How Fast Do the Spheres Move When Far Apart?

AI Thread Summary
The discussion revolves around calculating the speeds of two charged spheres when released from rest. Sphere A is fixed and has a positive charge, while Sphere B, also positively charged, is brought to a point near Sphere A. Participants express confusion about whether to calculate the velocities of each sphere individually or to average them, given that they have the same mass. A key point raised is the application of conservation of momentum, which indicates a relationship between the velocities of the two spheres. Understanding this relationship is crucial for solving the problem correctly.
asheik234
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Homework Statement


k = 9 * 10^9

Sphere A of mass m = 0.0004 kg holds a positive charge qA = 3.0 10^-5 C and is fixed in place. Point P is d = 0.03 meters away from Sphere A.

Sphere B is identical in mass to sphere A, but carries a charge of qB = 3.6 10^-5 C. Sphere B is brought from a distant location and fixed at point P.

Frensley_E-Potential_Points_009b.gif


If both spheres are released from rest at the same time, how fast do the spheres move when they are very far apart?

Homework Equations


KE = (1/2)mv^2
KE = qV

The Attempt at a Solution



I keep getting different speeds for each ball using the first equation, any help would be appreciated.
 
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Pls post your working, as per forum rules.
 
haruspex said:
Pls post your working, as per forum rules.
I'm not sure if I have to get the velocity of ball a or ball b, or get them both and average, I just need help on this part of the problem.
 
haruspex said:
Pls post your working, as per forum rules.
I'm not sure if I have to get the velocity of ball a or ball b, or get them both and average, I just need help on this part of the problem.
 
asheik234 said:
I'm not sure if I have to get the velocity of ball a or ball b, or get them both and average, I just need help on this part of the problem.

They're the same mass. What does conservation of momentum tell you about the relationship between their velocities?
 
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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