Aamc 3 #15

[chiddler]

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can I please have some help in figuring this out? though I understand the solution's math, I don't know how to reason through this question.

thanks.

 

[folktale]

If you add the 3N and 4N vectors, it will result in a 5N final vector that is in the opposite direction as the Vector F. In order to have translational equilibrium, the two opposite vectors have to be equal to each other. Thus, F has to equal 5N as well. It's a 3-4-5 triangle.

 

[MedPR]

Just slide the F vector to the bottom left hand corner of the sheet. Then it's a little more obvious that you are looking at a 3-4-5 triangle.

 

[chiddler]

i actually got that far. specifically, i'm having difficulty understanding what's going on with the angle, theta.

oh nvm figured it out. because opposite = 3 and adjacent = 4.

 

[dmf2682]

i actually got that far. specifically, i'm having difficulty understanding what's going on with the angle, theta.

OK, I see where you're having issues. Remember your SOH CAH TOA, where Tan = Opposite/Adjacent. So if theta = arctan .75, then you're opposite to 3 and adjacent to 4, essentially saying that the vector they're describing is opposite to the forces on the body. So.... if it's in equilibrium they're opposite but are they equal? Use pythag. to determine the hypotenoose (I know wrong spelling but I can't figure it out). Does that help any?