How Far Does a Charged Particle Travel Before Stopping Due to Repulsive Force?

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A charged particle with a mass of 7.2 x 10^-3 kg and a charge of -8 microC is fired towards a fixed charge of -3 microC from a distance of 0.045m with an initial speed of 65 m/s. The repulsive force between the charges increases as the particle approaches the fixed charge, complicating the calculation of how far it travels before stopping. The attempt to use Coulomb's law and equations of motion to find the deceleration and distance was unsuccessful due to the variable nature of the repulsive force. The discussion suggests using the initial kinetic energy and the work-energy principle to determine the change in voltage needed to overcome the kinetic energy of the particle. This approach may provide a clearer path to solving the problem.
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Homework Statement


A charge of -3 microC is fixed in place. From a horizontal distance of 0.045m, a particle of mass 7.2 x 10^-3 kg and charge -8 microC is fired with an initial speed of 65 m/s directly toward the fixed charge. How far does the particle travel before its speed is zero?


Homework Equations


equations of motion
Coulomb's law, to possibly find repulsive force?


The Attempt at a Solution


I tried to use Colomb's law to find the repulsive force, then F=ma to find the deceleration. After that I used equations of motion to find the distance to reach 0m/s. this didn't work, and I think it is because the repulsive force increases as the particle travels towards the fixed change.

I am stuck at how to solve this problem at this point.
Thanks everyone in advance for helping! =)
 
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The problem is that as it gets closer the field strength increases because of the decreasing distance.

But not to despair.

They give you the initial kinetic energy.

And you also know that W = q*ΔV

Figure then the change in voltage needed to overcome the kinetic energy of the particle?
 
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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