Solving a Magnetic Field Problem with Torques: Step-by-Step Guide

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The discussion focuses on solving a magnetic field problem involving torques on a cylinder, where the expected answer is 1.63A. Participants emphasize the need for the net torque to be zero and identify the magnetic force as a key torque-producing force. Clarification is sought on the torque equation and the roles of various parameters such as radius and angle. The importance of considering both torque and translational equilibrium is highlighted, particularly regarding the gravitational force acting on the cylinder. The conversation aims to guide the original poster through the problem-solving process effectively.
Tom McCurdy
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The Magnetic Field--HELP

I was hoping someone could help me on the following problem.

http://www.quantumninja.com/hw/question.jpg

I tried doing it with torques but nothing canceled out. The answer is supose to be 1.63A

If someone could walk me through it, that would be great... or at least help me get started.

(note: a B kinda got cut off in the diagram)
 
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The net torque on the cylinder must be zero. What torque-producing forces act on it? (Show what you did that didn't work.)
 
N i r L B sin (90-\theta) = MR^2

i= \frac{r}{sin(90-\theta}
 
Tom McCurdy said:
N i r L B sin (90-\theta) = MR^2
I assume this is your torque equation? Is the left hand side supposed to be the torque produced by the magnetic field on the current loop? What's the right hand side? (What is r? R?)

Again, what torque-producing forces act on the cylinder? We know one: the magnetic force. (That torque should be NILB(2R)\sin\theta.) What's the other?

Note: Don't forget that there must be translational equilibrium as well--consider forces parallel to the incline.
 
torque due to gravity?
 
Tom McCurdy said:
torque due to gravity?
The weight of the cylinder acts through its center, so it exerts no torque about that point.

What other forces act on the cylinder?
 
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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