I don't know where went wrong help needed

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The problem involves calculating the speed of a charged pellet accelerating between two parallel conducting plates with a potential difference of 4.50E+3 V. The initial calculation of work done on the charge was correct, resulting in 3.4875*10^-3 J. However, the error arose from using the mass in grams instead of kilograms, which is necessary for consistency with SI units. After converting the mass to kilograms, the correct speed can be recalculated. Proper unit conversion is essential for accurate results in physics problems.
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1. Two parallel conducting plates that are in deep space are brought to a potential difference of 4.50E+3 V, and a small pellet of mass 5.70 mg carrying a charge of 7.75*10^-7C accelerates from rest from the positive plate. With what speed will it reach the other plate?








It seemed pretty obvious for me that by multiplying the potential difference and the charge on the pellet, the work done on the charge will be calculated. This work is equivalent to the kinetic energy of the pellet,
So change in U = 4.5*10^3 V * 7.75*10^-7 C = 3.4875*10^-3 J
and change in U = Kinetic energy = 0.5*(0.0057g)*v^2
solving for V I got v= 1.106 m/s
but the answer is wrong... can someone give me a hint?
 
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Kilogram is the SI standard mass unit to use with Joules. Convert the mass accordingly.
 
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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