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course Phy 201
9/10 2 Questions and Problems
These should be submitted using the Submit Work Form. You can submit the entire document at once, or you can submit the document in parts.
Very Short Preliminary Activity with TIMER (should take 5 minutes or less once you get the TIMER loaded)
This exercise can be put off until you are near a computer. However it is best done before some of the problems that follow. If you can't do it before starting the problems, at least imagine doing it, actually doing the 8-counts and clicking an imaginary mouse, and making your best estimate of the time intervals.
Click the mouse as you start an 8-count, doing your best to count at the same rate you used in class. Complete four 8-counts and click the mouse again. Note the time interval required to complete your set of four 8-counts.
Repeat four more times.
Report your five time intervals in the first line below, separated by commas:
11.0, 11.0, 10.7 10.9, 10.8
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Based on your results, how long does your typical 8-count last?
Approximately 10.88
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Based on your result, what is the time interval of each of your counts?
10.88/32= 0.34 s
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If you counted the motion of a ball down the ramp, completing two 8-counts and 1-2-3-4-5 of a third, how long would you conclude the ball spend moving down the ramp? Based on the TIMER data you reported above, what do you think is the percent uncertainty in your result?
7.14 s
Percent uncertainty=1.7% Using the TIMER data, if the average is 10.88, it could be written 10.88 +/- .12 s .12/7.14 *100%=1.7%
That's consistent with the spread of your data. Don't be too optimistic, though; I'd round that up to 2%.
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Preliminary problems:
a. A ball travels down a ramp in 2 seconds, accelerating uniformly. Its initial velocity on the ramp is 20 cm/s and its final velocity is 40 cm/s.
• Reasoning from the definitions of velocity and acceleration, and assuming a linear v vs. t graph, how long is the ramp, and what is the ball's acceleration (i.e., rate of change of velocity with respect to clock time)?
A=(40 cm/s – 20cm/s)/2 s=10 cm/s^2
`dx= ((20cm/s +40cm/s)/2) * 2 s= 15 cm
Good, but I believe ((20cm/s +40cm/s)/2) * 2 s= 60 cm.
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• In the first line below list the quantities v0, vf, `ds, `dt and a for this motion and give the value of each (or as many as you were able to identify or reason out). In the second line identify which of the quantities were given, and which were reasoned out. In the reasoning process you would have found vAve and `dv; identify these quantities also and give their values.
v0—20cm/s vf—40 cm/s, `ds—15 cm, `dt—2 s, a==10cm/s^2
Given were v0, vf, and `dt. Found were `ds and a
vAve is 10cm/s and `dv is 20 cm/s
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b. A ball travels down a ramp for 3 seconds, starting with velocity 20 cm/s and with its velocity changing with respect to clock time at 10 cm/s^2.
• Reasoning from the definitions of velocity and acceleration, and assuming a linear v vs. t graph, how far did the ball travel along the ramp, and what is the ball's velocity at the end of the 3 seconds?
10 cm/s^2=vf- 20cm/s/3 s
30cm/s=vf-20cm/s
Vf=50cm/s
`dx=((50 cm/s + 20cm/s)/2)*3
`dx=105 cm
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• In the first line below list the quantities v0, vf, `ds, `dt and a for this motion and give the value of each (or as many as you were able to identify or reason out). In the second line identify which of the quantities were given, and which were reasoned out. In the reasoning process you would have found vAve and `dv; identify these quantities also and give their values.
v0 20cm/s, vf 50 cm/s, `ds 105 cm, `dt 3 s, a 10cm/s^2
Given V0, `dt, and a Identified vf and `dx
vAve 35 cm/s `dv 30 cm/s
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c. A ball travels 30 cm down a ramp in 5 seconds, ending with a velocity of 20 cm/s.
• Identify, by giving the value of each, which of the quantities v0, vf, a, `ds and `dt are given.
Vf—20 cm/s `dx—30 cm `dt—5 s
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• Identify which of the four equations of uniformly accelerated motion contain the three given quantities (identify all the equations that apply; there will be at least one such equation, and no more than two).
The First equation
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• For each of the equations you identified, identify the quantity that was not given, and do your best to solve that equation for that quantity.
V0 was not given
30 cm= ((V0+20 cm/s)/2) *5s
6cm/s=(( V0+20 cm/s)/2)
12 cm/s=V0+20 cm/s
-8cm/s=V0
&&&&&&&&& Can velocity be a negative number?
Absolutely. The ball can move forward or it can move backward. It can roll up a ramp, or it can roll down a ramp.
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d. A ball travels 30 cm down a ramp, accelerating at 10 cm/s^2 and ending with a velocity of 20 cm/s.
• Identify, by giving the value of each, which of the quantities v0, vf, a, `ds and `dt are given.
A 10cm/s^2 `dx 30 cm Vf 20 cm/s
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• Identify which of the four equations of uniformly accelerated motion contain the three given quantities (identify all the equations that apply; there will be at least one such equation, and no more than two).
The fourth equation
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• For each of the equations you identified, identify the quantity that was not given, and do your best to solve that equation for that quantity.
V0 was not given
400 cm/s= vo^2 + 2(10cm/s^2)(30cm)
400cm^2/s^2=v0^2 +600 cm^2/s^2
-200 cm^2/s^2=v0^2
14.1=v0
Good, but v0^2 can't be negative. So the given conditions are impossible.
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All students should be able to make a good attempt at the questions in the Preliminary Questions, though it is expected that there will be questions on some of the details.
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Excellent work. Not perfect, but close enough. See my notes and let me know if you have questions.
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