Vector problem from examkrackers problem 53

[dahmsom]

Can anyone explain why the answer is c? I don't get how the sum of all forces equals 0

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[MrRed]

The only answer that makes sense is C.
Draw the force body diagram, with the "body" as the point where the 3 forces meet. If you break up 2F into its components (draw a 30-60-90 triangle) you will see that the cos(theta) component ends up being sqrt(3)/2 x 2F = sqrt(3)F
and the sin(theta) component ends up being 1/2 x 2F = F
Thus the cos and sin components cancel the sqrt(3)F and F forces pulling in the positive x and positive y direction, respectively.

 

[edgerock24]

The only answer that makes sense is C.
Draw the force body diagram, with the "body" as the point where the 3 forces meet. If you break up 2F into its components (draw a 30-60-90 triangle) you will see that the cos(theta) component ends up being sqrt(3)/2 x 2F = sqrt(3)F
and the sin(theta) component ends up being 1/2 x 2F = F
Thus the cos and sin components cancel the sqrt(3)F and F forces pulling in the positive x and positive y direction, respectively.

Exactly.
OP, first draw the triangle (and its components) that's necessary that corresponds to 2F. Then, simply write out F = ma equations for the x and y directions.

For x:
sqrt(3)F - cos30(2F) = ma
sqrt(3)F - sqrt(3)/2 * 2F = ma
sqrt(3)F - sqrt(3)F = ma
0 = ma

For y:
F - sin30(2F) = ma
F - 0.5*2F = ma
F - 1F = ma
0 = ma

Also, perhaps we could pick C based off process of elimination:
A and D are saying the same thing, so we can rule them both out. Now, we're down to B and C. For B, the answer is referencing the objects velocity. Let's pretend as if we have done zero math at this point. Lets assume that the object DOES have an acceleration in some direction. This would mean that it is moving. Conversely, lets assume that all the accelerations are 0. Just because an object is not accelerating does not mean it is not moving. It is simply not speeding up or slowing down. Therefore, this is a bad answer (we can't gather any information regarding velocity based off of anything in the question, basically). Which leaves us with C as the only answer left and has to be true.

Not sure if this is the most sound way to solve this... @MrRed can likely confirm/deny my speculation as he clearly has a better grasp on the topic.