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course PHY 241
12/12/10; 16:00
Brief Edge EffectUses two ramps, dominoes, steel balls, rulers
See also Pictures_of_ball_and_ramps, which includes pictures and brief descriptions of basic setups.
Roll a ball down the incline from rest and allow it to roll off the edge and fall to the floor. Do five trials, measuring the time required to reach the end of the ramp and the horizontal projectile distance after leaving the edge.
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Used the results from “ball off ramp experiment;” if I missed something to do I will be glad to take care of that issue.
`dy = 80.7 cm
`dx = 20 cm
`dt ramp = 1.03 s, 1.063 s, 1.04s, 1.112s, 94.45 s.
`dt air = .375 s!, .449 s, 0.4219 s, .325 s, .4889 s.
???????????????????????... transition to sliding [not sure what this means for me to do.]???????????????????????
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... edge effect (short incline -> longer incline supported by flat domino)
Set up and check the system out:
Set up with the longer incline supported at one end by a stack of two flat dominoes, the shorter incline supported at one end by a domino lying on its long edge and at the other by the lower end of the long incline. Allow the ball to roll down the shorter incline, off the edge and up the long incline. See how far it gets up the longer ramp.
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21cm
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Position the ball with its center right above the edge of the shorter incline. When released the ball should immediately roll off the edge, gaining some horizontal velocity that will carry it a ways up the longer incline. Release it and see how far it gets up the longer incline.
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3.1 cm
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Repeat, this time with a domino pressed flat against the end of the short incline so that the edge of the ball is aligned with the edge of the incline. When the domino is removed the ball will therefore roll a distance down the incline which is equal to its radius, before rolling off the edge. See how far the ball gets up the longer incline.
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5.0 cm
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Repeat again, this time spacing the ball from the end of the short incline by a distance equal to the thickness of a domino. The ball will therefore roll a distance equal to the thickness of the domino, plus its radius, before reaching the edge. See how far the ball travels up the incline.
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5.45 cm
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Repeat with the following spacings from the end of the ramp:
• Spacing equal to the thickness of two dominoes.
• Spacing equal to the width of a domino.
• Spacing equal to the length of a domino.
• Spacing equal to the length of a domino, plus a domino width.
• Spacing equal to the length of two dominoes.
• Spacing equal to the length of two dominoes, plus a domino width.
Report your data below:
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All of these lengths are measured from zero being the point at which the center of the ball is on the edge.
2D thick: [1domino’s thickness = 0.9 cm] 6.59 cm
1D wide: [2.55 cm] `dx=6.8 cm
1D long: [5.15] 10.9 cm
1D(thick + long): 11.5cm
1D (wide + long):14.75
1D (2l): 18.5 cm
1D (2l+1w): 20.9
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The portion that was here I did in a prior lab 5 hours ago. It is titled “Brief_ball_off_ramp.”
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Analysis:
Each roll up the long incline corresponds to an increase in the PE of the ball, which can be calculated given the mass of the ball (we will assume mass 60 grams) and the change in its vertical position while on that incline.
Assume that the thickness of the two-domino stack supporting the long ramp is 1.8 cm, so that a ball which rolls all the way up the ramp from the bottom to the top would rise 1.8 cm while traveling 30 cm. Just to be sure you understand what this means, answer the following:
How much higher does the ball go if it travels 30 cm (yes, the answer should be really obvious)?
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How much higher would it go if it only traveled 10 cm along the ramp?
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How much higher would it go if it only traveled 3 cm along the ramp?
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How much higher would it go if it only traveled 1 cm along the ramp?
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How could you use that last result to figure out how much higher the ball goes if it travels 7 cm along the ramp?
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Your answers to that last series of questions should have been .6 cm, .18 cm, .06 cm and 7 * .06 cm = .42 cm. If you didn't get those, you should let the instructor know, because you're going to need to be able to figure out how far the ball rises along that ramp for each of your various trials.
You have observed how far the ball travels along longer ramp, from various starting positions on the shorter ramp.
For each trial, figure out how far the ball traveled along the longer ramp, and how much higher it was at its 'turnaround point' than when it first contacted the ramp. If you need to estimate anything in order to do your calculation, make a reasonable estimate.
If you're not sure of your calculations you can enter them here and submit this for further guidance. Otherwise you can leave the space below blank and move on.
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Assuming that the dominoes are .9 cm thick, 2.5 cm wide and 5.0 cm long, find the distance the ball rolled along the first incline before rolling off the edge. For your very first trial, where the domino was released just at the edge, you would report distance 0.
Now make a table with three columns. The first column will be the rolling distances you just calculated. The second column will be the corresponding distances the ball rolled up the longer incline. The third column will be the change in the ball's height as it rolled along the longer incline.
Give your table:
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Assume that on the first ramp, the ball descended .1 cm for every centimeter it rolled. Assume also a ball mass of 60 grams.
For each trial, figure out how much gravitational PE the ball lost while rolling down the shorter incline (not counting the fall from the edge of the first incline to the longer incline), and how much gravitational PE it gained while rolling up the longer incline.
Report your results in the form of a table showing PE gained on longer incline vs. PE lost on shorter incline.
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At what position on the shorter incline did the PE gained on the longer incline begin to exceed the PE lost on the shorter?
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Plot each line of your table as a point on a graph of y = PE gained vs. x = PE lost. Sketch the smooth curve that seems to best indicate the trend of your data. Sketch also the line y = x.
Describe your graph.
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How is it possible that the ball could have more KE when it reaches the longer ramp than the PE it lost on the shorter? Give your best explanation of how that might have occurred on some of your trials.
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You appear to have good data. See the appended instructions for analysis.
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