Calculating x and y Components of Equilibrium Forces

[kari82]

Three forces A, B, and C act on a body as shown (see attachment). A fourth force F is required to keep the body in equilibrium.


x-component of force F is closest to:

a.+32 N
b. +28 N
c. -28 N
d. -32 N
e. +19 N


y-component of force F is closest to:

a. +32 N
b. -32 N
c. -28 N
d. +24 N
e. +28 N

what i did was:

Fx=(force C)sinα=-50Nsin(-40)=32N

Fy=(force A)cosβ=30Ncos(35)=24N

IS this ok?

 

[cepheid]

No, there are a few problems with what you are doing. You need to add up the x-components of all three forces in order to find the resultant x-component. The force Fx should then be equal to the negative of this resultant force so that it cancels it out and leads to a new resultant of zero (when you include the fourth force F). Does that make sense? The same thing is true in the y-direction. Solve for Fy by figuring out the negative of the resultant of the y-components of the three forces that are there.

For some reason, you are not including all three forces. You have other mistakes as well -- for example, 50sin(40) is not in the x-direction at all.

 

[kari82]

I figured this was not correct.. Thank you very much for your help!