course phy 201
9/30 8:10 AM
Class 090928The following conventions will allow your instructor to quickly locate your answers and separate them from the rest of any submitted document, which will significantly increase the quality of the instructor's feedback to you and to other students.
When answering these questions, give your answer to a question after the **** and before the &&&&.
When doing qa's, place your confidence ratings and self-assessment ratings on the same line as the prompt.
If you don't follow these guidelines you may well be asked to edit your document to make the changes before I can respond to it.
Thanks.
Fractional cycles of a pendulum
Regard the equilibrium position of a pendulum as the origin of the x axis. To the right of equilibrium x values are positive, and to the left of equilibrium x values are negative.
Suppose you release a pendulum of length 16 cm from rest, at position x = 4 cm.
Estimate its position in cm, its direction of motion (positive or negative) and its speed as a percent of its maximum speed (e.g., speed is 100 % at equilibrium, 0% at release, and somewhere between 0% and 100% at every position between) after each of the following time intervals has elapsed:
• 1/2 cycle
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-4cm, ending the neg direction starting pos direction, 0%
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• 3/4 cycle
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0 cm, pos direction, 100%
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• 2/3 cycle
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-1.75 cm, pos direction, 60%
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• 5/4 cycle
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0cm, neg direction, 100%
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• 7/8 cycle
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2.875 cm, pos direction, 28%
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• .6 cycle
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-1.4 cm, neg direction, 66%
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Acceleration of Gravity
Drop a coin and release a pendulum at the same instant. Adjust the length of the pendulum so that it travels from release to equilibrium, then to the opposite extreme point and back, reaching equilibrium the second time at the same instant you hear the coin strike the floor. Measure the pendulum.
• Give your raw data below:
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used a nickel, pendulum was 7 cm long
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Show how to start with your raw data and reason out the acceleration of the falling coin, assuming constant acceleration:
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I know the displacement of the coin is 87 cm
I know that 1 cycle of my 7cm long pendulum = roughly .529 seconds
I am only completing 3/4 of a cycle though so it should only take .397 seconds
Dt= .397 seconds
Ds = 87 cm
Vo= 0
Based on this I can get the avg V which is = 219.14 cm/s
By drawing a trapezoid I can figure out the Vf = 438.29 cm/s
Then by putting the change in V over time I come up with
A= 1103.99 cm/s^2
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There are two delays between the events you are observing and your perceptions:
• How long after the coin strikes the floor do you hear it?
• How long after the light in the room reflects off the pendulum does it strike your eye?
• Is either delay significant compared to other sources of uncertainty in this experiment?
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No both are extremely small percentages. The chance that I misread the pendulum is much greater
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Introduction to Projectile motion
Time a ball down a ramp, and measure how far it travels in the horizontal direction.
• Give your raw data below:
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We used lines on a piece of paper as the measuring device for how far it was displaced from straight down.
Pendulum = 25 cm
4.25. ticks on ramp, 12.25 lines
4 ticks on ramp, 12.6 lines
4 ticks on ramp, 12.8 lines
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To keep things straight, let's use the following notation in the rest of this analysis:
• `dt_ramp is the time required to travel the length of the ramp starting from rest
• `ds_ramp is the displacement of the ball along the ramp
• vf_ramp is the ball's final velocity on the ramp
• `ds_x_projectile is the horizontal displacement of the ball between leaving the ramp and striking the floor
• `ds_y_projectile is the vertical displacement of the ball between leaving the ramp and striking the floor (for the tables in the lab we may assume that `ds_y_projectile is about 90 cm).
• `dt_projectile is the time interval between leaving the ramp and striking the floor
Answer the following questions:
According to the time `dt_ramp required to travel down the ramp and its length `ds_ramp, what are the average and final velocities on the ramp, assuming uniform acceleration?
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7.06 cm/tick , 14.12 cm/tick
7.5 cm/tick , 15 cm/tick
7.5 cm/tick , 15 cm/tick
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Moving at vf_ramp, how long would it take the ball to travel through displacement `ds_x_projectile?
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according to my measurement each line on the paper was about .7 cm therefore by multiplying each displacement I get a set of units that match my velocity:
my 3 displacements in cm are:
8.575
8.82
8.96
so it would take
.61 ticks
.588 ticks
.597 ticks
to travel the Ds x projectile
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Accelerating at 1000 cm/s^2, how long would it take the ball to fall from rest through displacement `ds_y_projectile?
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using the 3rd equation of motion I got .42 seconds
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In the time interval you just calculated, how far would the ball travel if moving at velocity v_f_ramp?
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on a 25 cm pendulum a tick = .5 seconds, .42 is only 84% of this meaning
that I multiply my earlier vf ramps by .84 giving me
11.86 cm
12.6 cm
12.6 cm
respectively on my 3 trials
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Accelerating at the rate you calculated in the preceding exercise, how long would it take the ball to fall from rest through displacement equal to `ds_y_projectile?
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1st This exact question is already asked above. 2nd In the preceeding exercise I came up with a distance not an acceleration. So not sure what ya want me to do here.
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Ball up and down ramp
'Poke' a ball (perhaps using your pencil as a 'cue stick') so that it travels partway up a ramp then
back. Observe the clock time and position at three events: the end of the 'poke', when the ball comes
to rest for an instant before rolling back down, and its return to its original position.
Choose your positive direction.
Up the ramp is positive
23 cm traveled
5 ticks overall
2 ticks up
Determine the initial velocity and acceleration of the ball for the interval between the first and second event.
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ds = 23 cm
vf = 0
dt = 2 ticks
avg v = 11.5 cm/tick
v0 = 23cm/tick
avg a = -11.5 cm/ tick^2
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Determine the final velocity and acceleration of the ball for the interval between the second and third event.
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v0 = 0
ds= 23 cm
dt= 3 ticks
v avg = -7.66 cm/tick
vf = -15.33 cm/tick
A = -5.11 cm/tick^2
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Do you think the acceleration of the ball is greater between the first and second event, or between between the second and third event? Or do you think it is the same for both? Give reasons for your answer.
I believe it is greater (based on magnitude not in a positive negative fashion) on the way up because it travels the same distance and stops in a shorter time.
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Are your data accurate enough to determine on which interval the acceleration is greater? If so, on which interval do you determine it is greater? If not, how accurate do you think your data would need to be to decide this question?
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according to my data it has greater acceleration (not counting the fact that both signs are negative) on the way up. Im not 100% sure with this reading though, it could be due to misreadings of my pendulum.
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Homework:
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