Vector Components physics homework

In summary, a 40 lb force vector that makes an angle of 120 degree counterclockwise from the -y direction can be expressed as Ax=-cos120 degree and Ay=sin120 degree
  • #1
Susanem7389
18
0
Determine the x and y components. A 40 lb force vector that makes an angle of 120 degree counterclockwise from the -y direction.

I did Ax= (40)(-cos120 degree) and Ay= (40)(sin120 degree)

I got the right answer, I just want to make sure that this is the correct way of solving the problem.
 
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  • #2
Susanem7389 said:
Determine the x and y components. A 40 lb force vector that makes an angle of 120 degree counterclockwise from the -y direction.

I did Ax= (40)(-cos120 degree) and Ay= (40)(sin120 degree)

I got the right answer, I just want to make sure that this is the correct way of solving the problem.

I read your earlier thread with Tiny_Tim and noticed that you wanted a rule as to when to use the formulas he suggested. When I was teaching, I used to tell my students to draw a careful diagram and label the angles the vector makes with each axis and work then use trigonometry to find the projection of the vector on to the axes. I think that way you will make fewer mistakes.
 
  • #3
Okay. Thank you. Also, was the way I solved the problem correct?
 
  • #4
Susanem7389 said:
Determine the x and y components. A 40 lb force vector that makes an angle of 120 degree counterclockwise from the -y direction.

I did Ax= (40)(-cos120 degree) and Ay= (40)(sin120 degree)

I got the right answer, I just want to make sure that this is the correct way of solving the problem.

Well, you said that you got the right answer, but I'm puzzled. Isn't your vector in the first quadrant making a 30 degree angle with the x axis?

Your solution is appropriate for a vector that makes an angle of 120 degrees with the Positive X axis.
 
Last edited:
  • #5
Yes, it is. I must have done something wrong with the equation. How would I fix it?
 
  • #6
The x-component of A is [tex]\hat x \cdot \vec A[/tex] (which is equal to [tex](1)|A|\cos\theta_{\mbox{\small between $\vec A$ and $\hat x$}}[/tex]).
The y-component of A is [tex]\hat y \cdot \vec A[/tex] (which is equal to [tex](1)|A|\cos\theta_{\mbox{\small between $\vec A$ and $\hat y$}}[/tex]).

You can also express the components as
[tex]A_x=A\cos\theta[/tex]
[tex]A_y=A\sin\theta[/tex]
where [tex]\theta[/tex] is the counterclockwise angle from the positive-x axis.
Note that this angle is in the range [tex]0\leq \theta < 360^\circ[/tex] (and so [tex]-1\leq \cos\theta\leq 1[/tex] and [tex]-1\leq \sin\theta\leq 1[/tex]).

The above are the best facts to remember.
If you need to work with other angles, you need to draw a good picture and express the given angle in terms of the angles above [and possibly use some trig identities, especially if you want a general formula using some other choice of angles or axes].

So, for instance, if you are given a counterclockwise angle [tex]\phi[/tex] with respect to the -y axis, what is the corresponding counterclockwise angle [tex]\theta[/tex] from the +x-axis?
 
  • #7
It would be the same numbers for both however the positive x direction, both the x and y component would be positive and for the negative y direction, both the x and y component would be negative. Thank you for your help.
 

Related to Vector Components physics homework

What are vector components?

Vector components are the individual parts of a vector that describe its magnitude and direction in a specific coordinate system. They are typically represented by two or three values, depending on the dimensionality of the vector.

How do you calculate vector components?

To calculate vector components, you can use trigonometric functions based on the given angle and the length of the vector. For example, if the vector is 5 units long and makes a 30 degree angle with the x-axis, the x-component would be 5*cos(30) = 4.33 and the y-component would be 5*sin(30) = 2.5.

What is the difference between scalar and vector components?

Scalar components only have magnitude and do not have a direction, whereas vector components have both magnitude and direction. Scalar components can be added or subtracted using simple arithmetic, while vector components must be added or subtracted using vector addition or subtraction.

Why do we use vector components in physics?

In physics, vector components are used to break down complex vectors into simpler parts that are easier to analyze and manipulate. They also allow us to apply mathematical operations, such as addition and subtraction, to vectors to solve problems in mechanics and other areas of physics.

Can vector components be negative?

Yes, vector components can be negative. This indicates the direction of the vector in relation to the chosen coordinate system. A negative component means that the vector is pointing in the opposite direction of the positive component.

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