Question of electricity net force

AI Thread Summary
The discussion revolves around calculating the net force on charge q1 (1.0 nC) due to two other charges, q2 (-3.5 nC) and q3 (6.0 nC), positioned on the positive x-axis. The user initially misrepresented the positions of the charges in their solution, leading to incorrect force calculations. After clarification, it was noted that q3 exerts a repulsive force on q1, while q2 exerts an attractive force, both directed to the right. The user initially subtracted the forces instead of adding them, which was the source of the error. Ultimately, understanding the correct direction of the forces and how to combine them is crucial for arriving at the right answer.
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Homework Statement



Three point charges are located on the positive x-axis of a coordinate system. Charge q1 = 1.0 nC is 2.0 cm from the origin, charge q2 = -3.5 nC is 4.0 cm from the origin and charge q3 = 6.0 nC located at the origin. What is the net force ((a)magnitude and (b) direction) on charge q1 = 1.0 nCexerted by the other two charges?

The online homework grader is marknig my answer for part a wrong. Can someone tell me what's wrong with my solution for part a? My work is in the attachment.

2. Homework Equations
see attachment

The Attempt at a Solution


[/B]
see the attachment for my solution. The online homework grader is saying my answer is wrong.
 

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Check the locations of the individual charges. q3 is at the origin according the problem description. Your image has it off to the right.
 
It looks like you maybe placed the charges in the wrong spots? q3 is at the origin, q1 is at 2cm and q2 is at 4cm. So there is a repulsive force to the right from q3 on q1, and an attractive force to the right from q2 on q1...

EDIT: Rats, rats, rats, rats, rats! :cry:
 
if the pic isn't clear enough, here is a close up.
berkeman said:
It looks like you maybe placed the charges in the wrong spots? q3 is at the origin, q1 is at 2cm and q2 is at 4cm. So there is a repulsive force to the right from q3 on q1, and an attractive force to the right from q2 on q1...

EDIT: Rats, rats, rats, rats, rats! :cry:
oh i fixed that. F_{q3q1} should be 1.35x10^-4. The answer though is sitll wrong. I subtract the two forces because one pair is attractive while the other force is repulsive. The answer I get is 5.625x10^-5. The answer from homework grader gave me is 2.1x10^-4. This is what you would get if you add the two forces. Why would you add them?
 
What directions do the two force vectors point? Make a sketch.
 
gneill said:
What directions do the two force vectors point? Make a sketch.
oh yeah. i see the problem. thank you.
 
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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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