#$&*
PHY 241
Your 'cq_1_09.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
A ball accelerates uniformly as it rolls 20 cm down a ramp, starting from rest, in 2 seconds.
What are its average velocity, final velocity and acceleration?
answer/question/discussion: ->->->->->->->->->->->-> :
v_0 = 0
'ds = 20 cm
'dt = 2 seconds
v_ave = 'ds/'dt
= 20 cm / 2 seconds
= 10 cm/s
'ds = v_0 * 'dt + .5 * a * 'dt^2
a = 2 * ['ds - (v_0 * 'dt)] / 'dt^2
= 2 * [2 m] / 4 s^2
= 1 m/s^2
@& If your answer was correct the ball would be moving at 2 m/s at the end of the ramjp, and would average 1 m/s. It would take only .2 sec to get down the 20 cm ramp.
This is clearly inconsistent with given information.
'ds - (v_0 * 'dt) is .2 m, not 2 m.
Average vel is 10 cm/s, final vel is 20 cm/s, `dv = 20 cm/s, a = 20 cm/s / (2 s) = 10 cm/s^2.
It's important to be able to use the equations, and you're in good shape there.
It's also important to visualize what's going on, which is easiest to do if you connect everything to the definitions and reason from there.
If the two don't reconcile, then you know there's an error.*@
v_f = v_0 + a * 'dt
= 0 + 1 m/s^2 * 2 seconds
= 2 m/s
#$&*
If the time interval is in error so that it is 3% longer than the actual time interval, then what are the actual values of the final velocity and acceleration?
answer/question/discussion: ->->->->->->->->->->->-> :
2 s * .03 = 0.6
2 + 0.6 = 2.6 is corrected time interval
a = 2 * ['ds - (v_0 * 'dt)] / 'dt^2
= 2 * [2.06 s] / 4.2436 s^2
= 0.97 m/s^2
v_f = v_0 + a * 'dt
= 0 + 0.97 m/s^2 * 2.06
= 2 m/s
@& 'ds - (v_0 * 'dt) is not 2.06 s.
Direct reasoning of accelerations would be more informative than the equations. The equations should give the same results as direct reasoning from definitions.*@
#$&*
What is the percent error in each?
answer/question/discussion: ->->->->->->->->->->->-> :
3 % error in acceleration.
0 % error in v_f
#$&*
If the percent error is the same for both velocity and acceleration, explain why this must be so.
answer/question/discussion: ->->->->->->->->->->->-> :
They aren't. I got 3% error for acceleration and 0 % error for final velocity. If the were the same, then I guess that would be because they both rely on each other. In order to solve for V_f, you have to find acceleration first.
#$&*
If the percent errors are different explain why it must be so.
answer/question/discussion: ->->->->->->->->->->->-> :
The reason they are different is becuase if an object is accelerating, it will reach a time destination quicker and velocity. If the object doesn't get to the time destination till alittle bit later, it's velocity will still be the same but the acceleration slightly slower.
#$&*
** **
25 minutes
** **
10/28/2011 1036 pm
self-critique #$&*
#$&* self-critique
self-critique rating
rating #$&*:
&#See any notes I might have inserted into your document, and before looking at the link below see if you can modify your solutions. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your old and new solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#
@& At least one of your results for percent error is incorrect.
&#Please see my notes and, unless my notes indicate that revision is optional, submit a copy of this document with revisions 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.
If my notes indicate that revision is optional, use your own judgement as to whether a revision will benefit you. &#
*@