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course PHY 241
9/18 9 pm
Class followup:`q001. Explain how you obtained the best data possible for the experiment with the domino and the pendulum.
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What were the maximum height at which the domino hit the floor first, and the minimum height at which the pendulum hit the wall first?
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What was the frequency of your pendulum?
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How much time elapsed from release until the pendulum hit the wall?
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Calculate the acceleration based on this time interval and the maximum height at which the domino hit the floor first. Explain the details of your reasoning.
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Calculate the acceleration based on this time interval and the minimum height at which the pendulum hit the wall first.
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`q002. How far apart were the two most widely separated balancing points for the unloaded steel ramp as it balanced on a domino?
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How far from the balancing point of the unloaded steel ramp was the balancing point when you had the ramp loaded with a domino near one end?
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How far was it between the two most widely separated positions of the domino at which the system remained balanced?
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Based on your results, which do you think weighed more when the loaded ramp was balanced, the part of the ramp on the 'longer' side, or the part of the ramp plus the domino on the other?
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`q003. A ball rolls 58 cm down a ramp, starting from rest, and ends up moving at 30 cm / second. Assuming uniform acceleration, how long did it take to roll down the ramp, and what was its acceleration?
**** Assuming uniform acceleration, the ball had an average velocity of 15 cm/s. This means it took the ball about 3.87 seconds to roll down the ramp, and its acceleration was about 7.75 cm/ s^2.
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`q004. University Physics students: Give your data for the experiment you did today.
**** Table for the marble:
Diameter = 2.59 cm
Ramp = 58.3 cm
Dominos Distance
1 6.7 cm
2 11.3 cm
3 15.0 cm
4 19.4 cm
5 23.3 cm
6 25.6 cm
Table for the steel ball:
Diameter = 2.55 cm
Ramp = 58.3 cm
Dominos Distance
2 13.6 cm
4 22.0 cm
6 28.7 cm
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Determine the acceleration of the ball on each ramp.
**** Marble:
Dominos Final Velocity Time Acceleration
1 16.75 cm/s 6.96 s 2.41
2 28.25 cm/s 4.13 s 6.84
3 37.5 cm/s 3.11 s 12.06
4 48.5 cm/s 2.40 s 20.21
5 58.25 cm/s 2.00 s 29.13
6 64.0 cm/s 1.82 s 35.16
Ball:
Dominos Final Velocity Time Acceleration
2 34.0 cm/s 3.43 s 9.91
4 55.0 cm/s 2.12 s 25.94
6 71.75 cm/s 1.63 s 44.02
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For the marble, sketch a graph of acceleration on the ramp vs. number of dominoes.
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For the ball, sketch a graph of acceleration on the ramp vs. number of dominoes.
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For the marble, at what average rate do you conclude that the ball's acceleration on the ramp changed with respect to the number of dominoes? Explain how you obtained your result.
**** To find the rate of change of acceleration, I took the graph of acceleration vs. the number of dominos and drew a line that came close to describing the points. The slope of that line is the approximate rate of change of acceleration, so acceleration is increasing by about (5.42 cm / s^2) / domino.
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For the steel ball, at what average rate do you conclude that the ball's acceleration on the ramp changed with respect to the number of dominoes? Explain how you obtained your result.
**** I found this answer the same as the one before. The acceleration of the ball is increasing by about (5.67 cm / s^2) / domino.
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`q005. University Physics students: The definitions of velocity and acceleration lead to the following equations for an object accelerating uniformly during an interval:
`ds = (vf + v0) / 2 * `dt
vf = v0 + a `dt.
Eliminate vf from the two equations to get an equation for vf^2. Explain your steps and give the resulting equation.
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Eliminate `dt from the two equations to get an equation for `ds. Explain your steps and give the resulting equation.
**** vf = v0 + a `dt.
vf - v0 = a `dt
`dt = (vf - v0) / a
Substitute this value in for `dt in the other equation.
`ds = (vf + v0) / 2 * `dt
`ds = (vf + v0) / 2 * [(vf - v0) / a]
`ds = (vf^2 - v0^2) / (2a)
vf^2 = v0^2 + 2a `ds
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Verify that there is at least one equation with each of the following combinations of variables:
`ds, a, vf
**** `ds = (vf^2 - v0^2) / (2a)
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v0, vf, `ds
**** `ds = (vf + v0) / 2 * `dt
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a, `dt, v0
**** vf = v0 + a `dt
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There are 10 possible combinations consisting of three of the variables v0, vf, `ds, `dt, a. List all ten:
**** `ds = (vf + v0) / 2 * `dt
1. v0, vf, `ds
2. v0, vf, `dt
3. v0, vf, a
4. v0, `ds, `dt
5. v0, `ds, a
6. v0, `dt, a
7. vf, `ds, `dt
8. vf, `ds, a
9. vf, `dt, a
10. `ds, `dt, a
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Is there any combination of three variables which does not appear in at least one of the equations?
**** No.
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Do all equations contain four of the five variables?
**** Yes.
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&#Very good responses. Let me know if you have questions. &#