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course phy 201
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:
5.258, 5.81, 5.123,4.228, 5.173
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Based on your results, how long does your typical 8-count last?
Around 5 seconds.
those were your intervals for four 8-counts; how long for a single 8-count?
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Based on your result, what is the time interval of each of your counts?
5
there are 32 counts in four 8-counts; each count is way shorter than 5 seconds
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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?
2.5 seconds around 15% uncertainity
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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)?
10cm/s
you need to show your reasoning; 10 cm/s is not correct but 10 cm/s^2 would be correct
you haven't found the length of the ramp
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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.
GIVEN= V0=20cm/s, Vf=40cm/s, ‘dt=2 second
REASON=‘dx,=20 vave=10cm/s, dv=20cm
Your given values are correct; most of your reasoned values were not.
You need to show the steps of your reasoning.
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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?
3.33cm/s^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.
Given=V0=20cm/s, ‘dt=3 seconds, vave=10cm/s^2
Reason=VF=40cm, ‘ds=3, ‘dv 4
REASON=‘dx,=20 vave=10cm/s, dv=20cm
Your given values are correct; your reasoned values are not.
You need to show the steps of your reasoning.
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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=20cm/s, ‘dt=5seconds, v0=0
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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).
Equation 1
`ds = (vf + v0) / 2 * `dt
Equation 2
vf = v0 + a `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.
‘ds or a
`ds = (vf + v0) / 2 * `dt
‘ds=(20cm/s+0)/2*5seconds
‘ds=(20cm/s)/2*5seconds
‘ds=10cm/s*5seconds
‘ds=50cm/s^2
Well done.
However in that last step cm/s * s = cm, so your `ds will be 50 cm, not 50 cm/s^2
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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, v0=0, vf=30 cm/s
a = 10 cm/s^2; watch the units
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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).
Equation 2
vf = v0 + a `dt
Good; the 4th equation also applies.
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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.
30cm/s=0+10cm/s ‘dt
30cm/s=10cm/s ‘dt
Divide by 10cm/s
3cm/s=‘dt
good, but accel is in cm/s^2, and the final calculation for `dt is (30 cm/s) / (10 cm/s^2) = 3 (cm/s) * (s^2 / cm) = 3 s.
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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.
30cm/s
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The final velocity of the ball on the ramp.
60
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The change in the velocity of the ball from start to finish.
6cm/s^2
cm/s^2 is not a unit of change in velocity
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The average rate of change of the velocity with respect to clock time.
6cm/s
cm/s is not a unit of acceleration
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The velocity of the ball at the midpoint of the ramp.
30cm/s
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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.
6cm/s
this isn't correct; you need to show your reasoning so I can tell what you are thinking and help correct it
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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.
Average velocity 300/7.4=40.54cm/s
Final velocity=300cm
ave velocity is good; final velocity isn't 300 cm. Among other things 300 cm isn't a velocity, it's a displacement.
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Using your results, find its acceleration.
vf = v0 + a `dt
300cm=0+a 7.4
Divide both sides by 7.4
a=40.54
300 cm isn't a velocity; you should find the correct final velocity and use it here. And you need to include units.
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Find the velocities v_mid_x and v_mid_t.
Mid x=150
Mid t=3.7
you would need to show your reasoning in detail
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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?
40.54=20/t
40.54/20=t
t=2.02
You haven't identified v0, vf, a, etc. for this interval.
That's where you need to start.
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Where would it be at the halfway clock time?
t=2.02/2
t=1.01
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How fast would it be moving at the midpoint between the two ends of the ramp?
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What would be its velocity at the halfway clock time?
300/2.02=148.51
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What would be the change in its velocity from one end of the ramp to the other?
300/2.02=148.51
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In all the remaining questions your first step needs to be to identify the relevant interval, then identify v0, vf, a, `ds, `dt.
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.
No I does not lose any speed because if it took 13 counts, it only took 24 to complete the 60 cm ramp.
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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 (imilar 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?
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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?
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How long should the ball have spent on the first ramp, if the acceleration was indeed constant?
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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?
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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?
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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?
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If not, what was the approximate percent difference in the accelerations?
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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 the midpoint
If the initial velocity is not zero, how will this affect the position at which the object reaches its average velocity?
The average velocity would be effect because it would take it quicker to reach the final velocity
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You do pretty well when you start by carefully identifying v0, vf, `dt, a and `ds, then apply the equations. You need to be more specific in your use of units.
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