Solve Physics Homework: Forces & Friction | Get Expert Help

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The discussion focuses on solving two physics problems related to forces and friction. For problem #7, it emphasizes drawing the string attached to a hook and understanding that the weight of the picture is supported by the vertical components of the tensions, while the horizontal components pull inward. In problem #8, it suggests creating free body diagrams for each mass, noting that the tension in the string is uniform due to the pulley having no mass. The discussion highlights the need to write equations for the unknown tension and acceleration to solve the problems simultaneously. Overall, the thread provides guidance on approaching physics problems involving tension and free body diagrams.
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I am having trouble solving this for my physics homework. Please help with these two problems!

http://img151.imageshack.us/img151/5049/scan1wd3.jpg

I just don't know where to start... please guide me..
 
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For #7, draw the string attached to the hook using the angles given. Assume the picture hangs evenly and the strings are attached to the picture symmetrically so each end of the string supports the same weight (this is implied by the stated angles). The weight of the picture is supprted by the vertical components of the tensions. The horizontal components of the tension pull inward on the edges of the picture.

For #8 draw a free body diagram for each mass. Since the pulley has no mass, the tension in the string is uniform. Each mass will move the same distance with the same speed and the same magnitude of acceleration. You should be able to write two equations involving the unknown tension and the unknown acceleration, and solve them simultaneously for both variables.
 
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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