Bryan Ritter
Physics 152-01
Final,Fall 2004

<< Miscellaneous`Units`

<< Miscellaneous`PhysicalConstants`

coulombconstant = (1/(4 π VacuumPermittivity))

Test Final

Question 1

Find the force that is applied to the +4 Coulomb charge in the digram below.

Force = k*((q*q)/(r^2))
\(Compomentalize\ the\ forces\ between\ the + 
      4\ Coulomb\ charge\ and\ the\ other\ two\ point\ \(\(charge\)\(.\)\)\)

f1x := 
      Cos[60  °]*
        coulombconstant*((2 Coulomb* 4 Coulomb)/(r^2))

f2x := 
      Cos[120  °]*
        coulombconstant*((3 Coulomb* 4 Coulomb)/(r^2))

total x - dir

totalx := f1x + f2x

Convert[totalx, Joule*Meter]

Convert[totalx /. r -> 1  Centimeter, Newton]

each y - dir

f1y := 
      Sin[60  °]*
        coulombconstant*((2 Coulomb* 4 Coulomb)/(r^2))

f2y := 
      Sin[120  °]*
        coulombconstant*((3 Coulomb* 4 Coulomb)/(r^2))

total y - dir

totaly := f1y + f2y

Convert[totaly, Joule*Meter]

at one Centimeter is

Convert[totaly /. r -> 1 Centimeter, Newton]

combine the compomentalized total forces into a resultant force magntitude

Convert[√((totalx^2) + (totaly^2)), Joule Meter]

Convert[√((totalx^2) + (totaly^2)) /. r -> 1 Centimeter, 
      Newton]

find the angle of the force

ArcTan[Convert[totalx /. r -> 1 Centimeter, Newton]/Newton, 
        Convert[totaly /. r -> 1 Centimeter, Newton]/Newton]/
      Degree

Question 2

How many electrons make up -3μ Coulombs of charge?

Convert[((-3 *
            Micro Coulomb)/(-ElectronCharge)),]

Questions 3-6

(Subscript[C, 1]) := 3 Pico Farad
(Subscript[C, 2]) := 6 Pico Farad
potential := 1000  Volt

Question 3

Compute the equivalent capacitance.

(Subscript[C, eq]) := (1/((1/(Subscript[C, 1])) + (1/(Subscript[C, 2]))))

N[Convert[(Subscript[C, eq]), Farad]]

Question 4

Compute the magnitudes of the charges on the capacitors.

Q = (Subscript[C, eq]) ΔV

Q = Convert[(Subscript[C, eq]) * potential, Coulomb]

N[%]

Since this is series the charges are the same this is for both of them

Question 5

Compute the potential difference across the capacitors.

V = (Q/C)

(Subscript[V, 1]) := Convert[(Q/(Subscript[C, 1])), Volt]
(Subscript[V, 2]) := Convert[(Q/(Subscript[C, 2])), Volt]

(Subscript[V, 1

      ])
N[(Subscript[V, 1]), 1]

(Subscript[V, 2])
N[(Subscript[V, 2]), 1]

Question 6

Compute the energy stored in the capacitors.

(1/2) QΔV

(Subscript[EnergyStored, 1]) := Convert[(1/2) Q*(Subscript[V, 1]), Joule]

N[(Subscript[EnergyStored, 1])]

(Subscript[EnergyStored, 2]) := Convert[(1/2) Q*(Subscript[V, 2]), Joule]

N[(Subscript[EnergyStored, 2])]

Question 7

\(Six\ billion\ billion\ electrons \((6*10\^18)\), \ 
    pass\ a\ point\ in\ a\ wire\ in\ 1\ second . \ \ What\ is\ the\ current\ in\ the\ \(\(wire\)\(?\)\)\)

Convert[((6*(10^18) ElectronCharge)/Second), Ampere]

Question 8

Two 3.0 gram balloons are suspended from a nail by strings 50 Centimeter long.  Each ballon has a +q, and there is an angle of 40° between the strings.  What is the charge q on each ballon?

Convert[
      PowerExpand[
        2*l*Sin[θ]*√(((m*g*Tan[θ])/k)) /. {l -> 
              50 Centimeter, θ -> 20  Degree, m -> 3 Gram, 
            g -> AccelerationDueToGravity, k -> coulombconstant}], 
      Coulomb]

Question 9

A 1500 Watt hair dryer is used for 10 Minute everyday.  If the cost of electricity is 8¢ per Killo Watt Hour, what is the cost of using the dryer for 30 Day?

Convert[
      1500 Watt ((10 Minute)/Day)*30 Day*((8  ¢)/(1000*Watt*Hour)), ¢]

Question 10

The effection resistance of a parallel circuit is...

b .  smaller than any individual resistor

Question 11

Three light bulbs are connected in a parallel circuit with a 12 Volt battery.  The resistance of each bulb is 24 Ohm.  What is the current produced by the battery?

R := 24  Ohm

(Subscript[R, eq]) := (1/((1/R) + (1/R) + (1/R)))

(V/R) = I

Convert[((12 Volt)/(Subscript[R, eq])), Ampere]

N[%]

Question 12

Two charges originally separated by 30 Centimeter are moved farther apart, until the force between them has decreased by a factor of 10.  How far apart are the charges then?

Solve[
          (1/10)*k*((q*q)/(((30 Centimeter))^2)) == k*((q*q)/(r^2)), 
          r][[2]];
r /. %

N[%]

N[%%, 2]

Misc

This was made by Bryan Ritter
using:
Mathematica 5.0
and GeoGebra 2.4