Goal: Contrast internal, external forces and net force.
Source: UMPERG
A toy
is made from two blocks and a spring as shown at right. When the spring
is compressed and suddenly released, the toy will jump off the table
surface. Which of the following is true about the net force on the toy
just after it is released?
Goal: Reasoning with 2nd law.
Source: UMPERG
Consider the three situations shown below. In each case two small carts
are connected by a spring. A constant force F is applied to the
leftmost cart in each case. In each situation the springs are
compressed so that the distance between the two carts never changes.
Which of the following statements must be true regarding the compression
of the spring in each case? Assume the springs are identical.
(5) The total mass is the same so the acceleration of the systems must
be the same. In each case the spring exerts the only horizontal force
on the cart to the right. The spring force must be largest for the 3M
cart and smallest for the M cart: B < A < C.
This item requires students to reason. It is difficult to resort to
equation manipulation to answer this question. One difficulty with the
problem is that it involves a complex system (two carts connected by a
spring).
Is it really possible to compress the carts so that they stay a fixed
distance apart? What forces act on each cart? Will the carts
accelerate or move with a constant velocity? Compare the carts
acceleration.
Draw a free-body diagram for each cart.
Define a new problem in terms of the carts on the right: Each cart is
given an applied force so that each has the same acceleration. How do
the applied forces compare?
Goal: Relate position/time graphs to force.
Source: UMPERG
Position vs. time graphs are given below for four different objects.
Which of the objects experiences a net force sometime during the time
period shown?
(8) is the appropriate response because both C and D experience a force
during the time interval. A and B have constant velocity because the
slope of their x vs. t plot is constant. Some students may not realize
that D experiences a force because they will reason that D has constant
velocity at any given time. However, D must experience a force to
change its velocity.
Recognizing the signature of acceleration from a plot of position vs.
time is an important skill for students to develop. Because of
familiarity, they may recognize the plot of position for a falling body
and reason that the object experiences a gravitational force. This
question requires two logical steps. First recognizing the consequence
of constant velocity and second recognizing that a change of velocity
indicates acceleration and therefore force.
Which objects have constant velocity throughout the time interval?
Which of the objects has the largest speed sometime during the time
interval?
Are all of the objects moving away from the origin?
Have students plot the velocity of each object over the same time
interval.
Have students move objects in a manner in accord with the plots. This
may cause them to realize when a force must be applied.
Goal: Reason and evaluate statements about a real-world situation.
Source: UMPERG
At the scene of an accident the car causing the crash left skid marks of
a length D. The accident reconstruction team did a test and found that a
police cruiser traveling at the speed limit produces skid marks of
length d < D. Which of the following statements is valid?
(4) is valid assuming that the usual kinetic friction model is
applicable. Some students may think that (3) is valid and indicate (3)
or (5). All of the others are definitely invalid. Since (1) is
invalid, (7) is also invalid.
This question seeks to encourage students to reason and analyze the
situation. It offers the opportunity to engage the students in a
discussion of the meaning of validity as well as the physics underlying
the various assertions.
How would reaction time influence the skid marks?
Suppose the car had several people inside. Would that have affected the
skid marks?
Suppose the test had been made with the same model car as the one in the
accident. Would that make the test more valid?
Allow students to form small groups according to their views and let
them present their arguments to the class. Have student ‘consultants’
suggest appropriate tests to determine if the car was speeding.
Goal: Link energy and kinematic quantities.
Source: UMPERG
Two masses, m and M, are released from rest at a height H above the
ground. Mass m slides down a curved surface while M slides down an
incline as shown. Both surfaces are frictionless and M > m.
Which of the following statements is true?
(4); even though both blocks arrive at the bottom with the same speed, m
has a larger initial acceleration and attains a larger speed faster than
M, despite having to travel a slightly longer distance. This item helps
to focus attention on identifying those salient characteristics of the
problem that relate to the time it takes the blocks to slide down the
ramps. Some students will cue on the distance traveled, some on the
differing masses of the blocks, some on m picking up speed faster than
M.
The curved surface makes it impossible for students to use either
kinematics or Newton’s Second Law to determine the exact time it takes m
to reach the bottom. Some students may correctly conclude that both
blocks arrive at the bottom with the same speed, and thereby erroneously
conclude that this must mean they arrive at the same time as well.
The curved track case also offers an opportunity to explore whether
students realize that the total work done by the gravitational force
goes into changing the kinetic energy of the block, even with a normal
force present since this normal force does no work on the block.
What features of the problem determine the time it takes the masses to
reach the bottom?
What’s the same about both blocks if they are released from the same
height? What’s different?
Does traveling a shorter distance always mean less time?
For those who answered (1), ask what would happen to the time it would
take M to reach the bottom if the 45° angle were made more, or less
steep (think of the top vertex of the triangle being on a hinge).
Clearly in the limit where M would drop vertically a distance
SQRT(H2+L2), the time it would take to reach the
other vertex of the hypoteneuse would be shorter than for any angle less
than 90°.
Commentary:
Answer
(2); This question seems difficult but it is available
to beginning students. Students can analyze the problem considering the
entire toy as a single system or decompose into the separate masses.
Viewed as a single system, since the center of mass accelerates up, the
net force must point up. Free body diagrams for each mass individually
would show no net force on the bottom mass (because the normal force
assumes a value necessary to balance gravity and spring force) and a
large net force on the upper mass (spring force exceeds gravity). If
sketched to scale, the two can be added showing that the net force
derives from the normal force on the lower block.
Background
This question is intended to have students distinguish between internal
and external forces. The question also can be approached in a variety
of ways.
Questions to Reveal Student Reasoning
Can the toy ever leave the surface? Would there be a net force if it
did leave the surface?