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- Thread starter BuBbLeS01
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cristo

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mjsd

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The Problem:

Three forces in the x-y plane act on a 3.70 kg mass: 14.50 N directed at 478.0°, 11.00 N directed at 117.0°, and 10.70 N directed at 222.0°. All angles are measured from the positive x-axis, with positive angles in the counter-clockwise direction. Calculate the magnitude of the acceleration.

What I did:

Fx1= 14.5 sin 478

Fx2= 11.0 sin 117

Fx3= 10.7 cos 222

sum= 14.65216223

Fy1= 14.5 cos 478

Fy2= 11.0 cos 117

Fy3= 10.7 sin 222

sum= -18.96093065

But what you are supposed to do is use cos for x comp. and sin for y comp. but they don't match up that way when using the trig functions.

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cristo

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[Isn't your quote from Einstein, mjsd?]

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mjsd

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but since all angles are measured from +ve x-axis anyway, things are so easy that you just plug in the angle: cos for x-comp, sin for y-comp. what do u mean by they don't match up??

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Yea I always draw a diagram but if you draw out those angles and vectors some of the require sine to find x-component and 1 requires cosine because its in another quadrant.

but since all angles are measured from +ve x-axis anyway, things are so easy that you just plug in the angle: cos for x-comp, sin for y-comp. what do u mean by they don't match up??

- #8

mjsd

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no, you don't. if you angle is defined from the +ve x-axis always, then cos will always give you the projection onto the x-axis (ie. x-comp) and sin will always give the y-comp.

eg. vector of length 1 angle is 120, that in the 2nd quadrant BUT the x-comp is still given by cos 120 = -0.5 you get a negative number.... reflecting the fact that you are in the 2nd quadrant. the confusion comes from the fact that you think the angle (120) is too large, and you have to take away 180 from it to get the acute angle.. but the point is that cosine function will automatically take care of that . If you evaluate instead

cos (180-120) = 0.5 (which is wrong.. and you need to put in a -ve sign yourself to fix it because the angle (180-120) is measured from the -ve x-axis. and if you use sin (180-120) or sin (120) that's absolutely wrong)

because in this case all angles are given relative to the +ve x-axis (going clockwise), you don't have to worry about anything at all. cos -> x-comp, sin -> y-comp.

eg. vector of length 1 angle is 120, that in the 2nd quadrant BUT the x-comp is still given by cos 120 = -0.5 you get a negative number.... reflecting the fact that you are in the 2nd quadrant. the confusion comes from the fact that you think the angle (120) is too large, and you have to take away 180 from it to get the acute angle.. but the point is that cosine function will automatically take care of that . If you evaluate instead

cos (180-120) = 0.5 (which is wrong.. and you need to put in a -ve sign yourself to fix it because the angle (180-120) is measured from the -ve x-axis. and if you use sin (180-120) or sin (120) that's absolutely wrong)

because in this case all angles are given relative to the +ve x-axis (going clockwise), you don't have to worry about anything at all. cos -> x-comp, sin -> y-comp.

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