Having lots of trouble with a few problems that are due tonight

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The discussion revolves around three physics problems related to capacitors, electric fields, and current through a resistor. The first problem involves calculating the plate area of a capacitor with a specified capacitance and distance, where arithmetic errors are suspected. The second problem requires determining the potential difference to balance an electron's weight, with incorrect calculations noted. The third problem focuses on finding the number of electrons leaving a battery, where an exponent error in the final answer is highlighted. Overall, participants emphasize the importance of careful arithmetic and showing detailed calculations to identify mistakes.
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having lots of trouble with a few problems that are due tonight...please help!

1. A 0.28F capacitor is desired. What area must the plates have if they are to be separated by 1.2mm air gap?

I used C=E0 (A/d) and I keep getting the same and wrong answer. What am I doing wrong?

2. What potential difference acting over a distance of 3.5cm would be needed to balance the downward force of gravity so that an electron would remain stationary? Assume the electric field is uniform.

I used V=mass of electron*gravity*0.035m/1.6*E-19, and that gave me the wrong answer. Help anyone.

3. A 9.4V battery is connected to a bulb whose resistance is 2.1ohms. How many electrons leave the battery per minute.

I used ohm's law I=9.4/2.1 to get the current 4.476C/s. Then I multiplied 4.476c/s*60s/1.6E-19 and got 1.68E-17 electrons/minute...and that answer was wrong...any help?
 
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Your methods all look correct. Show your work in the first two problems--I suspect an arithmetic error. That's what happened in problem 3: check those exponents.
 
I still keep getting the wrong answers can you show me what to do...I just plugged the numbers into the formulas
 
check your arithmetic

You know what to do, you are just making arithmetic errors. Show the actual numbers you are plugging into the equations.

For example, you showed your work for problem 3: The numbers are right, but the answer is wrong. Redo your calculation carefully. You messed up the exponent in the answer.
 
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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