Solving Force and Vector Problems: Tips and Examples

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The discussion focuses on solving force and vector problems, specifically addressing the calculations of force components. One participant calculated force 3 to be 78.1 N at an angle of 146.3 degrees but questioned the accuracy of this result. Concerns were raised about the x-component being incorrectly calculated as -65 N instead of the correct expression involving F2 and F1X. The vertical component was confirmed to be correctly calculated using sine rather than cosine. The conversation emphasizes the importance of accurately determining force components and angles in vector analysis.
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Well I just set the sum of x and y components equal to 0 and got: force 3 = -65N in x and 43.3N in y which gave me a magnitude of 78.1 N and 146.3 degrees counterclockwise from x-axis. Right? Wrong? Thanks for your help.
 
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Doesn't look right. I checked the vertical part - F1 has 25 N down. F3 should have 25 N up but, according to your answer, has 78.1*cos(146.3-90) = 43N up.
 
No, I don't think it's entierly correct.. I got my doubts first when it came to your angle - if you mean from the x-axis to the right (if you understand what I mean, I don't know the terminology at the moment), F3 is in the second quadrant, and if it's from the other x-axis, so to speak, it's in the fourth and neither make much sense.

I've been thinking for a while and it's your x-component that's wrong.. It's not supposed to be -65. It's supposed to be F2 - F1X, right? Redo this step.

Edit: Nah, the vertical's correct. The vertical is = F3 * sinθ, not cosθ. (In reply to what Delphi51 said (; )
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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