# Choosing different axes in the same system

• Carpetfizz
In summary, the answer provided in the solution guide for part a) is incorrect, and the answer provided with the different axis is correct.
Carpetfizz

## Homework Statement

Just doing some practice problems from past finals and I needed some help on this one. Sorry if my question doesn't exactly fit the template.

2) Relevant Equations / Information

For part a) and for M_1, I drew the axes such that the x-axis points to the top right, in the direction of motion of M_1, and the y-axes points up perpendicular to it. For M_2 I drew the axes such that the x-axis points to the bottom right and the y-axis points up perpendicular to it.

This is the answer the solution guide provided

The difference is that my axes for M_1 was flipped such that the x-axis pointed in the opposite direction to what is presented in the solution.

I'm curious as to why they chose to make the direction opposite to M_1's motion positive.

3) Attempt at Solution

I tried doing it both ways and it yielded two different answers

1. The way in the answer sheet:

$$T = \frac{M_1M_2g(\mu_1cos(\phi)+sin(\phi)+sin(\theta)}{(M_1+M_2)}$$

2. The way with the different axis:

$$T = \frac{M_1M_2g(\mu_1cos(\phi)+sin(\phi)+sin(\theta)}{(M_1-M_2)}$$

I'm not exactly sure how switching the axes gives the right answer or what the rationale behind doing that is. Any advice would be much appreciated.

Forget the math and look at it as a physicist: would the tension go to infinity if the two masses go to the same ##M## ?

Sorry, I'm not sure what you mean. Where in my question does it imply the two masses go to the same M and what does that mean?

Carpetfizz said:
Sorry, I'm not sure what you mean. Where in my question does it imply the two masses go to the same M and what does that mean?
$$T = \frac{M_1M_2g(\mu_1cos(\phi)+sin(\phi)+sin(\theta)}{(M_1-M_2)} = \infty$$ if $$M_1 = M_2$$

Okay that makes sense. I feel like you wouldn't get the quantity (M1-M2) unless you solved for T all the way through. Is there any way you can account for this edge case before you solve the problem?

Do the exercise for the case M1 = M2 first...

Carpetfizz said:
Okay that makes sense. I feel like you wouldn't get the quantity (M1-M2) unless you solved for T all the way through. Is there any way you can account for this edge case before you solve the problem?
The FBD in book is correct.
I can't tell your mistake because I have not seen your FBD and the description you provided is ambiguous.

## 1. How do I choose different axes in the same system?

To choose different axes in the same system, you can use the "Axes" menu in your software or program that you are using. This menu allows you to select the specific axes you want to use for your data visualization.

## 2. Can I change the axes labels in a graph or chart?

Yes, you can change the axes labels in a graph or chart by editing the axis properties. Most software and programs have options to customize the labels, font, and format of the axes to better fit your data and presentation.

## 3. How do I switch the axes on a graph or chart?

To switch the axes on a graph or chart, you can use the "Swap Axes" function in your software or program. This will interchange the horizontal and vertical axes, allowing you to view your data from a different perspective.

## 4. Can I have multiple axes on the same graph or chart?

Yes, it is possible to have multiple axes on the same graph or chart. This is especially useful when you have different types of data with different scales that you want to compare on one visualization. You can add additional axes through the "Axes" menu or by right-clicking on the graph.

## 5. How do I know which axes to use for my data?

The axes you choose for your data will depend on the type of data you have and the purpose of your visualization. It is important to consider the scales, units, and relationships between your data points when selecting axes. You can also consult with a data visualization expert for guidance on choosing the most appropriate axes for your data.

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