Goal: Unspecified.
Source: Unspecified.
Consider moving a positive charge from point P to the origin along the
different paths shown in the diagram below. For which path would you do
the most work?
Goal: Reason regarding circuits
Source: 283 Compare dissipated power with inductors
Consider the following circuits. Two identical batteries are
connected to two identical inductors in series with different resistors.
The switch is closed at t=0. Which is true regarding the energy
supplied by the battery to establish current I?
(4) It is not determined that either circuit can achieve the current I.
If I is to be interpreted as the ‘final’ current, then the answer is #2.
The lower the resistance the higher the final current. There is more
energy stored in the inductor if the final current is higher. In
addition, the energy dissipated in the resistor goes as i2R which is
larger for circuit B for every current larger than V/(2R).
Goal: Reason regarding circuits
Source: 283 compare dissipated energy
Consider the following circuits. Two identical batteries are connected
to two identical capacitors in series with different resistors. The
capacitors are initially uncharged. Which statement is true regarding
the energy supplied by the batteries to charge the capacitor?
(3) The energy dissipated in the resistor is independent of the
resistance. Consider a time when the capacitor contains some charge Q.
If an additional charge dq is added, the battery does work dqV and the
increment of stored energy in the capacitor is (Q/C)dq. By conservation
of energy, the difference must have been dissipated in the resistor. The
difference, [V-(Q/C)]dq is independent of resistance.
Goal: Hone the conservative nature of the electrostatic field
Source: 283-240 Work moving charge around
Two point charges are fixed on the x-axis. A positive charge from point
P to the origin along the different paths shown in the diagram below.
For which path would you do the most work?
(6) Relating the work done to the change in potential should be
stressed. Once this point is made, a good follow-up question is to ask
how much work would be done if one of the charges on the x-axis was
negative.
Goal: Distinguishing components of the Lorentz force
Source: 283 – effects of magnetic force
A charged particle moves into a region containing both an electric and
magnetic field. Which of the statements below are true?
- The particle cannot accelerate in the
direction of B.- The path of the particle must be a circle.
- Any change in the particle’s kinetic energy is caused by the E
field.
(3) The only cases that most students see is the one having E and B
perpendicular. As a result they discount the case of E and B parallel
and think statement A is also true.
Goal: Hone the concept of work for a thermodynamic system
Source: UMPERG-ctqpe190
An
ideal gas is taken around the process shown. The net work done
on the gas is most nearly…
(4) The work done ON the system is the negative of the area of
the triangle. Students selecting answer #1 or #3 need to be sensitized
to the difference between work done on the gas versus by the gas.
Goal: Problem solving and developing strategic knowledge
Source: UMPERG-ctqpe102
You are given this problem:
A
block sits on an incline with friction. Given the height of the
block, the angle of incline, the coefficient of kinetic friction, and
that block starts from rest, find the speed at the bottom of the
incline.
What principle(s) would you use to solve the problem MOST EFFICIENTLY?
(3) The velocity can be determined using kinematics, but the 2nd
law is also needed, i.e. #6.
Goal: Link work and potential
Source: 283-465 Interpreting voltage
The potential at two points in space is: V1=200 Volts,
V2=300 Volts. Which of the following statements is true for
moving a point charge, q, from point 1 to 2?
- The work done by an external agent to
move q from point 1 to 2 is positive.- Can’t determine the work
done because you don’t know the direction of V at the two points.- The work done by the electrical force exerted on q in moving it from
point 1 to 2 is: W = -q(100 Volts).
(3) is the best response. Statement A is true only if the charge
is positive. The important thing is to see if students correctly
envision the electric field lines as directed from higher potential to
lower.
Any response involving statement B should be discussed thoroughly as it
indicates confusion between fields and potentials.
Goal: Reasoning with kinetic energy and work
Source: UMPERG-ctqpe58
Two
blocks, M2 > M1, having the same kinetic energy
move from a frictionless surface onto a surface having friction
coefficient μk.
Which goes further before stopping?
(1) For a given amount of kinetic energy M1 will have a larger
velocity. The penetration distance depends upon the square of the
velocity.
Many students will notice that the relationship equating the kinetic
energy to work by friction has mass as a factor on both sides and will
answer #3. They are assuming that the masses have the same velocity, not
the same kinetic energy.
Goal: Reasoning with work
Source: UMPERG-ctqpe50
In which case would you do the least amount of work?
(6) This problem is intended to elicit a vigorous discussion of
work. Students have a difficult time reconciling the formal definition
of work with the colloquial one. Every one of the answers is defensible
depending upon one’s perspective. Lifting a heavy box requires doing
work against gravity. Putting it down actually requires that you do the
same amount of work. Gravity does no net work, but humans are not
conservative systems. Depending upon the surface it may be more
advantageous to push the box.
Commentary:
None provided.