Relating a_{2x} and a_{1x}/a_{1y}

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In summary: Yah...thanks for ur help...In summary, the problem involves a constraint on the relative accelerations of two blocks, with one block on an incline. The x-component of the acceleration of block 2, a_2x, can be expressed in terms of the acceleration components of block 1. The total accelerations of each block must be equal in magnitude, but travel in different directions. If the x-axis is parallel to the incline for block 2 and the y-axis is vertical, then the final answer is a_2x = -a_1y.
  • #1
polymerase
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In this problem, the fact that the length of the string does not change imposes a constraint on relative accelerations of the two blocks. Find a relationship between the x component of the acceleration of block 2, [tex]a_{2x}[/tex],and the acceleration of block 1. Pay careful attention to signs.

Express [tex]a_{2x}[/tex] in terms of [tex]a_{1x}[/tex] and/or [tex]a_{1y}[/tex], the components of the acceleration vector of block 1.

(the diagram is included)
 

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  • #2
Hint: How must the total accelerations of each block be related?
 
  • #3
Doc Al said:
Hint: How must the total accelerations of each block be related?

Equal?
 
  • #4
polymerase said:
Equal?
Exactly!
 
  • #5
Doc Al said:
Exactly!

so...a_2x = a_1y?
 
  • #6
polymerase said:
so...a_2x = a_1y?
Nope. Block 2 is on an incline. The magnitude of its total acceleration equals that of the other block, but they travel in different directions (obviously).

(I assume that x & y are horizontal and vertical. If x means parallel to the plane, then you are almost correct.)
 
  • #7
Doc Al said:
Nope. Block 2 is on an incline. The magnitude of its total acceleration equals that of the other block, but they travel in different directions (obviously).

(I assume that x & y are horizontal and vertical.)


...therefore FINAL answer is...a_2x = -a_y1??
 
  • #8
polymerase said:
...therefore FINAL answer is...a_2x = -a_y1??
If the x-axis is parallel to the incline for mass 2 and the y-axis is vertical for mass 2: Yes!
 
  • #9
Doc Al said:
If the x-axis is parallel to the incline for mass 2 and the y-axis is vertical for mass 2: Yes!

Yah...thanks for ur help
 

1. What does the notation a_{2x} mean?

The notation a_{2x} refers to a specific term or variable in a mathematical equation, where the subscript 2x indicates the value or coefficient associated with the variable x.

2. How is a_{2x} related to a_{1x}/a_{1y}?

The two terms, a_{2x} and a_{1x}/a_{1y}, are related through a mathematical equation or function. The specific relationship between these terms will depend on the context in which they are used and the specific values of a_{1x} and a_{1y}.

3. What does a_{1x}/a_{1y} represent?

The term a_{1x}/a_{1y} represents a ratio or fraction of two values, where a_{1x} is the numerator and a_{1y} is the denominator. This could be used to represent a variety of mathematical relationships, such as a slope or a conversion factor.

4. How can I solve for a_{2x} when given a_{1x}/a_{1y}?

The process for solving for a_{2x} will depend on the specific equation or problem. In general, you will need to rearrange the equation to isolate a_{2x} on one side, and then use algebraic techniques to solve for its value.

5. Are there any real-world applications for relating a_{2x} and a_{1x}/a_{1y}?

Yes, there are many real-world applications for this type of relationship. For example, it could be used to calculate the slope of a line in a graph, or to convert units of measurement. It could also be used in physics equations to represent the relationship between different variables.

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