Goal: Hone the concept of force, classify forces as contact and action-at-a-distance.
Source: UMPERG
A baseball is struck by a bat. While the ball is in the air, what
objects exert forces on the ball?
Goal: Hone the concept of normal force.
Source: UMPERG
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 normal force on the ball?
Enter (9) if the direction cannot be determined.
(1) By definition the normal force is always perpendicular to the
surface at the point of contact, independent of the motion of the object
and the shape of the surface. The direction of the normal force is away
from the surface and toward the object in contact with it.
When the normal force is introduced to students, a flat surface is used
to illustrate the concept. Flat surfaces are also used in the majority
of problems that students solve. This item extends the context so that
students consider the normal force exerted on an accelerated object
moving on a curved surface.
Those who answer (8) may be thinking that the normal force always
opposes the gravitational force, as when an object is resting on a
horizontal surface.
Students who answer (5) may be indicating the direction of the normal
force exerted on the curved track by the ball.
If a ball were on a flat horizontal surface, what would be the direction
of the normal force? What would be the direction of the normal force if
the ball were rolling across a flat horizontal surface? What would be
the direction of the normal force exerted on a block at rest on an
incline? What would be the direction of the normal force on a ball
rolling down an incline?
What direction(s) are perpendicular to the track at point B?
The direction of the normal force is essentially a matter of definition.
The track exerts a force on the ball. Dividing this force into a
component perpendicular to the surface (called the normal force) and a
component tangential to the surface (called the friction force) is a
choice, which is made because it is useful to do so. Definitions are
difficult to get across to students because there are no demonstrations
one can do to show that the normal force points in a particular
direction. The only thing one can verify is how the definition is
applied by students in a diverse set of contexts.
Goal: Identifying and classifying forces.
Source: UMPERG
Three blocks are stacked as shown below.
How many forces are acting on the bottom block (m3)?
(3); The gravitational force exerted by the earth, the normal force
exerted by the horizontal surface, and the normal force exerted by the
block with mass m2.
Some students have difficulty distinguishing between direct and indirect
interactions. Students may take the view that m1 directly
exerts a force on m3. This view is often verbalized as “the
weight of block m1 is exerted on m3.”
It is helpful to classify forces into action-at-a-distance forces, such
as gravity and electromagnetism, and contact forces. Students can then
employ a strategy for identifying all the forces since every object
touching a body will give rise to a force. The only exceptions are the
fundamental forces, which is an easily exhausted list.
Does m3 exert a force on m1?
What part of m2 interacts with m3? What part of
m1 interacts with m3?
Is weight a force? If so, what object exerts the force?
Can an object interact with another object without touching it? If so,
when? If not, why not?
Is the normal force exerted by m2 on m3 less than,
equal to, or greater than the weight of m2?
If one pushes on both sides of a bathroom scale the scale reading will
change. What does the scale measure. How is the reading related to the
forces exerted on the scale?
If bathroom scales are placed between the blocks, what forces would each
scale measure (assuming that the scales themselves have very little mass
compared to the mass of the blocks)?
Goal: Understanding action-reaction forces.
Source: UMPERG
A hammer strikes a nail driving it into a piece of wood. Which statement
below is true about the forces exerted during the impact?
(3) The forces are the same size (according to Newton’s third law).
Students’ natural inclination in situations like this is that a moving
object is a more active agent and therefore exerts a larger force, while
a stationary object is the more passive agent and exerts a smaller
force. Students also look at effects: the object that has the largest
change in motion has experienced the largest force.
How can you determine which object experiences the larger force? What
are some of the clues? Do we have any way to relate the effects we
observe to the size of the forces each object experiences?
Newton’s third law, while easily memorized as a principle, is hard to
develop as an intuition and to employ in reasoning about situations.
There is no single experience that can help. One needs to revisit the
third law often in many different contexts.
There are many situations one can use with students. Try a moving block
with a spring colliding with a wall (or another block that is
stationary). In this situation one can use the spring law to help
relate the forces.
Goal: Perceiving the presence of forces from changes in position.
Source: UMPERG
Below is shown a strobe diagram indicating the position of four objects
at successive time intervals. The objects move from left to right.
During the intervals shown, which of the objects experience no net force
in the horizontal direction?
(8); Objects with no net horizontal force will move with constant velocity. The objects moving with constant velocity are B and D. This question helps to reinforce the idea that it is change in motion, not motion itself, that requires a force.
Goal: Recognizing how the concept of force relates to interactions.
Source: UMPERG
A bowling ball rolls down an alley and hits a bowling pin. Which
statement below is true about the forces exerted during the impact?
(3); The forces are equal (independent of the masses and motions of the
interacting objects), as required by Newton’s Third Law .
In situations where a heavier, moving object collides with a lighter,
stationary object, students have a very strong intuition that the
heavier, moving object exerts a larger force on the lighter, stationary
object. This intuition is based on experiences like the following: when
a bowling ball hits a pin, the ball continues to move forward and the
pin goes flying off the lane. Students interpret the large change in the
pin’s motion as evidence that the ball (which is heavier than the pin)
exerts a larger force on the pin than vice versa. Often, when a car and
a truck collide, the car suffers much more damage than the truck, and so
students interpret this as evidence that the truck exerts a larger force
on the car. For background reading on helping students overcome this
persistent misconception see Thornton and Sokoloff: Sokoloff, D.R.
& Thornton, R.K. (1997), Using interactive lecture demonstrations to
create an active learning environment, The Physics Teacher, 27, No. 6,
340; and Thornton, R.K. and Sokoloff, D.R. (1998), Assessing student
learning of Newton’s Laws: The force and motion conceptual evaluation
and the evaluation of active learning laboratory and lecture curricula,
American Journal of Physics, 64, 338-352 (1998).
Which object, the bowling ball or the bowling pin, has the larger
acceleration? How do you know?
Which object experiences the larger net force? How do you know?
Would your answer to the original question change if a moving pin hit a
stationary bowling ball?
If you have MBL equipment and force probes, collide a moving cart with a
stationary cart of the same mass. Ask students to compare the forces
exerted on the two carts. Ask students to compare the velocities and
accelerations of the two carts. Repeat using different initial
conditions.
Draw a picture of a large moving cart colliding with a small stationary
cart. Draw a spring between the carts. Ask students how they would
determine the force on each cart given the spring constant and spring
compression.
Take a bathroom scale, place it between two students (a large strong
student and a slight student) and have them push as hard as they can
from either end without making the scale accelerate–observe the scale
reading. Repeat with the scale reversed. Ask if there is much
difference in the scale reading depending on which way the front of the
scale is facing. What does this imply about the forces exerted by the
strong and the slight student on each other?
Goal: Differentiate between instantaneous and average acceleration.
Source: UMPERG
Below is shown a strobe diagram indicating the position of four objects
at successive time intervals. The objects move from left to right.
During the intervals shown, which object would you estimate has the
largest average acceleration?
(3) Assuming that the question is referring to magnitude, the largest
average acceleration is experienced by object (C). The other three
objects appear to start and end with approximately the same velocity.
For object (C) the velocity decreases in magnitude as the object moves
to the right. Students who answer (5) because they realize that the
average acceleration of C is negative and think zero is larger should
not be considered wrong.
It is important for students to develop multiple ways of interpreting
concepts. This ensures that students are not just following rote
procedures to answer questions. Once an idea is understood students
should be able to use their understanding in a variety of contexts and
with a variety of representations.
The concept of average acceleration depends only on the initial and
final velocity over some specified time interval. Some students will
make their judgments on the basis of changes in the velocity at
different points in the motion.
How is the average acceleration determined? What is the difference
between average acceleration and instantaneous acceleration? Where is
the instantaneous acceleration greatest?
Draw velocity vs. time graphs for the objects (A) and (B). Analyze the
average acceleration (instantaneous acceleration) for different time
intervals (times).
Goal: Differentiate between magnitude and direction of acceleration.
Source: UMPERG
| Case | Column 1 | Column 2 |
| (A) | A car goes from 0 to 60 mph in 6s along a straight highway. |
A car goes from 60 to 0 mph in 6s along a straight highway. |
| (B) | A race car travels around a circular track at 50 mph. |
A race car travels around the same circular track at 100 mph. |
| (C) | A ball is thrown straight up. It rises 20 ft. Ignore the effects of the air. |
A ball is dropped straight down. It falls 20 ft. Ignore the effects of the air. |
For which cases is the acceleration the same for the motion described
in both columns?
(3) The only case having the same acceleration is C where the
acceleration is that due to the gravitational force. In case A, the
magnitude of the two accelerations is the same but one is positive and
the other negative, i.e. the vectors point in opposite directions.
[This assumes that the acceleration is uniform.] In case B, the
“direction” is the same, i.e. pointing toward the center of the circle,
but the magnitudes are different.
This question reveals whether students have the concept of acceleration
as a vector (i.e. has direction as well as magnitude). Some students
may ignore the magnitude completely and key on the direction. The
objective here is to have students indicate the concept of acceleration
that they are using to answer the question.
For which cases is the magnitude of the acceleration the same? the
direction?
For which cases does the acceleration change during the motion
described?
Have students draw a motion diagram (a strobe diagram with the velocity
vector indicated at each position). This diagram helps students to
associate the acceleration with a change in velocity.
Goal: Honing the idea of constant acceleartion.
Source: UMPERG
A baseball is shot into the air from a spring loaded cannon. The diagram shows the ball at five locations. At which location is the magnitude of the acceleration least?
The ball’s acceleration is 9.8 m/s2 (down) throughout its
entire motion (assuming air resistance can be neglected). Answer (8) is
the best choice.
Students should have some experience analyzing the velocity of objects
undergoing free-fall motion. Issues to consider: (1) Do students think
that the acceleration is zero at the maximum height, where the ball
momentarily stops? (2) Do students think that the acceleration points
in the same direction as the velocity? (3) Can students apply the
definition of acceleration to a familiar situation?
The goal is to have students confront existing misconceptions: 1)
Students often believe that the acceleration must point in the direction
of the motion; and 2) Students often believe that the acceleration is
9.8 throughout free fall but zero at the top of the trajectory since the
vertical speed is zero there.
Ask students to apply the operational definition of acceleration (take
the velocity vector just after C and subtract the velocity vector just
before C and divide by the time interval). Have them compare the x/y
component of the velocity just before C with the x/y component of the
velocity just after point C.
For students who persist in thinking that both the velocity and
acceleration are zero at the top of a trajectory, contrast the
subsequent motion with that of an object sitting at rest on a surface.
Goal: Differentiate velocity and acceleration in the context of free-fall motion.
Source:
A person throws a ball straight up in the air. The ball rises to a maximum height and then falls back down so that the person catches it. Consider the ball while it is in the air.
Which of the following statements are true?
A. Just after the ball leaves the person’s hand the direction of the acceleration is up.
B. The acceleration is zero when the ball reaches its maximum height.
C. The acceleration is about 9.8 m/s2 (down) when the ball is falling.
After the ball leaves the person’s hand, its acceleration is 9.8 m/s2 (down) throughout the entire motion (assuming air resistance can be neglected). Answer (3) is the best choice.
Use this item during kinematics, shortly after the introduction of “acceleration.” We suggest that students have some experience analyzing the velocity of objects undergoing freefall motion. Intended focus: (1) Do students think that the acceleration is zero at the maximum height, where the ball momentarily stops? (2) Do students think that the acceleration points in the same direction as the velocity? (3) Can students apply the definition of acceleration to a familiar situation?
The goal is to have students confront existing misconceptions:1) Students often believe that the acceleration must point in the direction of the motion; and 2) Students often believe that the acceleration is 9.8 throughtout free fall but zero at the top of the trajectory since the vertical speed is zero there.
Have students sketch the velocity of the ball as a function of time. Ask how the acceleration is related to this graph.
Using Microcomputer Based Lab software and a sonic ranger, generate a velocity graph for a cart going up and down an incline. Discuss how the graph relates to a velocity vs. time graph for a ball thrown vertically.
Commentary:
Answer
(6); the earth’s gravitational force (an “action-at-a-distance” force),
and air resistance (a contact force) are the only two forces being
exerted on the ball while in the air.
Background
It is common for students to think that motion requires a force; in some
cases this misconception is more specific, namely, that motion requires
a force in the direction of motion. For this assessment item, the
misconception manifests itself in the belief that there is a “force of
the bat” that propels the ball up during flight.
Questions to Reveal Student Reasoning
Ask students to state what forces are being exerted on the ball and what
object exerts each force.
How do you know when a force is being exerted by one object on another?
Do the sizes of the forces change? Do the directions of the forces
change? Describe how.
Do you have any control over the force of the bat on the ball? Can you
make it larger or smaller or change its direction once the ball is
flying through the air?
Suggestions
Ask students if they have a way of exerting a force on an object without
touching it. Invite them to move an object in the front of the room
without leaving their seats and touching the item.
If Newton’s Second Law has been introduced, attempt to relate the forces
exerted on the ball to the ball’s acceleration. See if students agree
that, if air resistance can be neglected, the ball has a constant
acceleration of 9.8 m/s2 toward the earth during its entire
trajectory. If they agree ask what they can conclude about the net
force on the ball while airborne.