#$&*
course phy 201
10/27 1:20 am
q001. The system with two weights suspended from a pulley is called an Atwood machine.When one domino was suspended from each side the machine was observed to accelerated from rest through 30 cm in about 3 seconds. When one paper clip was added it accelerated through the same 30 cm in about 2 seconds. With another added paper clip the time interval was about 1.7 seconds.
Find the acceleration for each trial.
****
Trial one: v0 = 0. vAve = 10 cm/s. vF = 20 cm/s. `ds = 3 seconds. `df = 20 cm/s aAve = 6.67 cm/s^2.
Trial Two: v0 = 0. vAve = 15 cm/s. vF = 30 cm/s. `ds = 2 seconds. `df = 30 cm/s. aAve = 15 cm/s^2
Trial Three: v0 = 0 cm/s. vAve = 17.65 cm/s. vF = 35.3 cm/s. `ds = 1.7 seconds. `df = 35.3 cm/s; aAve = 20.8 cm/s;
#$&*
Graph acceleration vs. number of paper clips and sketch the straight line that you think best fits the trend of your results.
****
#$&*
According to your results, what is the average rate of change of acceleration with respect to the number of clips?
****
roughly 7.5 cm/s^2 per paper clip.
#$&*
If the trend is in fact linear, how many clips would it take to result in an acceleration of 980 cm/s^2?
****
130.67 paper clips
#$&*
When two dominoes were suspended from each side, data similar to that obtained for the previous system indicated accelerations of 1, 7, 10 and 15 cm/s^2 for 1, 2, 3 and 4 added clips.
At what average rate was acceleration changing with respect to the number of clips?
****
3.5 cm/s^2
#$&*
@&
3 added clips resulted in a change of 14 cm/s^2, which would be an average rate of about 4.7 cm/s^2 / clip.
Looks like you divided the 14 cm/s^2 change in acceleration by the 4 clips. Easy error to make, but not quite right.
*@
For this system, what is the slope of a linear trendline for a graph of acceleration vs. number of clips?
****
3.5
#$&*
Which graph had the lesser slope?
****
They turned out to be roughly the same in my case
#$&*
What was it that was different about the two systems that resulted in different slopes?
****
The human eye will gauge things differently when given a graph. The points were not equidistant, so some differentiation is to be expected.
#$&*
If we conducted the same experiment for a system consisting of four dominoes, what do you think would be the slope of the graph of acceleration vs. number of clips?
****
3.5 cm/s^2
#$&*
If we conducted the same experiment for a system consisting of four dominoes, what do you think would be the average rate of change of acceleration with respect to the number of added clips?
****
3.5
#$&*
@&
You appear to be conjecturing that the same number of added paperclips will have the same effect on a greater number of dominoes.
Extending this reasoning to an exaggerated level, in order to make a point, suppose that there was a ton of dominoes on each side. Would you expect a single paper clip to change the acceleration of the system by 3.5 cm/s^2?
*@
`q002. Assume that at a length of 60 cm, a rubber band chain exerts no significant force, but that for every centimeter stretched beyond that length it exerts an addition 0.1 Newton of force. You don't need to know what a Newton is, but if you want something to relate to, a Newton is about the weight of a typical small-to-medium-sized apple grown on a typical backyard tree. I weigh about 800 Newtons. A liter of water weighs about 10 Newtons. A 20-ounce soft drink weighs about 6 newtons. A pound is about 4.4 newtons.
Now, if a given constant force was exerted on a ramp rotating on a domino, then the greater the distance through which the force is exerted, the further we would expect the ramp to coast after the force is removed. If the force was exerted through twice the distance, we might expect the ramp to rotate twice as far.
If we exerted a greater force through the same distance we would expect the ramp to coast further. If twice as much force was exerted through the same distance, we might expect the ramp to rotate twice as far.
Using these assumptions, reason out the following:
Suppose we extend the chain to a length of 68 cm, use it to set the rotating ramp in motion and find that the ramp coasts through 3600 degrees before coming to rest. If we had an additional chain identical to the first, and extended both to 68 cm, how far would we expect the same system to coast?
****
7200 degrees. Twice the force = twice the distance.
#$&*
How much force does the chain exert at the 68 cm length?
****
6.8 newtons
@&
The chain exerts no force when its length is 60 cm.
At 68 cm it's 8 cm longer, so would exert an additional 0.8 N of force, in addition to the 0 force exerted at the 60 cm length.
*@
#$&*
As the chain returns from the 68 cm length to its 60 cm length, does it exert a constant force, an increasing force or a decreasing force?
****
decreasing force
#$&*
What average force does the chain exert as its length decreases from 68 cm to 60 cm?
****
0.4 newtons
#$&*
Now if the chain is extended to 64 cm, how much force does it exert?
****
6.4 newtons
#$&*
What average force does it exert as its length decreases from 64 cm to 60 cm?
****
0.2 cm
#$&*
If the chain produces 3600 degrees of rotation when extended to 68 cm, how much rotation does it produce when extended to 64 cm, assuming that in each case it returns to its 60 cm length before releasing the ramp?
****
roughly 53 degrees per cm stretched, or per 0.1 newton; estimated rotation: 3392 degrees;
#$&*
@&
The chain isn't stretched 68 cm, it's 68 cm long. It's only stretched 8 cm.
It's not just the force (i.e., the Newtons) that result in the motion of the strap. It's also the distance through which the force is applied.
You'll want to rework this one.
*@
If we had two identical ramps, one on top of the other, through how many degrees do you think they would rotate if the rotation was produced by a single chain extended to a 68 cm length?
****
1800 degrees; force evenly divided between two ramps = half the force;
#$&*
@&
It's not the force alone that determines the result. The distance through which the force is exerted is equally important.
The key is the work done, not just the force exerted.
*@
If the original ramp was 2 feet long, then how far would we expect a ramp 1 foot long to coast, when the rotation is produced by a single 68 cm chain?
****
7200; half the size, moves twice as far from the same force;
#$&*
Would you expect the 1-foot ramp to have a greater or lesser coasting acceleration than the 2-foot ramp?
****
greater.
#$&*
"
@&
Pretty good overall, though on some questions you just asserted an answer without giving a reason.
There are a couple answers you'll want to revise.
&#Please see my notes and submit a copy of this document with revisions, comments 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. &#
*@