Turning simple concept of F=ma into a nightmare

[riseofphoenix]

2. A group of students performing Newton's Second Law experiment generated the graph shown below from their data. Which of the following statements is true regarding the trustworthiness of the data? (Select all that apply.)

a) The graph should have a positive y-intercept because a certain amount of mass is needed on the hanger to overcome the friction and create a net force in the forward direction.
b) Friction would cause the plot to be shifted upward such that the y-intercept is positive. c) Therefore the negative y-intercept indicates incorrect data. The negative y-intercept indicates the amount of friction force present.
d) The plot of the data crosses the x-axis at a positive value of the acceleration. This means that when the hanging mass is zero, the cart still has some acceleration, which seems contrary to Newton's Second Law.
e) The graph crossing the x-axis at some positive value of the acceleration indicates the presence of a non-zero acceleration, which is in agreement with Newton's Second Law.
f) The track was not level and the cart went downhill during the experiment, causing the cart to accelerate in the forward direction even when the hanging mass was zero.

–––––––

I've tried b, c, d and I got that wrong... But that was when I guessed. I tried, c and e, and got that wrong too. That time, I guess...

But after thinking about the question and looking closely at the graph, I tried a, b, c, and e and got that wrong too -.- THEN, I decided to think harder and I tried, a, b, and e and got that wrong.

I also tried b, d, and f and got that wrong -.-

So right now, I've done 5/6 submissions and I have one more submission left - I've looked at my notes and everything. Does anyone know the right answer to this question?

 

[haruspex]

There's no point in commenting on blind guesses. Please post your reasoning.

 

[barryj]

What do you mean by a hanging weight? Diagram would help.

 

[berkeman]

bump

Welcome to the PF.

Why did you necro-bump this thread? It is from the end of last year, and the original poster (OP) most likely has moved on well past this problem...

 

[mcwooten]

Sorry, I had the same exact problem.

 

[haruspex]

Sorry, I had the same exact problem.

Then please post your reasoning and proposed answers.

 

[mcwooten]

Well, so far I know from this post and my own attempts that these combinations DO NOT WORK:
b/c/d
c/e
a/b/c/e
a/b/e
b/d/f
a/b/c/d

Looking at the problem again, I'm thinking that the answer may be b/d, but to be quite honest, I'm completely lost.

 

[mcwooten]

http://physics.appstate.edu/sites/physics.appstate.edu/files/Atwood.gif

 

[haruspex]

First, can you verify this part of the OP:

b) Friction would cause the plot to be shifted upward such that the y-intercept is positive. c) Therefore the negative y-intercept indicates incorrect data. The negative y-intercept indicates the amount of friction force present.

Is that really how it's laid out? Not, perhaps:

b) Friction would cause the plot to be shifted upward such that the y-intercept is positive. Therefore the negative y-intercept indicates incorrect data.
c) The negative y-intercept indicates the amount of friction force present.​

?
Secondly, I'm not sure how literally to read the question "Which of the following statements is true regarding the trustworthiness of the data?". Only statement (b) (as modified above) is, strictly speaking, a comment on the data. Statement (a) is about what data would be expected; statement (e) is an interpretation of the data; statement (f) is a comment on the experimental set-up.

Thirdly, please post the answer that makes most sense to you (even if it has already been rejected) with your reasoning.

 

[mcwooten]

I agree that it is a poorly written question, and yes, b) and c) are separate as you have indicated.

The answer that makes the most sense to me is b/d (it may not have been originally, but in my mind I have already rejected other possible combinations because I know they were wrong) because:

1) If friction were negative, in this case, it would indicate that it was a supportive force aiding the acceleration of the cart rather than opposing it, which doesn't make sense.
2) A non-zero x-intercept indicates acceleration without any hanging mass, which suggests spontaneous acceleration without any causative force. This also doesn't make sense.

 

[haruspex]

I agree that it is a poorly written question, and yes, b) and c) are separate as you have indicated.

The answer that makes the most sense to me is b/d (it may not have been originally, but in my mind I have already rejected other possible combinations because I know they were wrong) because:

1) If friction were negative, in this case, it would indicate that it was a supportive force aiding the acceleration of the cart rather than opposing it, which doesn't make sense.
2) A non-zero x-intercept indicates acceleration without any hanging mass, which suggests spontaneous acceleration without any causative force. This also doesn't make sense.

I'm going to push you yet again on giving your reasons. What I'd like you to do is to go through each of a to f saying why you think it's true or false.
For now, I disagree with what you say in (2) above. You need to distinguish between a positive and negative intercept. What would a positive intercept indicate?

 

[mcwooten]

a) The graph should have a positive y-intercept because a certain amount of mass is needed on the hanger to overcome the friction and create a net force in the forward direction.
b) Friction would cause the plot to be shifted upward such that the y-intercept is positive. Therefore the negative y-intercept indicates incorrect data.
c) The negative y-intercept indicates the amount of friction force present.
d) The plot of the data crosses the x-axis at a positive value of the acceleration. This means that when the hanging mass is zero, the cart still has some acceleration, which seems contrary to Newton's Second Law.
e) The graph crossing the x-axis at some positive value of the acceleration indicates the presence of a non-zero acceleration, which is in agreement with Newton's Second Law.
f) The track was not level and the cart went downhill during the experiment, causing the cart to accelerate in the forward direction even when the hanging mass was zero.



a) False- A positive y-intercept indicates the opposing frictional force.
b) True- see above explanation
c) Not sure- I guess it could in this instance, but that shouldn't happen.
d) False- I don't really know why, but you indicated that my reasoning above was probably wrong
e) True?- Since d is false, maybe this is true because there is a non-zero acceleration due to the force of the hanging mass?
f) Not sure, but I think this is false b/c the friction force is presumably negative, which might suggest the track was not level and caused the cart to move in the BACKWARD direction.

 

[mfb]

A positive y-intercept indicates the opposing frictional force.

I agree. How does that differ from (a)?

c) Not sure- I guess it could in this instance, but that shouldn't happen.

See your analysis for (a).

d) False- I don't really know why, but you indicated that my reasoning above was probably wrong

I agree with your initial analysis, and I guess haruspex thought about the y-intercept in his reply.

e) True?- Since d is false, maybe this is true because there is a non-zero acceleration due to the force of the hanging mass?

Which hanging mass, if the graph crosses the x-axis?

f) Not sure, but I think this is false b/c the friction force is presumably negative, which might suggest the track was not level and caused the cart to move in the BACKWARD direction.

Friction is not negative. Where do you see a backwards (negative) acceleration?

 

[haruspex]

A positive y-indicates the opposing frictional force.

I agree. How does that differ from (a)?

To be clear, I think mfb is agreeing with your statement, quoted above, but not with the conclusion that (a) is false.

d) False- I don't really know why, but you indicated that my reasoning above was probably wrong

I agree with your initial analysis, and I guess haruspex thought about the y-intercept in his reply.

I think mfb meant to say I was thinking about the x-intercept. Well, I wasn't, but this brings up another subtlety in interpretation of the question. The question asks about the reliability of the data, not about the reasonableness of the straight line graph drawn from it. So I was answering based on whether the straight line projection should have a zero, positive or negative y intercept, not whether actual behaviour of the system would do that. A positive projected intercept should be expected.

e) True?- Since d is false, maybe this is true because there is a non-zero acceleration due to the force of the hanging mass?

Which hanging mass, if the graph crosses the x-axis?

In case that's not clear, mfb is asking "how large is the hanging mass when y=0?"

f) Not sure, but I think this is false b/c the friction force is presumably negative, which might suggest the track was not level and caused the cart to move in the BACKWARD direction.

Ask yourself what you would expect to see if the surface tilts down towards the pulley.

 

[mcwooten]

What I'm surmising from this information is that a/b/d would be the best answer, or a/b/d/e, since b suggest d must also be true...

 

[haruspex]

What I'm surmising from this information is that a/b/d would be the best answer, or a/b/d/e, since b suggest d must also be true...

a, b, d are all reasonable. I don't understand how you could choose e as well since the last phrase of it is in direct contradiction to the last phrase in d.
I still don't understand your objection to f. You didn't answer my question: what would you expect to see if the surface tilts down towards the pulley?

 

[mcwooten]

Thinking about it again, I suppose one would see the results from above if the track was tilted towards the pulley.

 

[mcwooten]

Correct answer was indeed a/b/d/f. Thanks for the help!

 

[Andrew Mason]

Thinking about it again, I suppose one would see the results from above if the track was tilted towards the pulley.

That would help explain the part of the graph above m = 0. But how does it explain the data from m < 0? How would you have negative hanging mass pulling on the cart?

AM

 

[haruspex]

That would help explain the part of the graph above m = 0. But how does it explain the data from m < 0? How would you have negative hanging mass pulling on the cart?

AM

There are no data below the line. The straight line fit is projected below the line, but the question relates to the data.