I know I need to show my work but the problem is that I don't even know where to begin. I am taking an online physics class with a teacher that is not willing to help. So any guidance would be much appreciated.
Consider the two vectors:
F1: (220N, 41°), F2: (50N, 139°)
The angles are measured from the positive x axis with the counter-clockwise angular direction taken as positive.
1.) What is in N, the x-component of the resultant vector F?
2.)What is in N, the y-component of the resultant vector F?
3.)What is in N, the magnitude of vector F?
I assume F=F1+F2
1 add the x components: 22Ocos41+50cos139
2 add the y components: 220sin41+50sin139
3 for the magnatude, then Magnitude=sqrt(x^2+y^2)
thank you! that helps so much!I was able to work other questions that were similar to this question thanks to you :)
What is in degrees as measured from the positive x in the counter-clockwise angular direction the direction of vector F?
To find the x-component of the resultant vector F, you'll need to use trigonometry and vector addition. Here's how you can do it step by step:
1.) Convert the given vectors into their x and y components using the given angles.
- For F1:
- The magnitude of F1 is 220N.
- The x-component of F1 can be found using the formula: F1x = F1 * cos(angle).
- The y-component of F1 can be found using the formula: F1y = F1 * sin(angle).
- For F2:
- The magnitude of F2 is 50N.
- The x-component of F2 can be found using the formula: F2x = F2 * cos(angle).
- The y-component of F2 can be found using the formula: F2y = F2 * sin(angle).
2.) Add the x-components of the vectors.
- Fx = F1x + F2x.
3.) Substitute the values of F1x, F2x, and solve for Fx.
Now, let's apply the steps to solve the problem:
1.) For F1:
- F1x = 220N * cos(41°).
- F1y = 220N * sin(41°).
- Calculate F1x: F1x = 220N * cos(41°) = 220N * 0.7547 ≈ 166.43N.
- Calculate F1y: F1y = 220N * sin(41°) = 220N * 0.6561 ≈ 144.34N.
2.) For F2:
- F2x = 50N * cos(139°).
- F2y = 50N * sin(139°).
- Calculate F2x: F2x = 50N * cos(139°) = 50N * (-0.6428) ≈ -32.14N.
- Calculate F2y: F2y = 50N * sin(139°) = 50N * 0.766 ≈ 38.3N.
3.) Finding the x-component of the resultant vector F:
- Fx = F1x + F2x = 166.43N + (-32.14N) = 134.29N.
Therefore, the x-component of the resultant vector F is approximately 134.29N.