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?
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: 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: 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 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: 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.
Commentary:
Answer
(3) Both blocks will experience the same acceleration. If they
have the same initial velocity, they will stop in the same time.