Tag Archives: Energy

A2L Item 262

Goal: Hone the concept of a collision

Source: CT151.2S02-43

A cart
of mass m is moving with speed v. Is it possible for the kinetic energy
or the momentum to be larger after a collision?

  1. No; it is impossible
  2. Yes; the kinetic energy can be larger
  3. Yes; the momentum can be larger
  4. Yes; both can be larger

Commentary:

Answer

(4) Many students get fixated on the idea that all collisions are head
on and cause the object to lose energy and momentum.

A2L Item 249

Goal: Reason regarding RC circuits.

Source: 283 – energy dissipated in RC circuit

Consider the following circuit. The capacitor is uncharged when
switch S is closed at t = 0. During the charging process the total
energy dissipated in the resistor is:

  1. V^2^/R
  2. CV^2^/2
  3. QV
  4. V/RC
  5. none of the above

Commentary:

Answer

(2) Students should recognize that if the capacitor ultimately is
charged to Q, the total work done by the battery is QV. Half of this is
stored in the capacitor and half is dissipated in the resistor.

A2L Item 250

Goal: Reason regarding RL circuits.

Source: 283 – energy dissipated in inductor

Consider the following circuit. The switch S is closed at t = 0.
The total energy dissipated in the resistor before the current reaches
its maximum value is:

  1. V^2^/2R
  2. LV^2^/2R2
  3. LV
  4. V/RL
  5. none of the above

Commentary:

Answer

(5) The total work done by the battery is QV where Q is a function of
time which is not limited. The total energy stored in the inductor is
finite. The difference must be the energy dissipated in the resistor.
Since it takes an infinite amount of time for the current to reach its
maximum value, the total amount of energy dissipated is also maximum.

A good follow up question is: Is there a time when the dissipated energy
is equal to the stored energy? If so, what is that time?

A2L Item 247

Goal: Link energy with electrical quantities

Source: 283 – energy in capacitor

Consider the following circuit. The capacitor is uncharged when switch S
is closed at t = 0. After current stops flowing and the capacitor is
fully charged the energy stored in the capacitor is:

  1. V^2^/R
  2. CE^2^/2
  3. QV/2
  4. V/RC
  5. none of the above

Commentary:

Answer

(3) The intent of this question is to provide students the opportunity
to distinguish a correct but uncommon form for the stored energy from a
number of other familiar forms.

A2L Item 248

Goal: Link energy with electrical quantities

Source: 283-energy in L

Consider the following circuit. The switch S is closed at t = 0.
After a long time the energy stored in the inductor is:

  1. L^2^/R

  2. RL^2^/2

  3. LV/2R

  4. V/RL

  5. none of the above


Commentary:

Answer

(5) This is a good time to discuss with students the general form of
energy expressions as 1/2 something times (something else)^2^.

A2L Item 219

Goal: Reason regarding capacitors

Source: 283-545 Adding capacitors in parallel

A capacitor having, C1, is connected to a battery until
charged, then disconnected from the battery. A second capacitor,
C2, is connected in parallel to the first capacitor. Which
statements below are true?

  1. Charge on C1 decreases.
  2. Total charge on C1 and C2 is the same as the original Q.
  3. The total energy stored in both capacitors is the same as the
    original U stored in C1.
  4. The potential (Voltage) across C1 decreases.
  5. All of the above.
  6. Only 1, 2, and 3 are true.
  7. Only 1, 2, and 4 are true.

Commentary:

Answer

(7) Statement #3 is the hardest for students to reason about. This is
most easily decided as incorrect if the two capacitors are taken as
equal.

A2L Item 217

Goal: Reason regarding capacitors and dielectrics.

Source: 283-535 inserting a dielectric changes a capacitor

A capacitor with capacitance C is connected to a battery until charged,
then disconnected from the battery. A dielectric having constant
κ is inserted in the capacitor. What changes occur in the charge,
potential and stored energy of the capacitor after the dielectric is
inserted?

  1. V stays same, Q increases, U increases
  2. V stays same, Q decreases, U stays same
  3. V increases, Q decreases, U increases
  4. V decreases, Q stays same, U decreases
  5. None of the above
  6. Cannot be determined

Commentary:

Answer

(4) It should be clear to students that the charge cannot change. Most
students recognize that capacitance increases when a dielectric is
inserted into a capacitor. The issue then becomes whether they
appreciate the relationships between C, Q, V and U.

A2L Item 218

Goal: Reason regarding capacitors

Source: 283-540 Adding capacitors in series

A capacitor, C1, is connected to a battery until charged, and
then disconnected from the battery. A second capacitor, C2,
is connected in series to the first capacitor. What changes occur in
capacitor C1 after C2 is connected as shown?

  1. V same, Q increases, U increases
  2. V same, Q decreases, U same
  3. V increases, Q decreases, U increases
  4. V decreases, Q same, U decreases
  5. None of the above
  6. Cannot be determined

Commentary:

Answer

(5) All quantities remain the same. Some students may consider the
capacitors to be connected in parallel despite the figure.

A2L Item 167

Goal: Problem solving

Source: UMPERG-ctqpe118

A mass
m slides down a frictionless track of radius R=0.5m. As the mass
reaches the bottom, relative to the center of curvature, its angular
velocity is most nearly:

  1. 6 rad/sec
  2. 8 rad/sec
  3. 12 rad/sec
  4. 15 rad/sec
  5. 20 rad/sec
  6. Cannot be determined

Commentary:

Answer

(1) The velocity near the bottom can be found using energy
conservation.

A2L Item 165

Goal: Problem solving and developing strategic knowledge

Source: UMPERG-ctqpe103

You are given this problem:

A
block sits on a frictionless incline. Given the angle of incline, the
distance along the incline, and that the block is initially at rest,
find the speed after traveling a distance d.

What principle would you use to solve the problem MOST EFFICIENTLY?

  1. Kinematics only
  2. F = ma or Newton’s laws
  3. Work-Energy theorem
  4. Impulse-Momentum theorem
  5. Angular Impulse-Angular Momentum
  6. 1 and 2
  7. 1 and 3
  8. 2 and 3
  9. None of the above
  10. Not enough information given

Commentary:

Answer

(3) The change in gravitational potential can be found directly.
Alternately, the work done by the gravitational force must be equal to
the change in kinetic energy.