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Unformatted text preview: Physics Honors Distributed By: Tyrone G Carter PHYSICS HONORS
GRAPHING EXERCISE: ELECTRIC POTENTIAL
1) NAME: _Tyrone G Carter _____ Calculate the magnitude of the force between a +1.0 C charge and a +1.0 mC charge that are distance r apart for each
value of r in the table below. Fill in the table.
r (m) r (m) F (N) r (m) F (N) r (m) F (N) 1.0 8.9900 1.7 3.1107 2.4 1.5608 4.0 0.5619 1.1 7.4298 1.8 2.7747 2.5 1.4384 5.0 0.3596 1.2 6.2431 1.9 2.4903 2.6 1.3299 6.0 0.2497 1.3 5.3195 2.0 2.2475 2.7 1.2332 7.0 0.1835 1.4 4.5867 2.1 2.0385 2.8 1.1467 8.0 0.1405 1.5 3.9956 2.2 1.8574 2.9 1.0690 9.0 0.1110 1.6
2) F (N) 3.5117 2.3 1.6994 3.0 0.9989 10.0 0.0899 Draw a set of axes and graph force F vs. distance r on the grid below. Distributed By: Tyrone G Carter TGC Physics Honors 3) Distributed By: Tyrone G Carter In chapter 6 you learned that the quantity called “work” is the
product of the force acting on an object and distance it travels:
W = Fx. If the force F is not constant, then work is the area
under the curve of a graph of force vs. distance F (N)
F The area bounded by the F curve, the xaxis, and two vertical lines at
x (m)
x1 and x2 is the work done by force F as the object moves between x1
x1
x2
and x2.
The work can be approximated by breaking up the area under the curve
into a series of rectangles. Each rectangle is one grid square wide. The
height of each rectangle is equal to the approximate value of F in the
middle of the rectangle. The total area under the curve is the sum of the
areas of all the rectangles.
Calculate the work W required to move one of the charged objects from point r1 = 1.0 m to each of the following
points r = r2 in the table below. Fill in the table.
r (m) r (m W (J) r (m W (J) r (m W (J) 1.0 0.0000 1.7 3.7137 2.4 5.2580 4.0 6.7881 1.1 0.8210 1.8 4.0079 2.5 5.4080 5.0 7.2489 1.2 1.5046 1.9 4.2712 2.6 5.5464 6.0 7.5535 1.3 2.0828 2.0 4.5081 2.7 5.6746 7.0 7.7701 1.4 2.5781 2.1 4.7224 2.8 5.7936 8.0 7.9321 1.5 3.0072 2.2 4.9172 2.9 5.9043 9.0 8.0578 1.6
4) W (J) 3.3825 2.3 5.0950 3.0 6.0077 10.0 8.1582 Draw a set of axes and graph W vs. r on the grid below. Distributed By: Tyrone G Carter TGC Physics Honors Distributed By: Tyrone G Carter 5) What is the intercept of your graph? What is its physical meaning?
The intercept of this graph is at r = 1.0 m. This means no work is done to move the charged object from r1 = 1.0 m to r2
= 1.0 m. 6) If you drew your graph correctly, it has a horizontal asymptote at W = 9.0 J. Does your graph show this? What is the
physical meaning of the asymptote?
Yes, my graph shows this horizontal asymptote at W = 9.0 J. This means that the maximum amount of work done on the
electric charge is 9.0 J. 7) Imagine that you release one of the charged objects from rest, while you keep the other one in place. The first time you
do it, you release the charge from location r = 1.0 m. The second time, you release it from location r = 10 m. In each
case, you measure the speed of the object after it has moved 1000 m. In which instance is its final speed greater? Why?
Higher final speed when released from: r = 1.0 m
Reason: There is higher kinetic energy in the charge released from r = 1.0 m after it has moved 1000 m. There is more
electric force acting on the charge over a longer distance on the charge released from r = 1.0 m. 8) Where is the potential energy of the system greater, at r = 1.0 m or at r = 10.0 m? Why?
The potential energy of the system is greater at r = 1.0 m because there is a higher kinetic energy in the charge released
at r = 1.0 m and therefore a higher potential energy since the potential energy is transferred into kinetic energy. 9) Recall from chapter 6 that the absolute value of potential energy is arbitrary. You can make it zero at any location that it
is convenient. When doing gravity problems, you often assumed that the potential energy on the floor is zero. You did
this because you know that objects fall to the floor. For charged objects, there isn’t any floor. Positive objects just
“want” to move away from other positive objects. They keep moving until they are as far away as possible…….until
they are infinitely far away from other positive charge. For this reason, the place where electric potential energy is
assumed to be zero is “at infinity”.
Recall from chapter 6 that work is the negative difference in the change in potential energy: W = U = Uo  Uf. Recall
from question #6 that the maximum amount of work that the system can do when beginning at r = 1.0 m is 9.0 J.
Use all of this information to answer the following question: What is the potential energy Uo at r = 1.0 m?
The potential energy Uo at r = 1.0 m is 9 J. 10) Rearranging the work equation gives: Uf = Uo – W. Use this equation (and your answer to #9, and the information in the
data table of #3) to calculate the potential energy Uf at each value of r = r2 in the table below. Fill in the table.
r (m) Uf (J) r (m Uf (J) r (m Uf (J) r (m Uf (J) 1.0 9.0000 1.7 5.2863 2.4 3.7420 4.0 2.2119 1.1 8.1790 1.8 4.9921 2.5 3.5920 5.0 1.7511 1.2 7.4954 1.9 4.7288 2.6 3.4536 6.0 1.4465 1.3 6.9172 2.0 4.4919 2.7 3.3254 7.0 1.2299 1.4 6.4219 2.1 4.2776 2.8 3.2064 8.0 1.0679 1.5 5.9928 2.2 4.0828 2.9 3.0957 9.0 0.9422 1.6 5.6175 2.3 3.9050 3.0 2.9923 10.0 0.8418 Distributed By: Tyrone G Carter TGC Physics Honors Distributed By: Tyrone G Carter 11) Draw a set of axes and graph Uf vs. r on the grid below. 12) Use the various tricks at your disposal (graphing calculators, Microsoft Excel, etc.) to determine the equation of the
curve you drew for #11 above. Explain how you found the equation.
Equation: y = 9.135x1.02
Method of finding it: I used Microsoft Excel’s treadline feature to calculate the equation of the curve. 13) Algebraically, what is the constant of proportionality? What physical quantities does it represent?
The constant of proportionality is kcq1q2. It is the product of the coulomb constant and the charges. It represents the
maximum work of the system. It also represents the maximum potential energy of the system. 14) What is the algebraic equation for the potential energy of a system of two charges a distance r apart? U=
15) Recall that electric field was the force per unit charge acting at a location in space. We can similarly define electric
potential, V, as the potential energy per unit charge at a location in space. According to the results of this exercise, what
is the equation for the electric potential a distance r from a charge? V= =
Distributed By: Tyrone G Carter TGC ...
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This note was uploaded on 08/29/2010 for the course PHYS 38234 taught by Professor Ramesh during the Spring '09 term at Berkeley.
 Spring '09
 Ramesh
 Physics, Work

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