Goal: Hone the concept of impulse
Source: UMPERG-ctqpe80
A MOVING car collides with a STATIONARY truck. Which of the following
statements is true about the magnitudes of the impulse on each due to
the other?
Goal: Reason with kinematics
Source: UMPERG-ctqpe75
Two identical steel balls are released from rest from the same height,
and travel along tracks as shown and labeled below.
Which ball reaches the end of its track first?
(2) The ball on track B accelerates down the second slope. A
component of this acceleration is in the x-direction. This means that
the x component of ball B’s velocity is never smaller than that of ball
A. Since the tracks have the same x-dimension, ball B gets there first.
A large majority of students choose answer C incorrectly thinking that
since the balls return to the same height, they have the same speed and,
therefore, arrive at the same time.
Goal: Reason with kinematics
Source: UMPERG-ctqpe76
Two identical steel balls are released from rest from the same height,
and travel along tracks as shown and labeled below.
Which reaches the end of its track first?
(2) The ball on track B accelerates down the second slope. A component
of this acceleration is in the x-direction. This means that the x
component of ball B’s velocity is never smaller than that of ball A.
Since the tracks have the same x-dimension, ball B gets there first.
A large majority of students choose answer C incorrectly thinking that
since the balls return to the same height, they have the same speed and,
therefore, arrive at the same time.
Goal: Reason with potential energy
Source: UMPERG-ctqpe68
Consider three spring systems having identical springs and
masses. Which of the 3 systems has the largest amount of stored energy?
(2) Students often forget to include the gravitational potential
energy and also have difficulty selecting a good reference point.
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: 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: Reasoning with energy
Source: UMPERG-ctqpe64
Two
masses, M > m, travel down the surfaces shown. Both surfaces are
frictionless. Which mass has the largest speed at the bottom?
(3) By energy considerations, both would have the same speed.
Students frequently get confused about the mass, thinking that the
larger mass has the greatest potential energy change and therefore has
the greatest speed.
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 …
(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.
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.
Commentary:
Answer
(3) The 3rd law requires that the impulses be equal. Even
students who understand the 3rd law have difficulty realizing that the
magnitude of the impulse on two interacting bodies is the same. Many
students, however, do not understand impulse enough to recognize the
association. Others do not read the problem carefully enough and answer
with regard to ALL the forces, not just the one due to the other
vehicle.