Resolving forces in the direction perpendicular to a line

AI Thread Summary
To resolve forces perpendicular to a line, it's essential to sketch the appropriate triangle for the forces F1 and F2. Using the sine or cosine rule can help in determining the components of these forces. The key is to focus on the forces that act perpendicular to the lever with respect to the fulcrum A. By accurately labeling the forces and applying basic trigonometry, the correct answers can be derived. Understanding these concepts is crucial for solving similar problems effectively.
Bolter
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Homework Statement
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Hi I'm very stuck on what to do for these 2 questions I got wrong

Screenshot 2020-10-16 at 12.17.44.png

Screenshot 2020-10-16 at 12.17.56.png


Can someone please help me on what triangle I need to sketch out in order to find the 2 components of forces for F1 and F2. I'm assuming you have to make use of the sine or cosine rule here

I'd be grateful for any help given! Thanks
 
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What have you done so far?
Remember that what counts here are the actual forces that are perpendicular to the levers, all respect to the fulcrum A.
 
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What are the horizontal and vertical components of force F1?
 
I actually managed to find the right answer at the end by drawing triangles and labelling the forces that are perpendicular to the line AB. Then with some basic trig I got the force needed
 
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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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