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course PHY 201
10/25 9pm
Acceleration vs. Ramp SlopeUsing the TIMER program, time a ball down the steel ramp when the ramp is supported by a single domino lying flat. Do five trials with this setup.
Report the median time, the distance the ball traveled from rest in this time, and the resulting acceleration.
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Median `dt=2.12s
`ds=30cm
vAVE=14.2cm/s
v0=0
vF=28.4cm/s
a=(28.4cm/s)/2.12s=13.4cm/s^2
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Report the rise and run between two points of the ramp and the resulting slope.
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rise=1cm
run=30cm
slope=.03
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Repeat with the domino lying on its long edge, so that the rise is equal to the width of the domino. Do five trials with this setup.
Report the median time, the distance the ball traveled from rest in this time, and the resulting acceleration.
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Median `dt=.78s
`ds=30cm
v0=0
vAVE=38.5cm/s
vF=77cm/s
a=(77cm/s)/.78s=98.7cm/s^2
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Report the rise and run between two points of the ramp and the resulting slope.
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rise=5.5cm
run=30cm
slope=.18
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Based on these two setups, at what rate does the acceleration of the ball appear to change with respect to ramp slope?
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569cm/s^20
1st acceleration=13.4cm/s^2
2nd acceleration=98.7cm/s^2
Change in acceleration=85.3cm/s^2
1st slope=.03
2nd slope=.18
Change in slope=.15
Change in acceleration with respect to slope=(85.3cm/s^2)/.15=569cm/s^2
proper terminology:
rate of change in acceleration with respect to slope=(85.3cm/s^2)/.15=569cm/s^2
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Now time the toy car down the wood ramp, using two different slopes. Be sure the ramp is straight. Suggestion: Use your textbook to help. Support it at one end with something reasonably rigid, whose thickness you can measure with good accuracy (for example a couple of CD or DVD cases would be a good choice, using one for the first setup, and both for the second). Using one hand hold the wood piece flat against the book, release the car with another hand, and operate the TIMER with your third hand. If you don't have three hands, adapt the suggestions accordingly. You might also find it helpful to use the steel ramp to press the wood ramp against the book.
For the first slope:
Report the median time, the distance the ball traveled from rest in this time, and the resulting acceleration.
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Median `dt=1.98s
`ds=40.5cm
V0=0
VAVE=20.5cm/s
VF=41cm/s
A=20.7cm/s^2
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Report the rise and run between two points of the ramp and the resulting slope.
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Rise=2cm
Run=40.5cm
Slope=.05
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For the second slope:
Report the median time, the distance the ball traveled from rest in this time, and the resulting acceleration.
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Median `dt=1.34s
`ds=40.5cm
v0=0
vAVE=30.2cm/s
vF=60.4cm/s
a=45.1cm/s^2
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Report the rise and run between two points of the ramp and the resulting slope.
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Rise=3cm
Run=40.5cm
Slope=.07
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Based on these two setups, at what rate does the acceleration of the ball appear to change with respect to ramp slope?
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1st acceleration=20.7cm/s^2
2nd acceleration=45.1cm/s^2
Change in acceleration=24.4cm/s^2
1st slope=.05
2nd slope=.07
Change in slope=.02
Change in acceleration with respect to slope=(24.4cm/s^2)/.02=1220cm/s^2
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This answer seems a little high given both of the slopes. I checked my calculations and they came out correct. Is this answer correct?
it's a little higher than the ideal, but within the range of results usually obtained
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Is acceleration independent of position and velocity?
You were asked previously to design an experiment to test whether acceleration is independent of position and velocity, on a ramp with constant incline.
Do a 30-minute preliminary run, using the TIMER. Just take whatever data you can in 15 or 20 minutes, and give a brief report of your setup, your data and your results. Try to be as accurate as possible within the 15-20 minute time constraint.
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Starting from rest, I observed 5 trials with 5 different distances; 10cm, 20cm, and 25cm
For 10cm:
V0=0
`ds=10cm
Median `dt=.96s
VAVE=10.4cm/s
VF=20.8cm/s
A=21.7cm/s^2
For 20cm
V0=0
`ds=20cm
Median `dt=1.36s
VAVE=14.7cm/s
VF=29.4cm/s
A=21.6cm/s^2
For 25cm
V0=0
`ds=25cm
Median `dt=1.53s
VAVE=16.3cm/s
VF=32.6cm/s
A=21.3cm/s^2
Next I observed 5 trials where I started the ball rolling 5cm away from the distances 10cm, 20cm, and 25cm.
For 10cm
`ds=10cm
`dt=.53s
V0=0
VF=37.8cm/s
VAVE=18.9cm/s
A=71.3cm/s^2
For 20cm
`ds=20cm
`dt=.94s
V0=0
VF=42.6cm/s
VAVE=21.3cm/s
A=45.3cm/s^2
For 25cm
`ds=25cm
`dt=1.1s
V0=0
VF=45.4cm/s
VAVE=22.7cm/s
A=41.3cm/s^2
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In the 2nd set of problems above, the initial velocity was not 0, however I didn’t start my count until the ball reached the mark of 10cm, 20cm, and 25cm. Is that the correct way to report the accelerations?
If you started your count when the ball was moving then initial velocity was not zero, and the step where you double the average velocity to get the final would not be valid.
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Good work on the acceleration vs. ramp slope.
See my note on the uniformity of acceleration experiment.
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