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course phy 231
this is the 2nd part of that homework.
Questions and ProblemsThese 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:
5.0,5.0,5.1,4.8,4.8
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Based on your results, how long does your typical 8-count last?
1.2 second. Added all times, divided by total intervals, then divided by 4(number of 8 counts)
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Based on your result, what is the time interval of each of your counts?
.15 seconds per “count” ..took 1.2 and divided by 8(each count)
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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?
1.95 seconds, 5 % uncertainty, thats the difference in my average of 8 counts and the max time or min time. (4.9/5.1) or (4.8/4.9)
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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)?
60 cm(s/2=((40-20)/2),a=10cm/s^2 ((40-20)/2)
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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=40cm/s,'ds=60cm,'dt=2seconds,a=10cm/s^2,vAve=30cm/s,'dv=20cm/s
v0,vf,'dt were given. The others were reasoned out.
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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?
'ds=105cm, vf=50cm/s
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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=50cm/s,'ds=105cm,'dt=3seconds,a=10cm/s^2,vAve=35cm/s,'dv=30cm/s
v0,'dt,and a were given. The rest were reasoned out.
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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.
'ds=30cm,'dt=5seconds, and vf=20cm/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).
'ds=((v0+vf)/2)'dt
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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, v0=-8cm/s &&& is the ball going up hill, and then going down?&&&
Some unspecified force is causing the ball to slow as it goes down the 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.
'ds=30cm,a=10cm/s^2,vf=20cm/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).
vf^2=v0^2+2a'ds
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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.
V0,20^2=v0^2+2(10)(30)
v0=(-200)^(.5) &&&&&nonreal answer, what did I do wrong?&&&&
Nothing. The given values 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.
Problems
1. Each ramp used in constructing the series of ramps used in today's lab was 24 inches long. The 5-ramp series had a length of 10 feet, or about about 300 cm. Assume that the ball takes 10 seconds to travel the length of the ramp when released from rest. If this time interval is accurate, then what is the value of each of the following:
The average velocity of the ball on the ramp.
vAve=30cm/s
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The final velocity of the ball on the ramp.
vf=60cm/s
300=((0+vf)/2)10
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The change in the velocity of the ball from start to finish.
'dv=60cm/s
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The average rate of change of the velocity with respect to clock time.
a=6cm/s^2
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The velocity of the ball at the midpoint of the ramp.
Vmidx=6(50)^(.5)
150=.5(6)('dt)^2
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The velocity of the ball at the clock time halfway between the start and the ball reaching the end of the ramp.
vmidx=6(5)=30cm/s
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Hint: sketch a trapezoid that you think represents the v vs. t behavior of the ball on the ramp (... time on each ... need equal-area divisions ... etc.)
It is expected that some phy 201 students will be able to make a good attempt on all the above questions, and all should be able to answer the first two and make a good attempt on the next two. University Physics students should be able to make a good attempt on all questions.
2. Based on your in-class counts and your timing of your counts, estimate as accurately as you can the time required for the ball to travel the length of this series of ramps, starting from rest.
Find the average velocity of the ball, and based on this result find its final velocity.
vAve=38cm/s,vf=77cm/s
you need to indicate how you got these results
e.g., give your count and the time interval you infer
then, since the procedure of the preceding problem is identical to this, you can just say 'using reasoning from preceding ...' and give your final .
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Using your results, find its acceleration.
A=9.9cm/s^2
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Find the velocities v_mid_x and v_mid_t.
vMidx=55cm/s,vMidt=38cm/s
(vmidx=vf^2=2(9.9)(150),vmidt=(9.9)(3.9)
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Everyone should be able to do the first. University Physics students should certainly be able to do the second, and General College Physics students should be able to make a good attempt.
3. If the ball was given an initial velocity of 20 cm/s, then given the acceleration you found in the preceding problem:
How long would it take the ball to travel the length of the ramp, and what would be its final velocity?
'dt=6seconds,vf=79.4cm/s
0=4.95'dt^2+20'dt-300(graphed, found positive zero)
Graphing isn't an acceptable method for solving these equations on a test. OK here, because I know you know how, but on a test do it analytically (i.e., use the quadratic formula).
In general you should solve the formula for the required variable, in symbols, then plug in your results.
'ds=20(3)+2(9.9)(150)
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Where would it be at the halfway clock time?
Vmidx=104.6cm
'ds=20(3)+.5(9.9)(3)^2
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How fast would it be moving at the midpoint between the two ends of the ramp?
vMidx=58cm/s
vf^2=(20)^2+2(9.9)(150)
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What would be its velocity at the halfway clock time?
Vmidt=49.7cm/s
vf=20+(9.9)(3)
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What would be the change in its velocity from one end of the ramp to the other?
59.4cm/s
79.4-20
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Had you solved the formulas symbolically you would have ended up with an expression that could provide insight into some of the 'open questions'.
Everyone should be able to make a good attempt at some of these questions. University physics students should be able to make a good attempt at all.
4. A ball requires a count of 24 to accelerate from rest down a 60 cm ramp. It rolls from that ramp onto an identical ramp with an identical slope, and requires 13 counts from one end of the ramp to the other. Does it lose any speed in making the transition? If you simply answer 'yes' or 'no' without supporting your answer in detail, you haven't answered the question.
Yes.by using the formulas for constant acceleration, I concluded that the final velocity at the end of the first 60cm ramp was 5cm/s, and the velocity and the end of the second ramp was 4.2 cm/s. So it slowed down from the beginning of the second ramp to the end of the second.
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This question is somewhat challenging. You should begin by figuring out everything you can from the given information. Then see how your information might be used to answer the question.
5. I just timed myself for five sets of counts, with four fast 8-counts in each set (similar to the preliminary exercise I asked you to do at the beginning of these problems). My times for the sets were all between 4.4 and 4.6 seconds. Starting with 1 at release and counting until the ball reached the end of the last ramp, I counted two sets of four 8-counts, plus a count of 1-2-3 at the end. On three additional repetitions I always got two sets of four 8-counts, and the counts at the end were always 1-2 or 1-2-3. Based on these figures:
What is the best estimate of the time required for the ball to travel the entire distance?
9.2 seconds., since you started at 1, it took between 65 and 66 actual “counts” to get to the end. If I use 65.5 counts and use 4.5 seconds(average time for 4 “8 counts”) as a scaler, I get my answer
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What is the percent uncertainty in the time required for the ball to travel down the ramp, based on the given information and without making any extraneous assumptions?
5% uncertainty, I recalculated the time with the given data, the most “extreme” answer that would be furthest from my previous answer. Using 4.6 as total time and using 66 counts I got 9.67 seconds. That's about 5% larger than my answer ((9.2/9.67)*100)
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How long should the ball have spent on the first ramp, if the acceleration was indeed constant?
2.9 seconds. (I'm assuming there are 5 ramps) I found acceleration, and then used one of the formulas using 1/5 total distance and solved for 'dt.
that would be valid if the velocity was constant, but the ball is speeding up so it won't spend the same time on each ramp
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If I got to the 8 of the third set of 8-counts by the time the ball reached the end of the first ramp, what was the acceleration on that ramp?
A=5.7cm/s^2, I knew 'ds, and calculated 'dt. So I used the formula for 'ds, and solved for a
you need to show what you used for `dt, and the symbolic form of your solution for a
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Everyone should be able to answer the first questions and make a good attempt on the others.
6. The ball is at the end of the first ramp when I reach the count 1 of the fourth set of 8-counts. Where will it be when I get to the 1 of the seventh set of 8-counts, assuming a constant acceleration throughout?
'ds=120.7cm. Just past the end of the fourth ramp. I calculated this by find a=5.3 cm/s^2 with the given data. Then used the formula for 'ds with this data to solve for 'ds.
you need to provide more documentation; state the quantities you used for the calculation and don't make the reader go back and look up the given data. It's easy and doesn't take long to provide sufficient documentation.
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7. I give the ball a quick flick, starting from the low end of the ramp, starting my count at 1 at the instant the ball leaves the end of my finger. It traveled up the ramp through one count of 8, and came to rest for an instant as I counted 5 during the next count of 8. I continued my count as it rolled back down, getting to the end of my third count of 8 and reaching 1-2 of the next set of 8 before the ball reached its original point.
Was the magnitude of the ball's acceleration the same going up as coming down?
no. simply because it took 12 “counts” to go up, and then it too 13 counts to go the same distance the other direction.
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If not, what was the approximate percent difference in the accelerations?
15% difference. I calculated the acceleration for going up was -21cm/s^2 and acceleration for coming down was 17.9cm/s^2. So thats a difference of 15%.
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8. If acceleration down a ramp is constant, then where will an object released from rest reach its average velocity? At half the total clock time. Because if v0=0, then vf/2 is the average. And the velocity reaches half of its maximum at the half clock time.
If the initial velocity is not zero, how will this affect the position at which the object reaches its average velocity? If the velocity is linear and the acceleration is constant. The vAve position will always be halfway down the ramp.
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Good. See my notes.
You do need to provide more documentation in some of your solutions, and I've given you some notes on what I mean by that.
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