Why is (B.y) for the y-component negative for sin30?

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In summary, the y-component for the sin30 is negative because it is actually sin(-30), indicating a displacement in the opposite direction of the reference positive direction. This makes sense when adding vectors in component form, as the y-component would be greater than the y-component of the 8.00N @ 40degrees vector, despite the vectors traveling in opposite directions from the x-axis. This sign convention is a matter of personal preference and consistency is key in using it effectively.
  • #1
yardy_genius
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Hello, can someone please explain why (B.y) for the y-component is negative for the sin30. thanks .
question is below.

[PLAIN]http://img710.imageshack.us/img710/6150/resulant.jpg [Broken]
 
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  • #2
The y-component for the sin30 is because it's actually sin(-30): the angular displacement is in the opposite direction of the reference positive direction. Intuitively, this makes sense because when you add the vectors in component form you would get a vector whose y-component is greater than the y-component of the 8.00N @ 40degrees vector despite the fact that the vectors shown are traveling in opposite directions from the x-axis, that is, their y-components should have opposite signs.
 
  • #3
Welcome to PF yardy_genius,

It's just a sign convention. By convention, you're taking "up" to be the positive y-direction and "down" to be the negative y-direction. You could just as easily adopt the opposite sign convention. All that matters is that you pick a convention and stick to it (i.e. use it consistently throughout the problem).
 
  • #4
WJSwanson said:
The y-component for the sin30 is because it's actually sin(-30): the angular displacement is in the opposite direction of the reference positive direction. Intuitively, this makes sense because when you add the vectors in component form you would get a vector whose y-component is greater than the y-component of the 8.00N @ 40degrees vector despite the fact that the vectors shown are traveling in opposite directions from the x-axis, that is, their y-components should have opposite signs.

thanks alot
 
  • #5
cepheid said:
Welcome to PF yardy_genius,

It's just a sign convention. By convention, you're taking "up" to be the positive y-direction and "down" to be the negative y-direction. You could just as easily adopt the opposite sign convention. All that matters is that you pick a convention and stick to it (i.e. use it consistently throughout the problem).

thanks , you guys really helped a lot
 
  • #6
No problem; glad I could help. Cepheid's answer is also pretty important, by the way. He touched on a way more critical point than I did, which is that you can use almost any convention that's convenient, so long as you stick to it (and make sure to revert it to the original terms if necessary/requested).
 

What is meant by calculating resultant?

Calculating resultant is the process of finding the magnitude and direction of the combined effect of two or more vectors. It is used in physics and engineering to determine the overall force or displacement of an object.

How do you calculate resultant?

To calculate resultant, you need to break down the vectors into their components, which are typically in the x and y direction. Then, you can use the Pythagorean theorem to find the magnitude and trigonometry to find the direction. Finally, you can combine the components to determine the overall resultant.

What is the difference between resultant and vector addition?

Resultant is the final combined effect of two or more vectors, while vector addition is the mathematical operation used to calculate the resultant. Vector addition involves breaking down vectors into their components and then adding them together to find the resultant.

Can resultant be negative?

Yes, resultant can be negative. This typically occurs when the direction of the resultant is opposite to the direction of one or more of the vectors being added. In this case, the negative sign indicates the direction of the resultant.

Why is calculating resultant important?

Calculating resultant is important because it allows us to determine the overall effect of multiple forces or displacements acting on an object. This is crucial in understanding the motion of objects and designing structures that can withstand various forces.

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