Goal: Recognizing forces on current elements
Source: 283 Force on a half-loop
A
semicircular wire lies in a plane as shown. The positive z-direction is
out of the plane. The wire has current, I, in the counterclockwise
sense, and it is in a uniform external magnetic field, B, directed along
the +y axis. What is the direction of the net force, if any, acting on
the wire?
Goal: Problem solving and developing strategic knowledge
Source: UMPERG-ctqpe104
You are given this problem:
A
block sits on a frictionless incline. Given the mass of the block, the
angle of incline, the distances d1 and d2, and
that the block starts from rest, find the time to travel from
d1 to d2.
What principle would you use to solve the problem MOST EFFICIENTLY?
(6) Students responding #1 are relying on memory and would have
difficulty if a force other than gravity was involved.
Goal: Hone the concept of conservative force
Source: UMPERG-ctqpe67
The
potential energy function for a certain body is shown at right. The
force associated with this potential is …
(1) It is remarkable how many students will select one of the
other answers. Many students do not recognize that you cannot have a
potential function unless the force is conservative.
Goal: Relate force to potential energy function
Source: UMPERG-ctqpe66
The
potential energy function for a certain body is shown at right. For
which points is Fx = 0?
(4) The force is given by the negative of the slope of the
potential function. Points 3 and 5 are equilibrium points, but only 3 is
a stable equilibrium point. Students frequently choose answer #2
thinking that the force is zero at these points.
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: 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: 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 …
(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.
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: 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.
Commentary:
Answer
(6) Since the current carrying semicircle lies in the x-y plane,
as does the magnetic field, the net force, if any, must point
perpendicular to the plane, or in the z direction. For the semicircular
wire, all force contributions add. There is no contribution to the net
force from current elements near the x-axis.
The force on the missing half of the loop would be out of the page.
Together both forces on a full loop would create a torque tending to
align the field of the current loop with the external field. If
appropriate relate this situation to the torque on a magnetic dipole.