course Phy 201
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:
We had ten thin rubber band chain with a paper clip at each end. I held the rubber band with the bag of dominoes attached to
the end, my partner read the readings. For our first trial 5, 81cm, trial two 4, 75cm trial three 3, 70.5cm trial four 2,
65cm trial five1, 60cm. Well as the data concluded the lighter the bag the shorter distance and less amount of energy
required.
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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.
Slope between trial 1 and 2, 1/5
Slope between trial 2 and 3, 1/5.5
Slope between trial 3 and 4, 1/ 4.5
Slope between trial 4 and 5, 1/6
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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:
We had ten thin rubber band chain with a paper clip at each end. I held the rubber band that held the bag of dominoes
attached to the end, my partner read the readings. Trial 1, 2, 31cm, trial two 4, 33, trial three 6, 35, trial four 8, 37
trial five 10, 39. Well as the data concluded when added more dominoes the rubber band had more force and the data showed
that every two dominoes the weight increased 2 cm.
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Graph length of doubled chain vs. number of dominoes, and calculate graph slope between each pair of points.
Slope between trial 1 and 2, 1
Slope between trial 2 and 3, 1
Slope between trial 3 and 4, 1
Slope between trial 4 and 5, 1
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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:
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Double the chain and repeat.
Give your raw data and your (supported) conclusions:
We used 10 thin rubber bands along with 2 paper clips, one located at each end of the model. I held the model while my
partner timed and located when the device changed direction. I am unsure how many times we twisted the rubber band. The
first direction went for 25 seconds when it changed direction it went for another 25 seconds when it changed direction it
went for 20 seconds when it changed direction again it went for 16 seconds and when it went back to the other direction it
went for another 16 seconds.
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How does period of the oscillation compare between the two systems?
The time was much shorter when we doubled the rubber band.
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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.
Yes there is a natural frequency and yes I feel that the frequency does depend on the number of dominoes, with more dominoes
it is hard to see the natural frequency with less it bounces more.
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How would you design an experiment, or experiments, to further test your hypotheses?
You could measure each bounce have a timer that measured closer than just seconds.
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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 bounces are harder to count because the chain is shorter. And I had more bounces than I did with the longer chain.
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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.
I found that with the shorter chain I had more bounces and also it was harder to count because the bounces were shorter.
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How would you design an experiment, or experiments, to further test your hypotheses?
Once again you could measure each bounce, have something that could measure closer than seconds.
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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 because we tested it. When the pendulum is out to the side it does not require or the band does not have as much stress
but when its straight down the chain is pulling more on the rubber bands
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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:
27cm, .25, 30cm
41 cm, .50, 40cm
67 cm, 0, 50cm
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Describe what you think is happening in this system related to force and energy.
When the rubber band is pulled at 50 cm it is requiring more force and with more force the domino shows more energy, and when
it is 30 cm it require less force because the you can see it in the rubber and how they are longer when it is 50cm.
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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:
Trial 1, 6 oscillations, 345 degrees
345/6=57.5
Trial 2, 4 oscillations, 290 degrees
290/4=72.5
Trial 3, 5 oscillations, 305 degrees
305/5-61
Trial 4, 8 oscillations, 660 degrees
660/8=82.5
Trial 5, 6.5 oscillations, 530 degrees
530/6.5=81.5
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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.
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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.
Positive-south
Negative-North
Vf-V0/2
Trial 1, 58 cm, 2 oscillations
Trial 2, 65 cm, 2.5 oscillations
0-58/2=29*2=58 cm/s
0-65/2=32.5=81.25 cm/s
Trial 1, 83cm, 3 oscillations
Trial 2, 52 cm, 2 oscillations
0-83/2=41.5*3=-124.5cm/s
0-52/2=26*2=-52cm/s
you haven't identified these calculations or what they mean, and you need to also include units at every step, with every quantity.
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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:
Average acceleration=change of velocity/time elapsed
Half Cycle= .5 seconds
Vf-Vo/’ dt=
Ramp 1 20cm-0cm/3seconds=6.66 cm/s
Ramp 2 40cm-0cm/5 seconds=8 cm/s
Ramp 3 60cm-0cm/6.5 seconds=9.23 cm/s
these appear to be average velocities, not accelerations
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Find the slope of each ramp.
20/3=6.66
40/5=8
60/6.5=9.23
These are not the ramp slopes.
What is the rise of the ramp in each case, and what is the run?
What therefore is the slope of the ramp in each case?
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Graph acceleration vs. ramp slope. Your graph will consist of three points. Give the coordinates of these points.
6.66
8
9.23
each point has two coordinates
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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.
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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?
-The push of the ball begins and when the ball reaches the end of the last ramp.
What are the initial velocity, acceleration and displacement?
Initial velocity-0
Acceleration- 15cm/s^2
Displacement-30cm
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? When the ball hit’s the second ramp and when it goes off the
ramp
What are the initial velocity, acceleration and displacement?
Initial velocity-30cm
Acceleration-30 cm/s^2
Displacement-30cm
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?
You haven't completed all the questions, but you have done most.
See my notes and let me know if you have questions.