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course phy201
9/23 950pm
120919Read Chapter 2 of your text. Based on what we've done so far you should find most of the chapter to be relatively easy reading.
As additional preparation for the Major Quiz, work out and submit the following:
Week 4 Quiz #2
Week 5 Quiz #1
Week 5 Quiz #2
Do the experiments
Error Analysis Part II, Data Program (if you cannot get the data program to run, just get your data and let me know; we'll go over equivalent Excel procedures in class and over a period of a couple of weeks we'll gradually work through the analysis using Excel)
and
Hypothesis Testing with Time Intervals (this requires the TIMER)
Complete
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qa_08
Spend a few minutes with each of the simulations
PHeT 3.51 Motion in 2D
PHeT 3.43 Projectile Motion
`q000. General College Physics: Give your data for today's experiment, along with a brief description of what you did.
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In class we used a rubberband to launch a metal strap. We used the same spot on the rubber band, but stretched it to different lengths before letting it go.
Here is data.
Rubberband length Degree of change
30cm 270
30cm 315
30cm 315
40cm 360
40cm 150 I think we messed up on this one
40cm 370
We also balanced a ramp on a dominoe with a dominoe as a counter balance on the other end, then slide the couneter balance to different spots to see how far each could be moved before it would fall.
When the dominoe was in the middle of the ramp, the sliding dominoe could be moved, 4.25 cm to the right or 3.5cm to the left before it would tip.
When the counter balance was placed at 3/4 the length of the ramp and the ramp was balanced, it could only move 4cm to the left or 3cm to the right before it would fall.
When the counter balance was placed near the end and the ramp was balanced, it could only be moved 1cm to the left or 4.5cm to the right before it would tip the ramp.
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`q001. If you balance the metal ramp on a domino, then place one domino at one end of the ramp, the ramp will not remain balanced. In order to maintain balance we will add a stack of two dominoes to the other side. Where should the two-domino stack be placed?
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About 1/3 of the distance from the middle to the end
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If you rotate the ramp, which will be moving faster, the domino at the end or the two-domino stack?
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Domino at the end
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`q002. In the experiment where you dropped the domino at the same time as you released the washer, you obtained an upper and a lower bound on the acceleration of gravity. What were these bounds?
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At 75 cm the pendulum hit first
At 65 cm they hit about the same time
at 55 cm the domino hit first
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You should have calculated accelerations, based on the period of the pendulum and the time of fall.
Assuming a .3 second time of fall, you would get the following:
For 75 cm fall, acceleration would be about 1700 cm/s^2.
For the 55 cm fall acceleration would be about 1200 cm/s^2.
What was the length of your pendulum, its period and the time interval from release to contact?
What therefore were your acceleration estimates?
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`q003. If a system has zero acceleration and is given a velocity of 1 millimeter per second, how fast will it be moving 10 seconds later?
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1 millimeter per second
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If a system is given a velocity of 10 cm/s toward the north, and has an acceleration of 1 cm/s^2 toward the south, what will be its velocity 15 seconds later?
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vf = 10cm/s + -1 cm/s^2 * 15s
vf = -5cm/s
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What will be its position at that time?
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2.5cm/s vave * 15s = 37.5cm
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`q004. If we had five dominoes on each side of an Atwood system, then assuming the dominoes to all have the same mass the system would have zero acceleration.
Suppose we had 15 dominoes on one side and 5 on the other. Clearly the system would accelerate pretty rapidly in the direction in which the 15-domino side descends. Now suppose we release this system and at the same time drop a domino, which falls freely to the floor. Which will have the greater acceleration, the Atwood system or the freely falling domino?
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The free falling domino would, because of the 5 dominoes on the other side of the atwwod system
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`q005. Our first model of the Atwood machine will be as follows: The machine consists of two equal masses suspended over a pulley of negligible mass and with negligible friction, plus an additional mass added to one side. We hypothesize that the acceleration of the Atwood system will be in the same proportion with the acceleration of gravity as the additional mass to the total mass of the system. As a first approximation we will use 1000 cm/s^2 as the acceleration of gravity.
Suppose the system consists of five dominoes on each side, all of equal mass, and an additional unspecified mass.
If the system accelerates at 20 cm / s^2, then what is the unspecified mass, as a percent of the mass of the system?
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1/50th
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What is the mass of the unspecified mass as a percent of the mass of a single domino?
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For a system consisting of 10 dominoes, and a small added mass that doesn't add much to the mass of the system, you figured that the added mass was 1/50 the mass of the system.
So it's 1/50 the mass of 10 dominoes.
What fraction, and what percent would the added mass then be of the mass of a single domino?
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If the unspecified mass was removed and a single domino added to one side, what would be the acceleration of the system?
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What percent of the mass of the system would be the mass of that one domino?
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If an additional four dominoes were added to the same side, what would be the acceleration of the system?
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If five more dominoes were added to the same side, what would be the acceleration of the system?
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`q006. If the slope of an incline is less than 0.1, then if friction has only negligible effects an object moving down the incline will accelerate at a rate equal to slope * acceleration of gravity. If a domino has thickness 0.9 cm and a ramp has length 60 cm:
What will be the acceleration of such an object on this ramp when it is supported by one domino?
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15cm/s^2
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What will be the acceleration of the object if the ramp is supported by four dominoes?
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60cm/s^2
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At what rate does the acceleration of the object change with respect to ramp slope?
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15cm/s^2 per domino
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Does the slope of the table affect the answer to the third question?
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no, it should be a constant
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`q007. Suppose the y axis of an xy coordinate plane points straight upward, and that a rubber band chain pulls straight down, in the negative y direction, on a paperclip at the origin. If no other force acts on the paperclip, it's going to accelerate in the direction of this force.
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In what direction would a second rubber band have to pull in order to balance this force and keep the paperclip stationary?
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In the postive y direction
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Suppose the only force available is directed at 10 degrees to the left of the positive y axis. Why is it impossible for this force alone to keep the paperclip stationary?
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Because of the slope at which the rubberband would be coming in at.
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Let's bring in a third rubber band, and let it act on the paperclip in the direction of the positive x axis. Is it possible to balance the system using this rubber band in combination with the previous force at 10 degrees to the left of the positive y axis? If so, what force do you think would be necessary, and what would be the force at 10 degrees to the left of the positive y axis, as percents of the original downward force?
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it might work if you lower the new rubberband by 10 degrees to the negative. Use about half the force as pulled on the y positive
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Assuming that the third force can, in some direction, balance the other two, in what direction do you think the amount of required force would be the least? In what direction do you think it would be the greatest?
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least would be toward the x positive direction. greatest from the y negative direction
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In what directions would it be possible for a third force to balance the other two?
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from the y negative direction
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`q008. University Physics: Suppose the tension in your rubber band chain is T(L) = 0.16 N / cm * (L - 20 cm). As its length changes from 20 cm to 25 cm:
What is its average tension?
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Based on the average tension, how much work is done by the stretching force?
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Obtain the same result using an integral.
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How much work is required to change its length from 20 cm to 20 cm + x? Answer by first finding the average force.
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Answer the same question using integration.
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Now suppose that the tension function is T(x) = k x. How much work is done in stretching the rubber band from stretch x_1 to stretch x_2?
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If as its stretch returns from x_2 to x_1 the rubber band does an equal amount of work on mass m, the kinetic energy 1/2 m v^2 of that mass will increase by an equal amount. What therefore will be its kinetic energy, and what will be its velocity, when its stretch reaches x_1?
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Assuming the rubber band force to be conservative, the work done to stretch from x_1 to x_2 is equal to its potential energy change between these two stretches. How does the potential energy change therefore depend on whether x_2 is greater or less than x_1?
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Verify that the equation
m x '' = - k x
is satisfied by each of the following functions, where omega = sqrt(k / m) and A, B and phi are constants:
x(t) = cos(omega * t)
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x(t) = A sin(omega * t + phi)
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x(t) = A cos(omega * t) + B sin(omega * t)
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`q009: University Physics: If the ramp of the first problem is rotating about its center with the single domino and the two-domino stack positioned as you said, what is the ratio of the kinetic energy of the two-domino stack to that of the single domino?
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Self-critique (if necessary):
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Self-critique rating:
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Very good, except for #2, which wasn't bad (you found your data, which beats most of the class), but you didn't calculate the accelerations.
Check my notes and see if you can get those accelerations. That shouldn't take you more than 5 minutes if you have the data for your pendulum. If you don't have that data it won't take you any time at all, because you won't be able to make the calculations.
&#Please see my notes and submit a copy of this document with revisions, comments and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes. &#
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