'ball down ramp' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Ball Down Ramp_labelMessages **
9/15 4:02 pm
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Timing a Ball down a Ramp
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A ball is timed as it rolls from rest to the end of a ramp. The slope of the ramp is varied. Preliminary conclusions are drawn about the motion and the effect of ramp slope. A subsequent lab exercise uses the data from this lab to reach additional conclusions.
Most students report completion times between 45 minutes and 75 minutes hour, with a few reporting times as short as 25 minutes or as long as 2 hours. Median time of completion is around 1 hour.
Timing Ball down Ramp
The picture below shows a ball near the end of a grooved steel track (this steel track is a piece of 'shelf standard'); the shelf standard is supported by a stack of two dominoes. Your lab materials package contains two pieces of shelf standard; the shelf standard shown in the figure is white, but the one in your kit might be colored black, gold, silver or any of a variety of other colors.
If a ball rolls from an initial state of rest down three ramps with different slopes, the same distance along the ramp each time, do you think the time required to roll the length of the ramp will be greatest or least for the steepest ramp, or will the interval on the steepest ramp be neither the greatest nor the least? Explain why you think you have correctly predicted the behavior of the system.
Your answer (start in the next line):
The interval will be the least for the steepest ramp. I predict this based on years of observation. A skier goes faster down an expert hill as opposed to the beginner one. A kid goes faster down a steeper slide than she does down a less steep one. A boy on a skateboard goes much faster down a steep hill than a rather gradual one.
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If we write down the slopes from least to greatest, next to the time intervals observed for those slopes, would you expect the time intervals to be increasing or decreasing, or do you think there would be no clear pattern? Explain why you think you have correctly described the behavior of the numbers in the table.
Your answer (start in the next line):
The time intervals would be decreasing as slopes increase. Again from years of observation, steeper slopes produce higher velocities which would mean shorter time intervals.
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Set up the shelf standard ramp on a reasonably level table, using a piece of 30-cm shelf standard and a single domino under the high end of the ramp. Position the dominoes so that the last .5 cm of the ramp extends beyond the point where the ramp contacts the domino,.and do the same in all subsequent setups.
Set the bracket on the table, touching the lower end of the ramp so that a ball rolling down the ramp will strike the bracket..
Mark a point about 3 cm below the top end of the ramp. Place a domino on the ramp to its high end is at this point, and place the ball just above the domino, so the domino is holding it back. Quickly pull the domino away from the ball so the ball begins to roll freely down the ramp. Allow the ball to roll until it strikes the bracket.
The bracket will probably move a little bit. Reset it at the end of the ramp.
Determine how far the ball rolled from release until it struck the bracket.
Now repeat, but this time use the TIMER. The first click will occur at the instant you release the ball, the second at the instant the ball strikes the bracket. Practice until you are as sure as you can be that you are clicking and pulling back the domino at the same instant, and that your second click is simultaneous with the ball striking the bracket.
When you are ready, do 5 trials 'for real' and record your time intervals.
Then reverse the system--without otherwise changing the position of the ramp, place the domino under the left end and position the bracket at the right end.
Time 5 trials with the ramp in this position.
In the space below, give the time interval for each trial, rounded to the nearest .001 second. Give 1 trial on each line, so that you will have a total of 10 lines, the first 5 lines for the first system, then 5 lines for the second system.
Beginning in 11th line give a short narrative description of what your data means and how it was collected.
Also describe what you were thinking, relevant to physics and the experiment, during the process of setting up the system and performing the trials.
Your answer (start in the next line):
1.732
1.699
1.746
1.607
1.668
1.996
2.059
2.105
1.965
1.996
All the above values are time intervals in seconds giving the time intervals for the ball to roll the length of the track. I used the timer program to record the time intervals. As I released the ball, I clicked the mouse, when the ball hit the bracket I clicked the mouse again. After five trials I reversed the direction of the track and performed 5 more trials. I made an informal prediction that the second of 5 trials would have on average longer time intervals. My house is old and not exactly level (is any house exactly level?) and so I figured the first 5 trials would have a slightly steeper slope than the second five trials and therefore the first 5 trials would be slightly faster. The data suggest this is true.
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Now place two dominoes under the right end and repeat the process, obtaining the time interval for each of 5 trials.
Then place the two dominoes under the left end and repeat once more.
Enter your 10 time intervals using the same format as before.
Your answer (start in the next line):
1.313
1.188
1.293
1.402
1.266
1.328
1.484
1.355
1.375
1.434
All values above are time intervals in seconds. Ramp is now supported on one end by two dominoes. First five are ball rolling right to left. Second five are ball rolling left to right.
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Repeat the preceding using 3 dominoes instead of 2. Enter your 10 time intervals using the same format as before.
Your answer (start in the next line):
1.078
1.250
1.266
1.105
1.250
1.156
1.184
1.277
1.105
1.105
All values above are time intervals in seconds. Ramp is now supported on one end by three dominoes. First five are ball rolling right to left. Second five are ball rolling left to right. Curiously, this time around the left to right rolls seem to be nearly as fast as the right to left rolls.
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Slight differences in slope make less and less difference as the slope, and therefore the time interval, decreases.
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Repeat the preceding again, still using the 3 domino setup, but this time place a CD or a DVD disk (or something of roughly similar thickness) on the 'low' end of the ramp. You need time only 5 intervals, but if you prefer you may use 10. Enter your 5 (or 10) time intervals using the same format as before.
Your answer (start in the next line):
1.109
1.184
1.059
1.137
1.203
1.219
1.141
1.156
1.188
1.109
All values above are time intervals in seconds. Ramp is now supported on one end by three dominoes and by a CD on the other end. First five are ball rolling right to left. Second five are ball rolling left to right.
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Repeat the preceding one last time, still using the 3 domino setup, but remove the disk and replace it with a piece of paper. You need time only 5 intervals, but if you prefer you may use 10. Enter your 5 (or 10) time intervals using the same format as before.
Your answer (start in the next line):
1.047
1.230
0.980
1.105
1.168
1.188
1.203
1.152
1.152
1.109
All values above are time intervals in seconds. Ramp is now supported on one end by three dominoes and by a single sheet of paper on the other end. First five are ball rolling right to left. Second five are ball rolling left to right.
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Do your results support or fail to support the hypotheses you stated in the first two questions, regarding the relationship between time intervals and slopes? Explain.
Your answer (start in the next line):
Some results support the hypotheses that as slope increases, time interval will decrease and that the trial with the greatest slope will have the shortest time interval. Just using the trials with the ball going from Right to Left, the ramp with one domino had the longest average time interval with an average of 1.690 seconds. The ramp with two dominoes was the next longest with an average time interval of 1.292 seconds. The ramp with three dominoes had the shortest average time interval with an average time interval of 1.189 seconds.
The ramps going Left to Right also supported the hypotheses. The ramp with one domino had the longest average time interval with an average of 2.024 seconds. The ramp with two dominoes was the next longest with an average time interval of 1.395 seconds. The ramp with three dominoes had the shortest average time interval with an average time interval of 1.165 seconds.
A few of the results fail to support this.
Putting the CD under the lower end of the ramp with three dominoes should have reduced the slope as compared to the three domino ramp. However in both the Right to Left and Left to Right trials, those with the CD were the faster of the two. Going Right to left, without the CD the average time interval was 1.189 seconds. In the same direction with the CD the average time interval was shorter at 1.1384. Going Left to Right, without the CD the average time interval was 1.165 seconds. In the same direction with the CD the average time interval was shorter at 1.162
A few reasons for the this unexpected set of results could be that the ramp was adjusted many times, It could have been that it was assembled slightly differently as time went on. This could affect results. Its is also possible that as time when on I got more adept and quicker at hitting the mouse in reaction to the ball reaching the end of the ramp.
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How do you think the average velocity of the ball is related to the slope of the ramp? Explain in as much detail as possible.
Your answer (start in the next line):
Despite some of the results failing to provide evidence to support the hypotheses, I think it is still safe to say that that average velocity of the ball increases as slope increases. If the `ds remains constant but `dt is decreasing, than average velocity will increase. In the trials not involving the CDs every time the slope increased, the time interval decreased. Thus the average velocity increased as slope increased.
I calculated the average velocity by dividing the length of the ramp from release point to end point which was 29.7 cm by the average time interval for each set of trials. I have my results in a table below.
The first column is the type of trial RL stands for Right to Left roll. LR stands for Left to Right roll and the digit represensts the number of dominoes in the stack. Thus LR2 means the ball rolled from left to right and had two dominoes in the stack proping up the high end of the ramp.
The second column is the average velocity in cm/s
RL1, 17.6
RL2, 22.9
RL3, 24.9
LR1, 14.7
LR2, 21.2
LR3, 25.5
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Good, but somewhere in close proximity to the table you need to specify the units of your results. It's clear that they are in cm/s, but this needs to be stated for potential readers who might not be completely confident.
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Speculate on what it is that causes the average velocity on these ramps to change with slope.
Your answer (start in the next line):
I speculate that it has to do with the force of gravity.
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How might you verify whether your speculations are indeed valid explanations?
Your answer (start in the next line):
At this point, I don't think I have enough knowledge of forces to suggest a way to verify this. The only idea I have is rather silly. It you held the track at an angle upside down in the air and put the ball on the underside of the track (ie the ball would have the track above it), it probably wouldn't roll along the track no matter how steep or gradual the track's angle was. The ball would simply drop to the ground. Gravity instead is the force moving the ball along.
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That's not a bad thought.
Here's a brief synopsis of the accepted explanation: Gravity pulls the ball down, which causes the ramp to bend and/or compress slightly and push on the ball. However the ramp can't push vertically, it can only push perpendicular to its direction. The gravitational force is directly downward, which is partly perpendicular to the ramp and partly in the direction parallel to the ramp. The component of the gravitational force perpendicular to the ramp is countered by the force exerted by the ramp. The component of the gravitational force parallel to the ramp is unopposed, and that's what accelerates the ball down the ramp.
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Do your data conclusively show that the disk made a difference?
Your answer (start in the next line):
My data shows that the CD made a difference, but as I explained above, it seemed to have made a difference in an unexpected way that goes against the reasoning of the earlier trials.
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Very good.
It's unlikely that the CD caused a speedup. You speculate on two possible explanations, both of which are very plausible.
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