two force vectors, f1 18N at 60 degree above the positive axis and F2 6.5N at 45 degree below the positive axis, are applied to a particle at the origin. what third force f3 would make the net force on the particle equal to zero
F1 + F2 + F3 = 0.
F3 = -(F1+F2)
F3 = -(18[E60oN]+6.5[E45oS]) =
-(18*Cos60+18*sin60 +6.5*Cos45+6.5*sin45
= -(9+15.6i + 4.6-4.6i) = -(13.6+11i) =
-13.6 - 11i = 21.6N.[39o] Below the negative X-axis.
f4
To make the net force on the particle equal to zero, we need to find a third force vector that will cancel out the effect of the other two forces. We can do this by finding the resultant vector of the first two forces and then finding the opposite vector to cancel it out.
Let's break down the given forces F1 and F2 into their x and y components. We'll use the standard coordinate system with positive x-axis to the right and positive y-axis upwards.
Force F1:
Magnitude = 18N
Angle = 60 degrees
The x component of F1 can be found using cosine:
Fx1 = 18N * cos(60 degrees)
The y component of F1 can be found using sine:
Fy1 = 18N * sin(60 degrees)
Force F2:
Magnitude = 6.5N
Angle = 45 degrees
The x component of F2 can be found using cosine:
Fx2 = 6.5N * cos(45 degrees)
The y component of F2 can be found using sine:
Fy2 = 6.5N * sin(45 degrees)
Now we can calculate the resultant vector by summing up the x and y components separately:
Resultant x component:
Rx = Fx1 + Fx2
Resultant y component:
Ry = Fy1 - Fy2 (since Fy2 is in the opposite direction)
To make the net force equal to zero, the resultant vector Rx and Ry should both be zero. We can set up the equations:
Rx = 0
Ry = 0
Substituting the expressions for Rx and Ry, we get:
Fx1 + Fx2 = 0
Fy1 - Fy2 = 0
Now we can solve these two equations to find the values of Fx1, Fx2, Fy1, and Fy2.
Once we have the values for Fx1, Fx2, Fy1, and Fy2, we can find the magnitude and angle of the third force vector F3 using the Pythagorean theorem and trigonometry. The magnitude of F3 will be the square root of the sum of the squares of the x and y components, and the angle can be found using inverse tangent.
Let's calculate the components and find the third force F3 using the given values.