Solving Vector Equations w/ A+B+C = 0

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Homework Help Overview

The problem involves vector equations where the sum of three vectors A, B, and C equals zero. Vector A points in the negative x direction, vector B is at an angle of 30 degrees above the positive x-axis, and vector C has a magnitude of 15.0 m, directed 40 degrees below the positive x-axis. The objective is to find the magnitudes of vectors A and B.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the components of vector C and how to express vectors A and B in terms of their components. There is exploration of the signs and values of the components based on the directions of the vectors. Questions arise about the correct representation of vector A and the implications of its direction on its components.

Discussion Status

Participants have established the component forms of the vectors and are working through the implications of setting the sum of the components to zero. There is some agreement on the values of certain components, but further clarification is sought regarding the relationships between the components of vector B and the known values from vector C.

Contextual Notes

Participants are navigating through the constraints of the problem, including the requirement that the sum of the vectors equals zero and the specific angles and directions given for each vector. There is an ongoing examination of the assumptions related to the components of the vectors.

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Homework Statement


Vector A points in the negative x direction. Vector B points at an angle of 30 degrees above the positive x axis. Vector C has a magnitude of 15.0 m and points in a direction 40 degrees below the positive x axis. Given that vectors A + B + C = 0, find the magnitude of vector A and vector B


Homework Equations


Sin = opp/hyp


The Attempt at a Solution


For vector C, I found the x direction to be 11.49 m and the y direction to be -9.64 m.

Other than that I have no idea where to begin.

thanks,
 
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nokitman said:

The Attempt at a Solution


For vector C, I found the x direction to be 11.49 m and the y direction to be -9.64 m.

Good. So we know C=11.49i-9.647j

so let's put A=ai+bj. It says A points in the negative x direction, so what should A really be ? (i.e. should the 'a' be +a or -a and what should 'b' equal to?)

So B acts at an angle of 30 degrees to the x-axis. If the magnitude of B is |B| then B=|B|(ci+dj)

so find A+B+C, grouping together the i and j terms.
 
like this ?

C = 11.49i - 9.647j
A = ai - bj
B = |B| (ci + dj)
_____________________ +

= (11.49 + a + |B|c)i - (9.647 - b + |C|d)j

Is that right? :confused:
 
nokitman said:
like this ?

C = 11.49i - 9.647j
A = ai - bj
B = |B| (ci + dj)
_____________________ +

= (11.49 + a + |B|c)i - (9.647 - b + |C|d)j

Is that right? :confused:

Sorry I made a mistake, let's take out the |B| and just have B=ci+dj

You should get A+B+C = (11.49+a+c)i + (-9.647-b+d)j

once again now, if A=ai+bj is in the negative x direction, what is b equal to? And what sign should the a really have ?
 
the "a" should be negative so A=-ai+bj, should the b also be negative?
 
nokitman said:
the "a" should be negative so A=-ai+bj, should the b also be negative?

right the 'a' should really be '-a'. So if the j component is the vertical component, and you know A is purely horizontal, what value should 'b' equal to?
 
b should be 0 in the A vector

C = 11.49i - 9.647j
A = -ai
B = ci + dj
_________________ +

= (11.49 -a + c)i + (-9.647 + d)j = 0

Is that correct? what's the next step?

Thank you
 
nokitman said:
b should be 0 in the A vector

C = 11.49i - 9.647j
A = -ai
B = ci + dj
_________________ +

= (11.49 -a + c)i + (-9.647 + d)j = 0

Is that correct? what's the next step?

Thank you

yes this correct. So if it is equal to zero, that means both the i and j components are zero, so what is d?
 
d= oi + oj

how does it get me to find the magnitude of A and B vectors?
 
  • #10
nokitman said:
d= oi + oj

how does it get me to find the magnitude of A and B vectors?

no no

we have A+B+C = = (11.49 -a + c)i + (-9.647 + d)j = 0 =0i+0j.

so when you equate components, what is d equal to?
 
  • #11
d is zero?
 
  • #12
nokitman said:
d is zero?

no if (-9.647 + d) =0 what is d? Do you know why (-9.647 + d) equal 0?
 
  • #13
sorry d is 9.647
 
  • #14
nokitman said:
sorry d is 9.647

ok good. Now we know for a vector say R of magnitude |R|, acting at an angle θ to the x-axis can be represented as R= |R|cosθi+|R|sinθj


Can you now make a similar comparison to the vector B with magnitude |B|? Are you able to see how 'd' relates to |B| at the given angle?
 
  • #15
vector B = |B|cos30i + |B|sin30j ?
is 9.647 the y component of vector B?
 
  • #16
nokitman said:
vector B = |B|cos30i + |B|sin30j ?
is 9.647 the y component of vector B?

yes, so now if d=|B|sin30 -> 9.647=|B|sinn30 what is |B| equal to?

When you get |B|, can you find what 'c' is equal to ?
 
  • #17
|B| = 11.139i + 19.294j?
 

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