Goal: Hone the concept of potential energy functions
Source: UMPERG-ctqpe65
The
potential energy function for a certain body is shown at right. If the
body is released from rest at a location corresponding to point 4, the
object would …
Goal: Reasoning with kinematics
Source: UMPERG-ctqpe63
Two
masses, M > m, travel down the surfaces shown. Both surfaces are
frictionless. Which mass has the largest average speed during
their motion?
(1) This problem is intended to promote discussion of average
speed. Both masses have the same speed at the bottom. Mass m has a
larger acceleration in the beginning because the circular track is
vertical at the outset. Although the angle of the incline is not
specified, the angle is irrelevant. All inclines will have the same
average speed. A simple graph of the speed of each mass versus time
shows that m will have the larger average speed.
Goal: Reasoning with energy
Source: UMPERG-ctqpe62
Two
identical blocks fall a distance H. One falls directly down, the other
slides down a frictionless incline. Which has the largest speed at the
bottom?
(3) The only force doing work is gravity and both block undergo
the same vertical displacement.
Goal: Reasoning with forces and kinematics
Source: UMPERG-ctqpe60 variant
Two
blocks, M2 = M1 but of different sizes, having the
same speed, move from a frictionless surface onto a surface having
friction coefficient μk.
Which stops in the shorter time?
(3) Both blocks will experience the same acceleration. If they
have the same initial velocity, they will stop in the same time.
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.
Goal: Link potential energy with work needed to assemble a charge configuration.
Source: 283-460 Lowest potential energy
Which of the following charge distributions has the lowest potential
energy?
(2) Encourage students to reason to the answer rather than write
formal expressions for each case. They should be able to perceive that
cases #1, #3 and #5 all have positive PE. Situation #4 has zero energy
as can be seen by assembling subunits, then moving the two positive
charges along the zero equipotential of the charges on the y-axis.
Finally, situation #2 is clearly negative.
A good follow-up question is to ask students to order the cases
according to increasing potential energy.
Goal: Problem solving with momentum
Source: UMPERG-ctqpe46
A
block slides along a frictionless surface and onto a slab with a rough
surface. The plot on the right shows the velocity of the blue slab as a
function of time. The slab has mass of 4kg and the block has mass of
2kg. If the block remains on top of the slab, what was its initial
speed?
(6) The block initially has velocity 3 m/s. This problem is
difficult for students. They generally have difficulty obtaining
relevant information from a diagram. In this case they must use the plot
to tell that the final velocity is 1 m/s.
Goal: Problem solving
Source: UMPERG-ctqpe44-46
A
block slides along a frictionless surface and onto a slab with a rough
surface. The plot on the right shows the velocity of the blue slab as a
function of time. The slab has mass of 4kg and the block has mass of
2kg. What is the friction force on the small block at t = 1 second?
(5) The acceleration of the slab can be found from the plot. The
only force on the slab in the horizontal direction is the friction force
so it must be responsible for the acceleration. The force on the block
can then be found using the 3rd law.
Goal: Link electric fields, work and potential energy
Source: 283-455 Change in Potential Energy when moving a charge
In each of the situations below a negative charge is moved along a path
from point A to point B in the presence of an electric field, as shown.
For which situation is the increase in potential energy the greatest?
(2) In case 1 the charge moves to a lower potential energy. In
case 3 the charge returns to a point having the same distance to the
plane of charge as it originally had, meaning no net work. In case 4 the
charge moves along an equipotential and no work is done. Students should
be asked to identify the charge configuration that could account for
each of these field situations. They can also be asked for which case is
the electrostatic potential change the greatest.
Commentary:
Answer
(2) At position 4 the object experiences a force toward the
origin given by the negative of the slope of the potential curve.
Frequently students interpret the fact that U is zero at point 4 to mean
that there is no force.