PHYS 142 Lecture Notes - Lecture 7: Electric Potential Energy

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7 Apr 2015

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Phys 142: electromagnetism and optics - lecture 7 : electric potential energy. The kinetic energy of a system, k, is the sum of the kinetic energies ki = 1/2mivi. 2 of all the particles in the system. The potential energy of a system, u, is the interaction energy of the system. The change in potential energy, u, is 1 times the work done by the interaction forces: If all of the forces involved are conservative forces (such as gravity or the electric force) then the total energy k + u is conserved; it does not change with time. If the force is not constant or the displacement is not along a linear path, we can calculate the work by dividing the path into many small segments. Electric potential energy is the equivalent of gravitational potential energy, but for electricity. The change in electric potential energy: uelec = welec where uelec = u0 + qes.

Related Questions

Which of the following statement are true mechanical energy? Include all that apply.

1.The total amount of mechanical energy of an object is the sum of its potential energy and the kinetic energy.

2. Heat is a form of mechanical energy.

3. The mechanical energy of an object is always conserved.

4. When non-conservative forces do work, energy is transformed from kinetic to potential (or vice versa), but the total mechanical energy is conserved.

5. A bowling ball is mounted from a ceiling by way of a strong cable. It is a drawback and released, allowed to swing as a pendulum. As it swings from its highest position to its lowest position, the total mechanical energy is mostly conserved.

6. When a friction force does work on an object, the total mechanical energy of that object is changed.

7. The total mechanical energy of an object remains constant if the only forces doing work on the object are conservative forces.

8. If an object gains mechanical energy, then one can be certain that a non-conservative force is doing work.

lilacplatypus580

Goal Apply conservation of angular momentum to a simplesystem.

Problem A student sits on a pivoted stool while holding a pair ofweights. (See Figure) The stool is free to rotate about a verticalaxis with negligible friction. The moment of inertia of student,weights, and stool is 2.25 kg Â· m2. The student is set in rotationwith arms outstretched, making one complete turn every 1.26 s, armsoutstretched.

Question If the student suddenly releases the weights, how does hisown angular momentum, rotational kinetic energy, and angular speedchange? (Select all that apply.)

His rotational angular speed decreases.
His rotational angular speed remains the same.
His angular momentum remains the same.
His rotational kinetic energy remains the same.
His angular momentum increases.
His angular momentum decreases.
His rotational angular speed increases.
His rotational kinetic energy increases.
His rotational kinetic energy decreases.

A star with an initial radius of 1.00 108 m and period of 30.0 dayscollapses suddenly to a radius of 1.00 104 m.

(a) Find the period of rotation after collapse.

(b) Find the work done by gravity during the collapse if the massof the star is 2.00 1030 kg.

The only force doing work on the system is gravitation, so the workdone by gravitation is the change in kinetic energy of the star.J

(c) What is the speed of an indestructible person standing on theequator of the collapsed star? (Neglect any relativistic or thermaleffects, and assume the star is spherical before and after itcollapses).

HINTS
* Do you expect the initial angular speed to be larger or smallerthan the final angular speed? How is angular speed related toperiod of rotation?

* Is the initial moment of inertia larger or smaller than the finalmoment of inertia?

* Is angular momentum conserved?

* As the star collapses, do you expect the period of rotation tobecome smaller or larger?

1.Two uncharged, conducting spheres, A and B, are held at rest oninsulating stands and are in contact. A positively charged rod isbrought near sphere A. While the rod is in place, the two spheresare separated. How will the spheres be charged, if at all, afterthey are separated?
Sphere A Sphere B
(a) positive positive
(b) positive negative
(c) negative positive
(d) negative negative
(e) zero zero

2. A charged conductor is brought near an uncharged insulator.Which one of the following statements is true?
(a) Both objects will repel each other.
(b) Both objects will attract each other.
(c) Neither object exerts an electrical force on the other.
(d) The objects will repel each other only if the conductor has anegative charge.
(e) The objects will attract each other only if the conductor has apositive charge.

3. An electron is moved from point A, where the electric potentialis VA = â240 V, to point B, where the electric potential is VB =â360 V. What is the change in the electric
potential energy?
(a) 1.92Ã10â17 J (b) 2.04Ã10â17 J (c) 5.75Ã10â17 J (d) 8.98Ã10â17 J(e) 1.05Ã10â16 J

4. A -2q charge is located a distance d to the right of a +4qcharge, along the x
axis. At which point (or points) along the axis does the electricfield go to zero? To
solve this problem, consider an observer at point P, which is anarbitrary distance x from the +4q charge. Find the value (orvalues) for x (in terms of the separation distance d) where thetotal electric field vanishes.
(a) The electric field is never zero in the vicinity of thesecharges.
(b) The electric field is zero at x = -0.328d.
(c) The electric field is zero at x = +4.22d.
(d) The electric field is zero at both x = -2.26d and x =+2.26d.
(e) The electric field is zero at x = +3.41d.

5. point A is a distance L away from a point charge Q. Point B is adistance 4L away from Q. What is the ratio of the electrostaticpotential at B to that at A, i.e., what is VB/VA?
(a) 1/16
(b) 1/9
(c) 1/4
(d) 1/3
(e) can not be determined without specifying Q and L

6. Which one of the following statements best explains why it ispossible to define an electric potential
in a region of space that contains an electric field?
(a) Work must be done to bring two positive charges closertogether.
(b) Like charges repel one another and unlike charges attract oneanother.
(c) A positive charge will gain kinetic energy as it approaches anegative charge.
(d) The work required to bring two charges together is independentof the path taken.
(e) A negative charge will gain kinetic energy as it moves awayfrom another negative charge.

PHYS 142 Lecture Notes - Lecture 7: Electric Potential Energy

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