Goal: Reasoning with dynamics
Source: UMPERG-ctqpe43
Block
m1 sits on block m2 and both sit on the floor of
an elevator at rest. When the elevator starts to move down, the normal
force on the upper block will …
Goal: Link work and potential change
Source: 283-450 Move q, do most work
For
the following situations consider moving a positive charge from very far
away to the origin along the y-axis. For which situation would you do
the most work?
(1) Students indicating #7 because they do not know if the masses
are charged should not be disconfirmed. If students key on magnitude
only they will likely choose answer #5.
Goal: Reasoning with circular motion
Source: UMPERG-ctqpe37
A small ball is released from rest at position A and rolls down a
vertical circular track under the influence of gravity.
When
the ball reaches position B, which of the indicated directions most
nearly corresponds to the direction of the ball’s acceleration?
Enter (9) if the direction cannot be determined.
(2) At position B the acceleration has a tangential component and
a radial component. Both components can be determined at position B.
Worked out carefully one gets 18 degrees above position #2. It is common
for students to neglect one component or the other.
Goal: Reasoning with dynamics
Source: UMPERG-ctqpe30
A
block of mass m, when placed on a rough inclined plane and moved, moves
down the plane with constant speed. If a block of mass 2m were placed
on the same incline and moved, it would …
The block will have the same motion. Both the gravitational force
and the friction force scale with the mass so there is no net force in
either case.
Goal: Link energy conservation and electromagnetism
Source: 283-421 Change of total energy
A
uniform volume distribution of charge has radius R and total charge Q.
A point charge -q is released from rest at point b, which is a distance
3R from the center of the distribution. When the point charge reaches a,
which of the following is true regarding the total energy, E?
(5) Students often forget to include the kinetic energy,
especially after a lot of discussion of potential energy. Many will
simply misinterpret the energy to mean potential energy. Teasing apart
these issues is important.
Goal: Hone the concept of electrostatic potential
Source: 283-420 Change of PE
A uniform volume distribution of
charge has radius R and total charge Q. A point charge -q is released
from rest at point b, which is a distance 3R from the center of the
distribution. When the point charge reaches a, which of the following is
true regarding the potential energy, U?
(7) Many students use an inverse square dependence appropriate
for fields. Others will take the field at b and multiply by the
displacement. Still others will assert that the potential doubles
because they are using the distance to the surface of the sphere.
Goal: Hone the concept of static friction
Source: UMPERG-ctqpe29
A block of mass m sits at rest on a
rough incline of angle θ. The coefficient of static friction is
μ.
The friction force on the block is
(2) this is all that is needed to hold the block at rest. Some
students will give #4 as the answer having specified the maximum static
friction force.
It helps to classify forces as model forces obtainable from a formula,
and procedure forces. Static friction is an example of a procedure
force, one that cannot be determined without application of the 2nd law.
Goal: Hone the concept of static friction
Source: UMPERG-ctqpe27
A mass of 5 kg sits at rest on an incline making an angle of 30° to
the horizontal.
If μs = 0.7 the friction force on the block is
(2) this is all that is needed to hold the block at rest. Some
students will give #4 as the answer having calculated the maximum static
friction force.
It helps to classify forces as model forces obtainable from a formula,
and procedure forces. Static friction is an example of a procedure
force, one that cannot be determined without application of the 2nd law.
Goal: Problem solving
Source: UMPERG-ctqpe23
If m2 = 2m1 , m3 = 3m1 and
the force that the surface exerts on the bottom block is 120N, the mass
of the large block is
Use g = 10 N/kg.
(3) the most common other answers are #1 and #6, each of which
represents a typical mistake students make. This problem presents a good
opportunity to encourage students to check their answer.
Goal: Link flux to field lines.
Source: 283-415 nonzero flux?
The circles in the picture below are Gaussian surfaces. All other lines
are electric field lines. For which cases is the flux non-zero?
(2) As “follow-up” it is good to ask questions about comparisons
between two or more of the situations. For example, which is flux is
larger, a or f? Such questions help determine what students are focused
upon; are they keying on number of lines, do they understand that the
flux can be negative.
Commentary:
Answer
(3) As it starts the elevator must accelerate downward and so
will the upper block. The only forces on the block are gravity and the
normal force. The normal force must diminish so gravity can provide the
downward acceleration.
Students answering #2 may have interpreted the question to mean ‘as the
elevator moves’ and think that the elevator moves with constant velocity.