Resultant vector relative to x and y axis.

[kaffekjele]

I was wondering if someone could have a look at my attempt at calculating the resultant vector of 3 forces. Figure is here:http://tinypic.com/view.php?pic=2psrllz&s=6, and from the top down the forces are F1=24,9kN, F2=12,7kN and F3=21kN. The angles are(again from the top down) 56,4°, 15,3° and 40,6°.

I start by calculating the force in x-direction:

[itex]Rx= 24,9*cos56,4°+12,7*cos15,3°+21*cos55,9° = 37,8kN[/itex]

y-direction:

[itex]Ry= 24,9*sin56,4°-12,7*sin15,3°-21*sin55,9° = -7,15*10^-4[/itex] -which is obviously wrong, but I can't see where the error is.
(English is not my first language, so I apologize for any word and grammar mistakes.)

 

[rude man]

Why do you think it's "obviously wrong"?

 

[kaffekjele]

I'm not 100% sure(I'm fairly new when it comes to mechanics and physics as a whole), but when I go on to calculate the resultant vector and the corresponding angle based on the numbers in my first post I get:

[itex] R=\sqrt{Rx^2+Ry^2} = +\sqrt{37,8^2+(-7,158*10^-4)^2}≈37,8[/itex]

I then use inverse tan Ry/Rx to get the angle:

[itex] tan^-1 Ry/rx = tan^-1 (-7,15*10^-4)/37,8 =-0,001°
[/itex]

To me this looks like an unlikely answer, and when I try to enter them into the task I get a message with "wrong".(It's a web based service so I only get "right" or "wrong" - no indication of where I've made an error, so I'd really appreciate it if someone could take a look at my calculations.

 

[rude man]

I'm not 100% sure(I'm fairly new when it comes to mechanics and physics as a whole), but when I go on to calculate the resultant vector and the corresponding angle based on the numbers in my first post I get:

QUOTE]

Your answers are essentially correct. I computed Ry = -7.16e-4, Rx = 37.80 and θ = -1.085e-3 deg = -0.001085 deg.

 

[Nickie]

I commend you for attempting to calculate the resultant vector of these forces. Your approach seems to be correct in using trigonometry to decompose the forces into their x and y components. However, there are a few potential errors in your calculations.

First, make sure you are using the correct angle for F2. In your description, you listed it as 15.3°, but in your diagram it appears to be 14.7°. This small difference could affect your final result.

Second, check your use of the sine function. Remember that sine is opposite over hypotenuse, so for F3, the angle you should use is 55.4°, not 55.9° as you have written.

Lastly, make sure you are using the correct units for your forces. In your diagram, the forces are listed as kN (kilonewtons), but in your calculations you have used N (newtons). This could also affect your final result.

Overall, I suggest double checking your angles and units, and also considering using a calculator or software to help with the calculations. Keep up the good work!