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course 201
9/20, 10:44pm
Class 090916Note: When answering these questions, give your answer to a question before the &&&&. This is different than my previous request to place your answer after the &&&&.
Thanks.
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Calibrate Rubber Band Chains:
Calibrate a rubber band chain (i.e., find its length as a function of the force exerted to stretch it) using 1, 2, 3, 4 and 5 dominoes. Give your raw data below in five lines, with number of dominoes and length of chain separated by a comma, and an explanation following in subsequent lines:
1, 59
2, 62
3, 64
4, 68
5, 72
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Graph chain length vs. number of dominoes, and calculate graph slope between each pair of points. Give your results below. Table form would be good, with columns for length and number of dominoes, rise, run and slope. However as long as you include an explanation, any format would be acceptable.
Length Dominos Rise Run Slope
59cm 1 59 1 59
62cm 2 62 2 31
64cm 3 64 3 21.333
68cm 4 68 4 17
72cm 5 72 5 14.4
slope is rise / run, which is `dy / `dx
it's not y / x
slope involves changes from one point to the next
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Double the chain and calibrate it using 2, 4, 6, 8 and 10 dominoes. Give your raw data below, in the same format as before:
2, 64
4, 66
6, 69
8, 72
10, 75
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Graph length of doubled chain vs. number of dominoes, and calculate graph slope between each pair of points.
Chain Dominos Slope
64cm 2 32
66cm 4 16.5
69cm 6 11.5
72cm 8 9
75cm 10 7.5
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Rotate the strap using the chain
Suspend the strap from your domino chain, supporting the strap at its center so it will rotate in (or close to) a horizontal plane, sort of like a helicopter rotor. Rotate the strap through a few revolutions and then release it. It will rotate first in one direction, then in the other, then back in the original direction, etc., with amplitude decreasing as the energy of the system is dissipated. Make observations that allow you to determine the period of its motion, and determine whether its period changes significantly.
Give your raw data and your (supported) conclusions:
-The strap speeds up all the way until its unwound, then starts slowing down as it winds back up, this continues again once it stops and and starts spinning the opposite direction.
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Double the chain and repeat.
Give your raw data and your (supported) conclusions:
-The same thing appears to be happening but as a more extreme pace.
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How does period of the oscillation compare between the two systems?
-When doubled over, it seems to reach both extremes at a faster rate than when just hanging normally.
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'Bounce' the dominoes on the end of the chain
'Bounce' a bag of dominoes on the chain. Is there a natural frequency? Does the natural frequency depend on the number of dominoes? If so how does it depend on the number of dominoes?
You might not be able to give complete answers to these questions based on your data from class. Give your data, your conclusions, and you hypotheses (i.e., the answers you expect to get) regarding these questions.
-The natural frequency is determined by the dominoes. The more dominoes you add, the more it weighs, which causes it to elongate the stretch.
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How would you design an experiment, or experiments, to further test your hypotheses?
-You could measure the bounce of the bag with different amounts of dominoes.
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Repeat for doubled chain. How are the frequencies of doubled chain related to those of single chain, for same number of dominoes?
-The frequency of the doubled chain are much more rapid than the single.
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You might not be able to give complete answers to these questions based on your data from class. Give your data, your conclusions, and you hypotheses (i.e., the answers you expect to get) regarding these questions.
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How would you design an experiment, or experiments, to further test your hypotheses?
-You can put an item under the bag at a standstill and if it hits the item, you know it changes length.
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If you swing the chain like a pendulum, does its length change? Describe how the length of the pendulum might be expected to change as it swings back and forth.
-Yes. It stretches out at the trough of the cycle.
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Slingshot a domino block across the tabletop
Use your chain like a slingshot to 'shoot' a domino block so that it slides along the tabletop. Observe the translational and rotational displacements of the block between release and coming to rest, vs. pullback distance.
Give your results, in a series of lines. Each line should have pullback distance, translational displacement and rotational displacement, separated by commas:
40cm, 90cm, 3
30cm, 46.5cm, 1
50cm, 166cm, 6
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Describe what you think is happening in this system related to force and energy.
-The further you pull it back, the more force is being unleashed on the domino block.
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Complete analysis of systems observed in previous class
Rotating Strap:
For last time you calculated the average rate of change of position with respect to clock time for each of five trials on the rotating strap. This average rate of change of position is an average velocity. Find the average rate of change of velocity with respect to clock time for each trial. As always, include a detailed explanation:
1-35 degree/s^2, 2-17.2 degree/s^2, 3-24.2 degree/s^2, 4-19.9 degree/s^2, 5- 33.3 degree/s^2
you haven't shown how you got these results; I can't tell whether they follow from your data or not
however in other postings I've given you a number of notes on related questions, and don't expect this to be a problem for you
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(Note: Since the system is rotating its positions, velocities and accelerations are actually rotational positions, rotational velocities and rotational accelerations. They are technically called angular positions, angular velocity and angular accelerations, because the position of the system is measured in units of angle (e.g., for this experiment, the position is measured in degrees). These quantities even use different symbols, to avoid confusion between rotational motion and translational motion (motion from one place to another). So technically the question above doesn't use the terms 'position', 'velocity', etc. quite correctly. However the reasoning and the analysis are identical to the reasoning we've been using to analyze motion, and for the moment we're not going to worry about the technical terms and symbols.)
Atwood Machine:
Find the average rate of change of velocity with respect to clock time for each trial of the Atwood machine.
1- 6.9cm/s^2, 2-7cm/s^2, 3-11.8cm/s^2, 4-11.9cm/s^2
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Hotwheels car:
For the Hotwheels car observed in the last class, double-check to be sure you have your signs right:
• You pushed the car in two different directions on your two trials, one in the direction you chose as positive, and one in the direction you chose as negative.
• You will therefore have one trial in which your displacement was positive and one in which it was negative.
• Your final velocity in each case was zero. In one case your initial velocity was positive, in the other it was negative. Be careful that your change in velocity for each trial has the correct sign, and that the corresponding acceleration therefore has the correct sign.
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New Exercises
Exercise 1:
A ball rolls from rest down each of 3 ramps, the first supported by 1 domino at one end, the second by 2 dominoes, the third by 3 dominoes. The ramp is 60 cm long, and a domino is 1 cm thick. The motion is in every case measured by the same simple pendulum.
It requires 6 half-cycles to roll down the first, 4 half-cycles to roll down the second and 3 half-cycles to roll down the third.
Assuming constant acceleration on each ramp, find the average acceleration on each. Explain the details of your calculation:
1- 1.67cm/hc^2, 2-3.75cm/hc^2, 3-6.67cm/hc^2.
-To find acceleration, you take the average rate of velocity and divide it by change in clock time. As the ball continues to roll, the average rate of acceleration for each ramp increases.
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Find the slope of each ramp.
-Ramp 1 - 1/60 slope, Ramp 2- 1/30 slope, Ramp 3 – 1/20 slope.
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Graph acceleration vs. ramp slope. Your graph will consist of three points. Give the coordinates of these points.
-(1.67, 1/60), (3.75, 1/30), (6.67, 1/20)
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Connect the three points with straight line segments, and find the slope of each line segment. Each slope represents a average rate of change of A with respect to B. Identify the A quantity and the B quantity, and explain as best you can what this rate of change tells you.
-A will be the average altitude of the line segment and the B will be the slope.
you haven't calculated your graph slopes
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Exercise 2: A ball rolls down two consecutive ramps, starting at the top of the first and rolling without interruption onto and down the second. Each ramp is 30 cm long.
The acceleration on the first ramp is 15 cm/s^2, and the acceleration on the second is 30 cm/s^2.
For motion down the first ramp:
What event begins the interval and what even ends the interval?
What are the initial velocity, acceleration and displacement?
Using the equations of motion find the final velocity for this interval.
Using the final velocity with the other information about this interval, reason out the time spent on the first ramp.
For motion down the second ramp:
What event begins the interval and what even ends the interval?
What are the initial velocity, acceleration and displacement?
Using the equations of motion find the final velocity for this interval.
Using the final velocity with the other information about this interval, reason out the time spent on the first ramp.
Challenge Exercise:
The first part of this exercise is no more challenging than the preceding problem. It uses the result of that problem:
A ball accelerates uniformly down a ramp of length 60 cm, right next to the two 30-cm ramps of the preceding exercise. The ball is released from rest at the same instant as the ball in the preceding exercise.
What is its acceleration if it reaches the end of its ramp at the same instant the other ball reaches the end of the second ramp?
-30cm/s^2.
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The second part is pretty challenging:
The 60 cm ramp is made a bit steeper, so that its acceleration is increased by 5 cm/s^2. The experiment is repeated. How far will the ball on this ramp have traveled when it passes the other ball?
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see my notes and let me know if you have questions