he magnitudes are F1 = 1.81f,F2 = f,and
F3 = 2.00f,where f is a constant.
(a) Use the coordinate system shown in the figure above to find
R = F1 + F2 + F3
in component form in terms of f.
(b) If x = 0.25,
what is
Ry?
To find R = F1 + F2 + F3 in component form in terms of f, we need to break down each force vector into its x and y components and then add them up.
(a) First, let's find the x and y components for each force vector:
For F1 = 1.81f:
- The x component, F1x, is given by F1x = F1 * cos(θ), where θ is the angle between F1 and the x-axis.
- The y component, F1y, is given by F1y = F1 * sin(θ).
For F2 = f:
- Since F2 is along the y-axis, its x component, F2x, is 0.
- The y component, F2y, is simply F2 itself.
For F3 = 2.00f:
- The x component, F3x, is given by F3x = F3 * cos(θ), where θ is the angle between F3 and the x-axis.
- The y component, F3y, is given by F3y = F3 * sin(θ).
(b) To find Ry when x = 0.25, we need to substitute the value of x into the y-components of each force vector and then add them up:
Ry = F1y + F2y + F3y
Remember, F1y, F2y, and F3y are already expressed in terms of f, so there's no need to substitute the value of f into the equation.
By performing these calculations, you would get the answers to both parts of the question.
1st: To find R for part a), f1x,f1y,f2x, f2y, f3x, f3y.
2nd: f1x=0,f1y= -1.81, f2x=-.866,f2y=.500,f3x=1.00,f3y=1.73
3rd: To finf R, add all the fx together on one side and fy together on the other side.-->R=(0+-.866+1.00)i+(-1.81+.500+1.73)j
4th: answer of R-->R=.134i+.420j
5th: To find Ry for part b), we know Rx=.25i take it and divid by.134 and get .536
6th: answer for Ry,take .420 and divide by.536 and get .784 as answer.