Goal: Problem solving
Source: UMPERG-ctqpe162
A uniform disk with R=0.2m rolls without slipping on a horizontal
surface. The string is pulled in the horizontal direction with force
15N. The disk’s moment of inertia is 0.4 kg-m2. The friction
force on the disk is:
Goal: Problem Solving
Source: UMPERG-ctqpe164
A uniform disk with mass M and radius R sits at rest on an incline
30° to the horizontal. String is wound around disk and attached to
top of incline as shown. The string is parallel to incline. The
tension in the string is :
(4) This problem can be solved a variety of ways. The simplest method is
to balance torques about the contact point. This situation is an
excellent one for discussing the advantages of thinking about preferred
points about which to write the rotational dynamics equation.
Goal: Problem solving
Source: UMPERG-ctqpe88
Two blocks, M=2m, sit on a horizontal frictionless surface with a
compressed massless spring between them. After the spring is released
M has velocity v. The total energy initially stored in the spring was:
(3) The big mass has kinetic energy mv2 and the small mass
has energy 2mv2. Some students may answer (6) because they
have confused M and m. It is important to determine the reasons that
any student might select (7). They might be unwilling to assume that
the system is initially at rest. Students taking this perspective
should not be disconfirmed but congratulated for making a critical
interpretation of the wording.
Goal: Hone the concept of heat and distinguish from internal energy.
Source: UMPERG-ctqpe191
Which of the following phrases best describes heat?
(4) Many students are confused about what heat is because the term is
not used consistently. ‘Heat’ is usually used to refer to the thermal
energy that flows into or out of a body. So ‘heat’ is not equivalent to
‘energy’ and it is inappropriate to refer to the heat possessed by a
body. Unfortunately, the redundant phrase ‘heat flow’ is often used in
texts. In addition, students frequently attribute any loss of coherent
energy to friction, which has converted the energy into ‘heat’.
Goal: Reasoning about adiabatic expansion.
Source: UMPERG
An ideal gas is allowed to expand slowly. The system is thermally
isolated.
Which statement regarding the final temperature is true?
(1) For adiabatic expansion, TV(γ-1) is constant.
Since the volume increases, the temperature must decrease.
This result can be reasoned by considering the fact that work is done by
the gas. Since there is no heat transfer, the internal energy must
decrease. Since the internal energy of a perfect gas depends only upon
temperature, the temperature must decrease.
Goal: Hone the concept of internal energy and heat.
Source: UMPERG-ctqpe180
Body A has a higher temperature than body B. Which of the following
statements is true?
(3) Only statement (3) is always true. Placed in contact, heat will flow
from the higher temperature body to the other regardless of the masses
of the bodies.
The ‘feel’ of a body’s temperature depends upon the material and the
rate of heat conduction. Body A could be much smaller than body B and,
therefore, contain much less energy than body B even though at a higher
temperature. Likewise, if body B is smaller it can absorb less energy
from a third body than body A even though it has a lower temperature.
Goal: Reasoning about adiabatic expansion.
Source: UMPERG
An ideal gas is allowed to expand slowly. The system is thermally
isolated.
Which statement regarding the final pressure is true?
(1) For adiabatic expansion, pVγ is constant. Since
the volume increases, the pressure must decrease.
This result can also be reasoned by realizing that the gas won’t expand
unless the external pressure on the piston is reduced. The gas expands
because the piston moves to equalize the internal and external pressure.
Goal: Problem solving
Source: UMPERG
A quantity of gas is confined to a cylinder. The cylinder is vertical
and capped by a moveable piston of mass 2 kg and area 0.1 m2.
The gas is heated until the piston rises 20 cm. The amount of work done
by the gas is most nearly
(1) This problem helps interrelate concepts from mechanics and
thermodynamics. The work can be determined from the work done against
the gravitational force.
Goal: Hone angular kinematic quantities and distinguish them from linear kinematic quantities.
Source: UMPERG
A mass moves in a circle with uniformly increasing anglular velocity.
As the angular velocity ω increases, the linear acceleration of
the mass has…
(4) This requires exploration. Some students may think that the
direction is changing because the acceleration points toward the center
of the circle. They may be unaware that there is also a component of the
acceleration in the tangential direction.
Some students may answer (3) thinking only of the radial acceleration
and that ‘towards the center’ is a direction.
Goal: Hone angular kinematic quantities and distinguish them from linear kinematic quantities.
Source: UMPERG
A mass moves in a circle with uniformly increasing angle.
As the angle θ increases, the linear acceleration of the mass has
…
(2) Students have a lot of difficulty reconciling linear kinematics with
angular kinematics. Unless shown how to take derivatives in polar
coordinates, or shown how to represent rotational kinematic quantities
as vectors, students can only memorize specific relationships.
Some students may answer (1) thinking that ‘towards the center’ is a
direction.
Commentary:
Answer
(4) This problem can be done without the arithmetic complication of
finding the mass from the center-of-mass moment of inertia. This is an
excellent problem for stressing multiple solution methods. This is a
situation where two equations are needed. They can be either the linear
dynamical relation and a rotational dynamical relation, or just two
rotational relationships about different points. Some students may
answer (7) because they are unfamiliar with the expression for moment of
inertia about the CM or because they do not know the Parallel Axis
theorem.