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course Mth 174
9/15 12
Report your counts for the five trials with the toy car going in the first direction in the first line below, separated by commas. Report you counts for the five trials with car going in the opposite direction in the second line below, separated by commas.5, 3, 2, 3, 3
3, 2.5, 3, 3, 2
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Report the five resulting accelerations for the first direction in the first line below, separated by commas, and use the same format to report in the second line the five for the second direcion. Starting in the third line show the details of how you found one of your accelerations.
4, 12.2222, 19, 12.6667, 12.2222
28, 14.4, 13.3333, 15.1111, 21.5
!!!!!All measurments are in cm/s^2!!!!!!!!!!!
`dts/`dt = vAve
vAve*2 = vf
vf/`dt = a(while v0 = 0)
a = Δv/Δt = (vfinal - vinitial) / (tfinal - tinitial)
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How far from the lower end of the ramps did you have to position the two balls in order to synchronize their consecutive time intervals with the time interval for the third ball released from rest at the top of the third ramp?
For ramps A & B, they were placed 9.5 cm from center of ball to end of ramp. While ramp C was 31 cm from end of ramp.
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You didn't time the intervals for either trial. Suppose that the ball on the third ramp required 3 seconds to travel the 30-cm length of that ramp. What was the acceleration of that ball? Report the acceleration in the first line. Explain how you found it starting in the second line.
`dts/`dt = vAve = 30/3 = 10
vAve*2 = vf = 10*2 = 20
vf/`dt = a(while v0 = 0) 20/3 = 6.6667 cm/s^2
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Assuming the 3-second interval for the ball on the third ramp, what was the time interval for ball released on the first ramp, and what was the resulting acceleration? Report the acceleration in the first line, and explain how you calculated it starting in the second line.
???I guess we are to use our data for this part, I didn’t see any measurement?????
`dts/`dt = vAve = 9.5/1.5 = 6.3333
vAve*2 = vf = 6.3333*2 = 12.6667
vf/`dt = a(while v0 = 0) 12.6667/1.5 = 8.4444 cm/s^2
Assuming the second ball hit at exactly the same time as the third ball and no time was lost during second ball being started. Then due to balls being same distance from end of ramp and traveled at pretty much the same rate due to having same altitude (I know it is very unlikely these balls traveled at exactly the same rate, but should be fairly close). Then the first ball took approx. 1.5 sec(half of the 3 sec).
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Are your two results for the accelerations reasonably consistent? Why would you or would you not expect them to be so?
I guess I was under the impression that the third ball would have had a greater acceleration.
To the extent that the ramps and the balls are identical and at the same slope, and that the balls roll smoothly, the accelerations should be the same. This is of course something we will check out later.
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Are your results in any way relevant to the problem of ordering v0, vf, `dv, v_mid_x, v_mid_t and vAve? If so, what conclusions can you draw?
?? I’m not so sure what is meant by “any way relevant to the problem of ordering”??????
But this entire experiment was centered around v0, vf, vAve, v mid t. We had to, by trail, calculate the `dv and vAve of the third ball to get a general idea of placement of the other balls. As well as needing to get an idea of vAve of balls one and two. We needed an idea of v mid t of ball three that way we would know that the second ball should already be in route towards the end of the ramp.
??????I’m not sure I answered this question correctly, but I hope I have shown some sort of insight?????
Good insight. What do you know now that you didn't know before about the order of v_mid_x, `dv, vAve and v_mid_t? What additional insight can you gain about this question using the equations of motion? You also have insights from the Galileo questions you've recently seen in calculus.
Don't try to answer these questions all at once, but think about them for 10-15 minutes every day or two, jot down ideas to help you remember what you were thinking, and it will eventually all 'gel'.
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Good work throughout. See my notes.
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