Download Measuring the Motion of a Toy Car

P
Grade 5
Developed By:
The MAPs Team
Meaningful Applications of Physical Sciences
Dr. Michael H. Suckley
Mr. Paul A. Klozik
Materials in this manual are based upon the Grade
Level Content Expectations provided by the
Michigan State Board of Education. The activities
and support materials have been inspired by
Operation Physics. Participants registered for this
workshop have permission to copy limited portions of
these materials for their own personal classroom use.
Grade 5 Measuring Changes in Motion
A. Introduction
1. Grade Level Curriculum Expectations ------------------------------------------------------- 35
2. Naive Ideas Concerning Forces and Motion ------------------------------------------------ 4
B. Newton’s First Law --------------------------------------------------------------------------------- 5
1. Motion
a. Measuring the Velocity of Various Objects ----------------------------------------------- 6
b. People Walk - Velocity ----------------------------------------------------------------------- 9
c. Measuring the Motion of a Toy Car -------------------------------------------------------- 10
2. Inertia
a. Fundamentals ---------------------------------------------------------------------------------- 11
b. Using Your Marbles -------------------------------------------------------------------------- 12
C. Newton’s Second Law ------------------------------------------------------------------------------ 13
1. Acceleration (change in velocity)
a. Observing Acceleration ---------------------------------------------------------------------- 14
b. People Walk - Acceleration ---------------------------------------------------------------- 15
c. Acceleration A More Complete Picture --------------------------------------------------- 18
2. Fundamentals of Force
a. Observing Forces (using the “Gizmo”) ---------------------------------------------------- 20
b. Finding the Forces----------------------------------------------------------------------------- 21
c. Understanding Types of Force --------------------------------------------------------------- 26
d. Forces in a Collision -------------------------------------------------------------------------- 28
e. The Falling Cup-------------------------------------------------------------------------------- 29
3. The affect of Mass on Acceleration ------------------------------------------------------------ 30
D. Newton’s Third Law --------------------------------------------------------------------------------- 31
1. Equal and Opposite -------------------------------------------------------------------------------- 32
2. Equal and Opposite another Look --------------------------------------------------------------- 33
E. Appendix
1. Vendor List ----------------------------------------------------------------------------------------- 36
2. Making Formulas Out of Words ----------------------------------------------------------------- 37
3. K-7 Standard Science Processes ----------------------------------------------------------------- 38
4. Physical Science Grade Level Content Expectations ----------------------------------------- 39
5. Grade Level Mathematics Expectations ------------------------------------------------------- 40
Measuring Changes in Motion © 2009 ScienceScene
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Introduction
Isaac Newton was born in 1642 and died in 1727. He
was an English physicist, mathematician, and natural
philosopher and is considered one of the most important
scientists of all time. Newton formulated laws of universal
gravitation and motion, laws that explain how objects move
on Earth as well as through the heavens.
Newton took known facts and formed mathematical theories to explain them.
He used these theories to predict the behavior of objects in different circumstances
and then compared his predictions with what he observed. Finally, Newton used his
results to check—and if need be, modify—his theories. He was able to unite the
explanation of physical properties with the means of prediction. Newton began
with the laws of motion and gravitation he observed in nature. Then he used these
laws to convert physics from a mere science of explanation into a general
mathematical system with rules and laws.
It is the purpose of this booklet to investigate Newton’s Three Laws of
Motion. The battery powered racecars, stopwatches, batteries, and most of the
materials used in the experiments were obtained at our local Dollar Store. The
stopwatches were modified by the addition of two external sensors. The sensors
turn the stopwatch on and off eliminating the human error created when timing an
event. A racetrack was also added to provide a consistent surface for the cars. The
track is made from corrugated plastic (8-mm) which allows the sensors to be
inserted.
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Naïve Ideas Concerning Motion
1.
Time can be measured without establishing the beginning of the interval.
2.
The location of an object can be described by stating its distance from a given point, ignoring direction.
3.
The distance an object travels and its displacement are always the same.
4.
An object’s speed is the same as its velocity.
5.
If an object is accelerating, then the object is speeding up.
6.
An object’s acceleration cannot change direction.
7.
Acceleration always occurs in the same direction as an object is moving.
8.
If an object has a speed of zero (even instantaneously), it has no acceleration.
9.
The only “natural” motion is for an object to be at rest.
10. If an object is at rest, no forces are acting on the object.
11. Only animate objects can exert a force. Thus, if an object is at rest on a table, no forces are acting on it.
12. Force is a property of an object. An object has force, and when it runs out of force it stops moving.
13. The motion of an object is always in the direction of the net force applied to the object.
14. Large objects exert a greater force than small objects.
15. A force is needed to keep an object moving with a constant speed.
16. Friction always hinders motion. Thus, you always want to eliminate friction.
17. Frictional forces are only due to irregularities in surfaces moving past one another.
18. Rocket propulsion is due to exhaust gases pushing on something behind the rocket.
19. When dropped in a vacuum, objects of different masses fall at different speeds.
20. When dropped in a vacuum, objects fall at constant speeds.
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Motion and Newton’s First Law
The study of motion is sometimes referred to as classical mechanics
which is divided into two areas of study; statics and dynamics. Statics is the study
of equilibrium. in which forces balance each other and thereby cancel out any
movement. Rigid frameworks, such as a bridge, a vehicle chassis, or the timber
frame of a house or roof are examples of statics. If the forces acting on a system
do not cancel each other, motion will result. The analysis of this kind of situation
falls within the study of dynamics or of moving bodies.
Newton produced the first laws that described the motion of bodies.
Newton maintained that a constantly moving body does not require force to
maintain the motion. If an unbalanced force acts on a moving body, a change in
motion will occur. This changing motion is referred to as acceleration. Uniform
motion in a straight line is "natural" and will continue indefinitely unless some
unbalanced force acts on the body. This is the essential content of Newton's first
law of motion. Newton's First Law states that any body moving uniformly in a
straight line [or at rest] will remain in uniform motion [or at rest], unless acted
upon by some unbalanced force. Inertia is the property of matter that tends to
keep a body in motion when in motion, or at rest when at rest.
When discussing motion of a body in a uniform straight line or at rest we
usually use the term speed. Speed does not indicate direction only distance per
unit of time. Scientists use the term velocity which includes the direction of the
motion as well as the speed. Observing linear motion with constant speed
requires that the measurement of two quantities: the distance traveled by the
object (d), and the time taken for the object to travel such distance (t). Speed is
obtained by dividing the distance traveled (d), by its corresponding time (t).
speed (v) = (distance traveled by the object (d)) / (time of travel (t))
or
v= d /t
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Measuring the Velocity of Various Object
1. Measuring the velocity of a battery powered toy.
a. Obtain a small toy, which is the moving object to be used in this experiment.
b. Make a racetrack. Mark a starting line, and 1.00 meter from that a finish line. Call this distance x, measure it
with the meter rule, and record this exact distance.
c. Release the moving object approximately .25 meter in front of the starting line. Begin timing when the car
passes over the starting line, and clock the time that it takes to travel the distance x. Call this time (t).
d. Repeat this procedure several times, until you are satisfied about two ideas: (the car should be moving when it
passes the two points.)
1) The vehicle is indeed traveling with a velocity that can be reasonably called constant, (uniformly,
steadily, in a straight line)
2) The time for each run is about the same, (not unusually high or low).
e. Compute the velocity of the moving object, using the ratio v = x / t and record.
f. Collect three sets of data and calculate the average velocity.
g. Repeat for the second car.
2. Measuring the velocity of water level rise.
a. Turn the water on at a moderate rate. Keep this flow constant for both beakers.
b. Fill the 400-ml. beaker with any amount (approximately one fourth of the
beaker) of water, while timing (t).
c. Mark the top of the water, and measure its distance in meters from the bottom
of the beaker to the top of the water.
d. Repeat this for two additional readings.
e. Compute the distance (x) of the water level rose using:
x1 = L1 - L0
x2 = L2 - L1
x3 = L3 - L2
f. Compute the velocity of water flow using: v = x / t.
g. Repeat this for two additional readings.
h. Obtain average velocity of the water flow.
i. Repeat for a 250 ml beaker.
10
9
8
7
6
5
4
3
2
1
3. Measuring the speed of the second hand of a clock.
a. Select a wall clock which has a second hand .
b. As the outer end of the second hand rotates around the center of the clock, it travels a certain distance (x), in a
given time (t).
c. Choose a number of full revolutions (N), express it in seconds, and record it under time (t) on the data sheet
provided.
d. Compute the distance traveled by the outer point of the second hand by noting:
1) The tip of the second hand moves in a circle. In order to find the distance traveled, we must find the
circumference of that circle. To determine the circumference, we must measure the radius (r) of the
circle in meters. The radius is the distance between the center of the clock, and the tip of the second
hand. Double that figure to obtain the diameter, and multiply that result by pi (3.14).
2) The total distance traveled would be the number of full revolutions(N) multiplied by the distance traveled
or x = (N) x 2r x 3.14. Call this distance x, and record.
e. Compute the speed using: v = x / t
f. Repeat for a wristwatch which has a second hand.
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4. Measuring the velocity of a bouncing ball.
a. The total distance (x) that the ball traveled is equal to the sum of the heights
x1, x2 and x3. The initial height is x1, the final height is (x3) and the
average of x1 and x3 is x2. The total distance (x) that the ball traveled is
equal to the sum of the heights (x = x1 + x2 + x2 + x3). The heights are
most easily measured by bouncing the ball near a wall, using the brick
divisions to help in the measurement of the height of the bounce.
b. The time (t) taken for the ball to make two bounces would be measured
from the starting point (the release point), to the end point (the top of the
second bounce).
c. Compute the average speed using: v = x / t.
d. Collect three sets of data and calculate the average velocity.
e. Repeat for the second ball
X1
X2
X2
X3
5. Measuring the velocity of Sound.
a. Note: Light travels at a velocity of 186,000 miles per sec., or 299,793 Km per sec. Sound travels at a velocity of
330 meters per sec. For most short distances of less than several kilometers, light would reach us from some
point almost instantaneously, while sound would take considerably longer. This difference in velocity will be
used to determine the time (t) needed for sound to travel a given distance (x). Set observers with stopwatches
approximately 300 meters from a person with a speed of sound device. The speed of sound device emits a
sound and a bright light at the same moment. (Check with lab assistant for exact location and pre- measured
distance (x)).
b. When the observers are ready, signal to the person with the sound device to activate the device. The observers
will see the light, at which time they must immediately start their timers, and turn them off when they hear the
sound. This difference represents the time (t) taken for the sound to travel to the observers.
c. Compute the velocity using: v = x / t.
d. Take the outdoor air temperature, and calculate the speed of sound using the temperature method V= 330 m/sec.
+ (.6 x temp.). This will be considered the theoretical.
e. Compute your error and percentage of error.
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Linear Motion with Constant Speed/ Velocity
( Record Data in Meters, for example 0.2501-m, and Seconds )
Object
1. Toy Cars
2. Flowing Water
3. Clock Hands
4. Bouncing Ball
Distance
Time
Speed
Average
Distance
Time
Speed
Average
Battery Powered Car
Pull Back Car
400-ml. Beaker
250-ml. Beaker
Wall Clock
Wrist Watch With Second Hand
Tennis Ball
Super Ball
Trial 1
Trial 2
Trial 3
Trial 1
Trial 2
Trial 3
Trial 1
Trial 2
Trial 1
Trial 2
Trial 3
Trial 1
5. Sound
Trial 2
Trial 2
6. Calculate the percentage of error for the speed of sound.
OC
a. air temperature
c. error =
m/sec
b. speed of soundtheo . =
m/sec
d. % error =
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People Walk - Velocity
Purpose: Provide practice in measurement, timing with a
stopwatch, collection of data and graphing.
Directions:
1. Survey your classroom and mark off a walking path, in meters, as long
as possible.
2. Students will be both walkers and timers.
Finish
Start
Student Name
Trial – sec.
1
2
3
Average
seconds
Distance
meters
Speed
m/s
1.
2.
3.
4
5
6.
7.
8.
9.
10.
Average:
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Measuring the Motion of a Toy Car
Objective: To measure the speed and velocity of a toy car.
Materials: track, stopwatch with electronic sensors, racecar with a magnet attached
Purpose: To collect the data to measure velocity.
t0
t1
.50-meters
Finish Point
Starting Point
Procedure:
1. Connect the electronic sensor to the stopwatch and insert one of the sensors into the slot at the starting point and
the second sensor at the finish point or .50-meters from the first sensor. When the racecar is released the magnet
will activate the first sensor, turning on the stopwatch, and when the racecar passes over the second sensor the
stopwatch will be turned off.
2. Release the racecar at the starting line and
obtain the time for .50-meters. Repeat
this procedure until:
a) The vehicle is indeed traveling
with a velocity that can be
reasonably
called
constant,
(uniformly, steadily, in a straight
line)
b) The time for a run should be
about the same for most runs,
(not unusually high or low).
4. Obtain the time for three trials and determine the average time to travel between t 1 and t0.
5. The velocity between t0 and t1 is equal to distance/time or .500-m / (t1 - t0 ).
6. Repeat the experiment using a distance of .350-m. and compare velocities.
Trial 1
Trial 2
Trial 3
Average
Distance
Velocity
Sec.
Sec.
Sec.
Sec.
meters
Meters/sec
.500
.350
7. Graph the three trials using time (sec) on the x-axis and distance (meters) on the y-axis.
8. What does the graph show you? Discuss the results.
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Inertia
Objective: Explain the resistance of a body to change its state of motion.
Materials: battery powered car, one film canisters, C-cell battery
Purpose: Use a battery and a toy racecar to observe inertia.
Procedure:
Part A – Inertia and Balanced Forces
1. Place the film canisters on a solid surface.
2. Place the battery on top on the film canisters.
3. Attach the “string” to the film canister and the racecar as indicated in
the picture. Make sure the string is taut and begin moving the car.
As the car moves the battery and film canister move with the
racecar.
Part B – Inertia and Unbalanced Forces
1. Attach the “string” to the film canister and the racecar as indicated
in the picture.
2.
Start the car moving. The car will be fully accelerated when the
car reaches the end of the string. The racecar will have enough
force to pull the film canister out from under the battery. The
inertia of the battery will cause the battery to remain at rest and
drop straight down to the tabletop immediately, beneath its starting
point.
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Inertia - Using Your Marbles
Objective: Explain the resistance of a body to change its state of motion.
Materials: a marble, two five-ounce paper cups, masking tape, and a yardstick
Purpose: Challenge your friends to move a marble from one paper cup to another without touching either the marble or the
cups. Then show them that it can be done with the help of the force of inertia.
Procedure
1. Cut one cup down so that the sides are about one inch tall.
2. Tape this cup to one end of the yardstick and place the marble in
it.
3. Tape the taller cup about four inches along the yardstick from the
first.
4. Tape the other end of the yardstick to the doorframe at floor
level. The tape forms a hinge so that the stick can be raised.
5. Raise the end of the yardstick until it is about twenty inches
above the floor.
6. You are now ready to move the marble without touching either
cup.
7. Release the yardstick with a light downward push.
The marble should fall into the other cup. How does this come about?
The marble falls in a straight line under the force of gravity. The cups
follow a curved path, as is shown in the diagram. It may take a little practice to push down with the exact force so that the
marble lands in the other cup.
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Newton’s Second Law – Acceleration
Newton's second law relates the mass, acceleration and the forces
acting on a body. Specifically, Newton's Second Law describes what
happens when an unbalanced force is applied to a moving body. The
change in the motion of an object depends upon the size of the force, and
the mass of the object. The greater the unbalanced force on a body, the
greater the acceleration. A smaller acceleration will occur if one were to
increase the mass of the object and used the same unbalanced force. The
change of motion takes place in the same direction as the unbalanced force
acts.
F=mxa
Acceleration occurs when the velocity (direction and speed) of an
object changes. Acceleration is the measure of how much the velocity
changes during a certain period of time. We have analyzed the kind of
motion in which the speed of the moving object was constant during the
entire run (trial). You are familiar with the changing speed of your car in
traffic, as you step on the accelerator to pass a slow moving vehicle. If
you think for a moment about moving objects (cars, birds, bees, etc.), you
will recognize that it is uncommon to actually find objects always moving
at a constant speed. Therefore, the concept of motion with a uniformly
changing speed is a must for studying motion.
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Observing Acceleration – A Toy Car
Objective: To measure the acceleration of a toy car.
Materials: track, stopwatch with electronic sensors, racecar with a magnet attached
.500-meter
.350-meter
.150-meter
t2
t0
t1
B
Starting Point
A
1. Obtain the time for .350-meters distance by connecting the electronic sensor to the stopwatch and inserting one of the
sensors into the slot of the plastic racetrack at the starting point (t 0) and the second sensor at the point (t1) or .350meters from the first sensor. Release the racecar at the starting point (t 0) and record the time. Run three trials. The trails
should be consistent, if they are not, repeat until you obtain consistent times.
2. Obtain the time for .500-meters distance by inserting one of the sensors into the slot of the plastic racetrack at the
starting point (t0) and the second sensor at the point (t2) or .500-meters from the first sensor. Release the racecar at the
starting point (t0) and record the time. Run three trials. The trails should be consistent, if they are not, repeat until you
obtain consistent times.
3. Calculate the time for the .150-meters distance (t1→ t2) by subtracting t1 from t2 (t2- t1).
4. Calculate the average time needed to travel the 0.350-m and the 0.150-m distances.
5. The average velocity (v1) at position A is equal to distance/time or .350-m / t1.
The time to travel between t2 and t1 is: t2 - t1
The velocity (v2) at position B is equal to distance/time or .150-m / (t2 - t1).
6. Calculate the time TA and TB where the average velocity actually occurs.
Time at point A: TA = t1 / 2
Time at point B: TB = (t2 + t1) / 2
7. Calculate the change in velocity (∆v), using: ∆v = (velocity B – velocity A)
8. Calculate the change in time (∆t ) between point B and point A: ∆t = T B - TA
9. Calculate the acceleration of your car, between point A and point B.
a =
∆v / ∆t
0.350-m
t0→ t1
0.500-m
t0→ t2
0.150-m
t1→ t2 (t2- t1)
First time trial time trial
Second time trial
Third time trial
(4) Average Time
(5) Average velocity v = d/t
(6) Time (when average velocity occurred)
v1 for 0.350-m
v2 for 0.150-m
Position A
TA = t1/2
Position B
TB = (t2 + t1) / 2
(7) v = change in adjacent velocity
v= v2 – v1
(8) T = change in time between adjacent velocity
t = TB – TA
(9) a = acceleration between points
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a = v / t
People Walk - Acceleration
Purpose: Provide practice in measurement, timing with a stopwatch, collection of data and graphing involving
acceleration.
Directions:
1. Survey your classroom and mark off a six meter walking path, into two meter segments
2. Have one student be the walker, one student be the starter, and the rest of the students placed at point’s t1, t2, and t3 to be
timers
3. Each trial begins with the starter saying “GO” and all timers start their stopwatches. When the walker passes them they
turn off their stopwatch.
4. The started records all the times on the master sheet and begins the next trial.
A
Start
d = 2.0-m
t1
t0
d = 2.0-m
Data Collection and Analysis
t0
First time trial
Second time trial
0
0
Third time trial
0
Average time
0
Time to travel 2.0 meters
Average velocity v = d / t
(d = 2.0 meters)
C
B
d = 2.0-m
t2
t1
t2
t3
t1 - t0
t2 - t1
t3 - t2
Point. A
V1 = 2.0 / (t1-t0)
Point. B
V2 = 2.0 / (t2-t1)
Point. C
V3 = 2.0 / (t3-t2)
Measuring Changes in Motion © 2009 ScienceScene
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t3
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Point. A
Average time the velocity actually
occurred
T= change in time between adjacent velocity
V= change in adjacent velocity
a (acceleration) = V / T
Point. B
T1=(t0+t1)/ 2
Point. C
T2=(t1+t2) / 2
T3=(t2+t3) / 2
T1 = T2 -T1
T2 = T3 -T2
V1 = V2 -V1
V2 = V3 -V2
a1 = V1 / T1
a2 = V2 / T2
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Acceleration A More Complete Picture
Objective: To measure the acceleration of a trolley from rest to the bottom of an incline.
Materials: track, stopwatch with electronic sensors, racecar with a magnet attached
Purpose: To collect the data to calculate acceleration.
1. This is a large group cooperative project.
2. Timers will be placed at each interval marked on a suspended wire.
3. Start the trolley and all the timers at to when the trolley passes each interval, the timers at that interval must stop
their stopwatches.
4. The timers will average their times, and record that average as a single trial. Repeat to obtain a total of three trials.
5. Calculate the accelerations of your trolley
6. Describe the calculated accelerations and compare them to the actual trolley track.
7. Graph the average of the three trials using time (sec) on the x-axis and distance (meters) on the y-axis.
8. What does the graph show you? Discuss the results.
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t0
Trial #1 0.00
Trial #2 0.00
Trial #3 0.00
1. Av. Time (seconds)
t1
t2
t3
t4
t5
t6
t1 - t0
t2 - t1
t3 - t2
t4 - t3
t5 - t4
t6 - t5
0.00
2. Time to travel 2.00 Meters"
V1=2/(t1-t0) V2=2/(t2-t1) V3=2/(t3-t2) V4=2/(t4-t3) V5=2/(t5-t4) V6=2/(t6-t7)
3. Av. Velocity for 2.00 Meters
T1=(t0+t1)/2 T2=(t1+t2)/2 T3=(t2+t3)/2 T4=(t3+t4)/2 T5=(t4+t5)/2 T6=(t5+t6)/2
4. Av. time velocity Actually occurred
∆T1=T2-T1
∆T2=T3-T2
∆T3=T4-T3
∆T4=T5-T4
∆T5=T6-T5
5. ∆ T = Change in time between adjacent velocity
∆V1=V2-V1 ∆ V2=V3-V2 ∆V3=V4-V3 ∆V4=V5-V4 ∆ V5=V6-V5
6. ∆V = Change in adjacent velocity
A1= ∆V1/∆T1 A2=∆V2/∆T2 A3=∆V3/∆T3 A4=∆V4/∆T4 A5=∆V5/∆T5
7. Acceleration = ∆V / ∆T
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Observing Forces
Objective: To observe the force and its effect on a toy car.
Materials: battery powered toy, bubble level accelerometer used to measure force, 15 cm. string with loop at each end,
suction cup pivot-point, and one student
Purpose: To collect the data to observe the direction of force on a moving car.
Bubble Level
Accelerometer
Procedure:
1. Locate the accelerometer or "force detector" on your car and
observe the bubble in the accelerometer with the car resting
flat on the table. Adjust the accelerometer by bending the
wire so that the bubble is centered. Record your
observation.
2. Release the car. Observe any motion of the bubble in the
accelerometer. Record your observation of the movement of
the bubble for forward movement.
3. Make the car go backwards in a straight line. Observe any motion of the bubble in the accelerometer. Record your
observation of the movement of the bubble for backward movement.
4. To observe the force associated with circular motion:
a. Find a smooth surface approximately 25-cm. in diameter. In the center
of this area attach the suction cup pivot point using a drop of water.
b. Obtain the 15-cm. piece of string, from the kit, with a loop at one end
and a hook at the other end. Attach the hook to the metal loop near the
middle of the car. Loop the other end of the string around the pivot
point.
5. Release the car. Observe any motion of the bubble in the accelerometer.
Record your observation of the movement of the bubble for the circular
motion.
Movement of the Car
Direction of movement of the accelerometer bubble
None
Forward
Backward
Circular
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Finding the Forces
Materials:
1.
set of six arrows
2.
clean paper for drawings
3.
500-gram hooked mass
4.
rubber band
5.
wire spring
6.
platform spring scale
7.
strong laboratory table
8.
sponge or foam rubber
9.
two identical books
10.
meter stick
11.
soy car(powered) or air puck
12.
13.
14.
15.
16.
17.
l8.
19.
20.
21.
22.
graduated cylinder (100 ml)
marble (so fit graduated cylinder)
glycerin (to fill graduated cylinder)
paper towels or coffee filters
washer or coins
scissors
tape
string
3x5card
Hair dryer)
Ping Pong ball
Before you begin, obtain or make a set of six paper or cardboard arrows two short arrows, two medium arrows and two long
arrows. These arrows represent what physicists call “vectors.” These arrows can be labeled to represent various types of
forces. As you do this activity you are to label your arrows to indicate the names of the forces needed to explain your
observations. Use names like gravity, hand, table, etc.
You are to determine all the forces that act on each of the numbered items, and then label and attach the arrows to the item to
show the name, the direction, and the relative size of all forces acting on the item. When physicists draw diagrams like this,
they are called “free body diagrams.” It is customary so place the arrows with the tail of the arrow at the point where the force
is applied to the object or at the center of the object. Physicists call the point ax the center of the object the object’s “center of
mass.” Placing the arrows on real objects in this way is not always possible, but do the best you can.
Obtain several sheets of paper on which to draw a “free body diagram” for each of the activities below.
How do you recognize the presence of forces acting on a particular object?
First, remember that everything that touches an object exerts a force on that object. So the first question to ask is, “What
touches this object?” In addition a few forces (gravity, magnetism and static electricity) act even though they do not touch the
object. Physicists call these non-touching forces “action at a distance.”
Second, remember that if the object is not accelerating the forces must be balanced (i.e. the net force is zero). If the object is
accelerating, then all the forces are not balanced. One way to show an unbalanced situation is so use arrows of different
lengths.
If you would like some background on forces and how to locate them, ask the workshop leader to help you.
The Activities
1a Get a 500-gram booked mass. (We will call it the HM.) Have someone hold it in their outstretched hand. Use the
arrows so indicate all the forces acting on the HM. Care must be taken in all of these activities to distinguish between
the object that the force acts ON. and the source of the force.
1b. What happens to the HM if you push UP harder with your hand? Which arrow (i.e., force) is affected by pushing UP
harder? How was the arrow affected? How should the free-body diagram be changed to show this? What happens to
the HM when you push UP on it harder?
1c. What happens if you quickly remove your hand from under the HM? Which arrow (Le., force) is affected by the
removal of your hand? How was the arrow affected? How should the flee-body diagram be changed to show this?
What was the result of this action on the motion of the HM?
2a. Hang the hooked mass from a rubber band. While you do this watch the shape of the rubber band. Use the arrows to
indicate the forces acting on the HM. What must the rubber band do in order to exert a force on the HM?
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2b Hang the hooked mass from a spring, While you do this watch the shape of the spring. Use the arrows to indicate the
forces acting on the HM. What must the spring do in order to exert a force on the HM?
What is similar about the forces on items (hand, rubber band, and spring supporting the HM in 2a and 2b above?
3a Place the HM on a platform spring scale. Add the arrows representing the forces acting on the HM. What is the
common name for the gravitational force acting on an object?
3b. Attach a string to the HM . Describe the forces acting on the string and HM.
3c. Now release the string and drop the HM. (Please catch it.’) Review what happens when an unbalanced force acts on
the HM. What forces acting on the HM were affected by releasing the string?
4a. Place the hooked mass on a soft sponge or piece of foam rubber. The sponge should be soft and about the size of the
HM. Push the HM with a slight horizontal force. The force you apply should be large enough to affect the sponge,
but not so large as to make the sponge or the HM slide. Add arrows to indicate all the forces acting.
4b. Remove the sponge from under the HM, and let the HM rest on the table. NOW when you push on the HM without
causing it to move, what are the characteristics of the force that is counteracting your push?
You will notice that as you gradually increase the horizontal force you are exerting on the HM, the HM will
eventually start to slide across the table. Can you push the HM so that it moves with constant speed in a straight
line.?
Add arrows to the sliding HM to show all the forces acting on it.. How do the arrows on the sliding HM compare
with the arrows on the stationary HM in part 4a? (This is the last activity with the hooked mass.)
5.
Attach a suing to a toy car or a low-friction air puck or the flying Pig so that it runs in a circle at constant speed on
the table or in the air. Add arrows to indicate the forces acting on it. [Note: Physicists call a force than keeps an
object moving in a circle with constant speed a centripetal force. Centripetal, though, is the name of a direction
(toward the center), not the name of a type of force, so you should not label any of your arrows centripetal force. Use
the name of the type of force].
6.
Place a coin at the edge of the table. Give it a flick with your finger so it hits the floor some distance away. Make a
free-body diagram showing the forces acting on the coin (1) setting on the table, (2) while your finger is in the
process of flicking it and (3) while it is moving through the air.
In 3b. you dropped a 500-gram mass. Compare your diagram for that with the one you just made.
7.
Out of a 3 x 5 card, make a device that allows you to flick one coin at the same time that you simply drop a second
coin. See the diagram below. Make a free-body diagram showing the forces on the coins while they are moving
through the air.
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Circular Motion
The following diagram helps to explain the circular motion of an object. This motion depends on the object’s inertia,
straight line direction the object wants to travel, and the force applied by a string pulling the object towards the
center of the circle.
ID=Inertia direction
ID
ID
CP
R3
IdID
Rx=Resultant of Inertia & Center Pull
ID
D
RIdI
4
D
CP
dir
ect
ion
CP
CP
dir
ect
ion
CP=Center Pull
direction
ID
CP
ID
CP
dir
ect
ion
R2
R1
=
CP
ID
ID
ID
ID = Inertia Direction is really the Inertia an object has at that point. It also wants to travel in that direction at that instant,
especially if it was released at that instant.
CP = Center Pull or better known as centripetal force. This is the force that is directed (towards the center of rotation). The
object is pulled towards the center of rotation, by the string at that instant. This force is the one that keeps the object
traveling in a circle.
R1 R2 R3 R4 etc are the RESULTANT of the object and the direction of the object at that point or instant. This results from
“Force” ID and the “Force” CP acting on the object at that instant.
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Finding the Forces – Teacher Notes
Idea:
> Remember that forces ALWAYS ACT IN PAIRS.
> This activity is designed to help participants learn to identify forces acting on objects.
> It reinforces the idea that objects accelerate when forces are out of balance (or an unbalanced force) is acting on the
object.
> Also objects may move even when one or more forces are acting on it.
Student Background
> Participants should know the definition of acceleration and that acceleration is the result of unbalanced forces.
> They should know that inertia is not a force.
Advance Preparation:
> Get all of the material you will use in your class ahead of time.
Management Tips:
> The workshop is a set of activities in the format of a self paced tutorial.
> Demonstrate making a free-body diagram before participants begin.
> Depending on the group of students, it may be helpful so stop after every few activities for group discussion.
> Regarding activity 5 avoid using the term centripetal force, until you have explained it.
“The force of the string on the car” causes fewer problems.
Points To Emphasize In The Summary Discussion:
>To recognize the presence of forces, remember that everything that touches an object exerts a force on that object.
> If one force acts on an object and it isn’t accelerating, there must be some other force acting on the object to balance
the first.
> Friction is a helpful force, useful for starting and stopping .
> When forces act by contact, there is a stretching, compression or deflection of the objects, even if the amount is too
small to be seen.
> A few forces (gravity, static electricity and magnetism) act even though they do not touch the object.
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Answers For Free Body Diagrams
1a. At Rest
1b. Pushed up 2a. At Rest
1c Acceleration
2a. At Rest
2b. At rest
3a. At Rest
3b. At Rest
3c At Acceleration
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4a. At Rest
4b. Moving With Constant Speed
5. Moving With Constant Speed
but accelerating
6. At rest and Accelerating
7. Accelerating
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Understanding Types of Forces
FOR YOUR INFORMATION
Definitions of Forces
• Force is defined as any influence (push or pull) or (action) that results in accelerating motion or deforming an object.
In the metric unit of measurement it is measured in Newtons.
• Study on FORCES indicate that an object at rest may be acted upon by two or more forces, like the force of a table
and the force of gravity, which all add to zero; inertia is not a force; acceleration is proportional to the net force, not
to the applied force.
• Have you noticed how many different names we have used for forces? Names like net, gravity, the force of the table.
friction, unbalanced force and more. We have developed the habit of naming forces based on their cause. Even net
force is a term that says that the important force is caused by all of the forces acting together.
• We can also described forces in terms of the direction in which they act. We can use directions like up, down, left,
opposite, east, etc. Describing the directions forces act has been so obvious we haven’t had to pay much attention to
the names we used until now.
Types of Force
• If the sum of all the forces acting on an object is zero, then the object is not accelerating. This means that the object
is at rest or is moving with constant velocity.
• A net force is needed to make an object accelerate. When there is a net force acting on an object, the object will
accelerate with an acceleration that is proportional to the force and inversely proportional to the mass of the object.
In addition, the direction of the acceleration will be in the direction of the net force. ( F = m a)
• Forces always come in pairs. These pairs of forces are sometimes called action and reaction. The action force and the
reaction force ALWAYS act on different objects.
• There are only four kinds of forces: 1. the gravitational force, 2. the electromagnetic force, 3. the weak nuclear force
and 4. the strong nuclear force. Only the gravitational force and the electromagnetic force affect objects around us in
ways we are likely to notice.
Circular Forces
• When objects move in straight lines, the directions of the forces acting are constant. But when objects move in
circles, a force acts with a direction that none of the above descriptions fits. This direction is toward the center of
the circle. We call this direction CENTRIPETAL {CEN – TRIP – PET – TAL }.
• Many people mistakenly believe that centripetal force is the name of a the force. The truth is a force toward the
center of the circular path can be caused by a lot of things: gravity causes the centripetal force on the earth as it
orbits the sun, static electricity causes the centripetal force on an electron as it orbits the nucleus of an atom, a string
(held together by electric forces between atoms) causes the centripetal force on something tied to it and swung in a
circle, etc.
• In MOTION it was shown than when an object changes direction, it’s velocity is changing. Acceleration is defined
as something that happens when velocity changes, not just speed. When an object is accelerating, there is a net
force acting. When a net force acts toward the center of a circle, the object moves in a circle. Since a net force is
acting, the object must be accelerating. This is correct even if the object is not changing speed. The direction of a
force that acts toward the center is called ‘centripetal’.
• A force away from the center is called ‘centrifugal’ (CEN-TRIF-U-GAL). Many people mistakenly think that when
an object is moving in a circle, there is a force acting on the object in a direction away from the center of the circle.
They don’t know that inertia is not a force! Although there is the strong sensation that an outward force must act on
an object moving in a circle or turning a corner, the only force that contributes to the circular motion is one that acts
centripetally — toward the center.
Gravitational Force
• All objects attract all other objects with a force called gravitational force.
• The size of the gravitational force is affected by the distance between the objects and the mass of the objects.
• Weight is the force of gravity on an object by the earth when the object is at or near the surface of the earth.
• The force of gravity between the sun and the planets keep the planets from moving through space in straight lines.
The force of gravity between the planets and their moons have the same effect. The shape and relative motions of the
galaxies are the results of the gravitational force. The ultimate fate of the universe is determined by the force of
gravity.
Electromagnetic Force
• Scientists believe that what we usually call electric force and magnetic force are really the same thing.
• Electric forces act on objects when the object carries a net electric charge or a non-uniform distribution of charge.
• The size of an electric force depends on the amount of charge and the distance between the charged objects.
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•
•
•
•
•
•
Magnetic forces are commonly observed between two magnets or between a magnet and some metals.
Magnetic force is also observed around a moving electric charge. In fact, physicists believe that all magnetic forces
are produced by moving charges. (Electrons surrounding some atomic nuclei give rise to the magnetism associated
with permanent magnets.)
Magnetic forces act on moving electric charges.
The size of magnetic forces on a moving charge depends on the amount of moving electric charge, the speed of the
moving electric charge, the direction of the electric charge’s motion relative to the direction of the magnetic field and
the intensity (i.e., strength) of the magnetic field.
The size of magnetic forces between magnets or between a magnet and any object depends on how many “magnetic”
atoms are present in the objects, on how the atoms of the materials are arranged, the exact type of atoms the material
is made of and the distance between the objects.
All other observable forces are manifestations of the electromagnetic force.
Frictional Force
• Frictional forces are often classified as sliding, rolling, static and fluid.
• Sliding and rolling frictional forces result when solids in contact pass by each other. Static frictional force results
when solids are in contact, at rest and when a force or forces are trying to cause them to move with respect to each
other. Fluid frictional force results when a solid is moving through a gas or a liquid.
• Most examples of accelerating objects rely on friction. A car, for example, starts moving, speeds up, turns corners,
slows down and stops only because of friction.
• Our ability to grasp things, to walk and to sit in chairs depends on friction.
• Frictional force often causes the wearing away of surfaces. Lubricants are used to reduce frictional force in many
machines.
• Frictional force causes kinetic energy to be transformed into thermal energy. (The Concorde airliner gets so hot
during normal flight that it expands several inches due to the heating.)
Normal Force
• “Normal” means “perpendicular to”.
• Whenever an object is placed on a surface, a force acts normal to the surfaces in contact. This causes the supporting
surface to sag. Since this sagging is slight, it often goes unnoticed. However, it is always there and the resulting force
of the surface attempting to return to its original position is perpendicular to the surface. This force is called the
normal force.
• The lower surface pushes upwards because its molecules are stretched and/or compressed. The electric forces among
the molecules give rise to the force.
Tension Force
 Tension force is the force exerted by a string, spring, beam or other object which is being stretched compressed. The
electric forces among the molecules give rise to the force.
 The tension force is always directed along the length of the string, beam, etc.
Pressure Is Not A Force.
• Pressure is equal to the force divided by the area over which that force is exerted. (P = F/A)
• Solids, liquids and gases can apply pressure.
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Forces in a Collision
Objective: To observe force and its effect.
Materials: 2 force scales, 2 bathroom scales
Purpose: To collect the data to observe the direction of force.
Procedure:
1. The diagram above shows a child and an adult pushing on each other. (They are holding bathroom scales to measure
the forces exerted.) Predict how they will move. Explain your prediction. (Does the answer depend on who does the
pushing? What if both push at the same time?)
2. Which scale will show the biggest number? (The reading on a scale measures the force acting on the person holding
that scale.)
3. Suppose the situation was slightly different than in the illustration. For each situation below, predict how the
readings on the scales would compare with each other. Explain your predictions.
a. If the adult’s chair was backed up against a wall, how would the readings on the scales compare with each
other?
b. If the child’s chair was backed up against a wall, how would the readings on the scales compare with each
other?
c. If both chairs were backed up against a wall, how would the readings on the scales compare with each
other?
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The Falling Cup
Objective: To observe the force of gravity.
Materials: stool or chair, foam cup, water, wastebasket
Purpose: To collect the data to observe the direction of force.
Procedure:
Before beginning the demonstration, poke a hole in the bottom and/or in the side of the foam cup. Use a heavyweight
foam cup. While covering the holes in the cup, fill it about 3/4 full of water.
Stand on a stool while holding the water-filled cup in one hand and covering the holes with your thumb and forefinger.
While holding the cup, release your fingers, allowing water to flow into a barrel or wastebasket and record your
observations.
Predict what will happen when the cup and the water are dropped.
Drop the cup and the water and record your observations.
Indicate why this happened and suggest one or more reasons for what was observed.
During discussion, point out that all objects fall with the same accelerated motion in the absence of any external
influence. (The water in the cup is massive enough to make the effect of air friction on the cup negligible.) The object in
this case is often called a “freely falling body”. Also point out that no water will flow out when the cup is dropped
because both the water and the cup are falling with the same motion. You might use this opportunity to discuss
weightlessness.
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The Affect of Mass on Acceleration
Objective: Explore the relationship between force, mass, and acceleration
Materials: battery powered car, C-cell battery, rubber band
Purpose: Observe the affect of mass on the acceleration of the car.
Procedure:
1. Place the car on a solid surface.
2. Run the car approximately .50-meter and observe the speed of the car.
3. Place the battery on top of the car. Use the rubber band to hold the battery in place.
4. Start the car and as the car moves observe any change in the speed of the car.
5. Observe and record the difference in speed with the additional mass of the battery and without the additional mass of
the battery.
Observations:
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Newton’s Third Law – Action and Reaction
Newton's third law, expresses the relationship between action force
and reaction force. This law frames the principle that can be observed in a
rocket, in which the backward expulsion of gases causes a reactive force
that drives the payload forward. Newton's Third Law indicates that for
every action, there is an equal and opposite reaction. One example is the
rotating lawn sprinklers that spin when water squirts from their nozzles.
Such sprinklers have two or four arms, and as the water emerges from the
nozzles, the arms are pushed around in the opposite direction spraying
water over the lawn. Another example is stepping out of a boat onto the
dock. You push against the boat, pushing it backwards, as you go forward
onto the dock. Other examples could include the rocket engines of the
space shuttle, shooting a rifle, a released balloon filled with air, a
skateboard and the jet propulsion engine.
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Equal and Opposite
Objective: Explain how one force produces an equal and opposite force
Materials: battery powered car, slippery plastic 8-cm. X 8-cm.
Purpose: To investigate Newton’s Third Law by observing the movement of the slippery plastic as the racecar accelerates.
Slippery
Plastic
Procedure:
1. Crumple the plastic until it looks very wrinkled. (This reduces surface contact and thus less friction)
2. Place the slippery plastic on a solid, flat surface.
3. Place the car on top on the slippery plastic as shown.
4. Start the car and carefully observe the car and the slippery plastic.
5. Write your observations of both the car and the slippery plastic.
Observations:
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Equal and Opposite, another Look
Objective: Explain how one force produces an equal and opposite force
Materials: battery powered car, two soda cans, plastic 8-cm. X 75-cm.
Purpose: To investigate Newton’s Third Law by observing the movement of the slippery plastic as the racecar accelerates.
Procedure:
1. Place two soda cans on a flat surface approximately 25-cm apart.
2. Place the plastic on top of the soda cans.
3. Place the car on top on the plastic as shown.
4. Start the car and carefully observe the car and the plastic.
5. Write your observations of both the car and the slippery plastic.
Observations:
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Appendix 1
Vendor List of Materials Used In Physical Science
1-800-255-6124
Operation Physics Supplier
Arbor Scientific
P.O. Box 2750
Ann Arbor, Michigan
48106-2750
1-800-367-6695
Astronomy
Learning Technologies, Inc.
Project STAR
59 Walden Street
Cambridge, MA 02140
1-800-537-8703
The best diffraction grating I've found
Radio Shack
See Local Stores
Discount Science Supply (Compass)
28475 Greenfield Road
Southfield, Michigan 48076
Phone: 1-800-938-4459
Fax: 1-888-258-0220
Educational Toys
Oriental Trading Company, Inc.
P.O. Box 3407
Omaha, NE 68103
1-800-228-2269
Laser glasses
KIPP Brothers, Inc.
240-242 So. Meridian St.
P.O. Box 157
Indianapolis, Indiana 46206
1-800-832-5477
Rhode Island Novelty
19 Industrial Lane
Johnston, RI 02919
1-800-528-5599
U.S. Toy Company, Inc.
1227 East 119th
Grandview, MO 64030
Mouser Electronics
958 N. Main
Mansfield, TX 76063-487
1-800-346-6873
All Electronics Corp.
905 S. Vermont Av.
Los Angeles, CA 90006
1-800-826-5432
Chemistry
Flinn Scientific Inc.
P.O. Box 219
Batavia, IL 60510
1-708-879-6900
Rainbow Symphony, Inc.
6860 Canby Ave. #120
Reseda, California 91335
1-818-708-8400
Holographic stuff
Electronic Kits
Chaney Electronics, Inc.
P.O. Box 4116
Scottsdale, AZ 85261
1-800-227-7312
Electronic Kits
Lasers
Metrologic
Coles Road at Route 42
Blackwood, NJ 08012
1-609-228-6673
laser pointers
Magnets
The Magnet Source, Inc.
607 South Gilbert
Castle Rock, CO. 80104
1-888-293-9190
Dowling Magnets
P.O. Box 1829/21600 Eighth Street
Sonoma CA 95476
1-800-624-6381
Science Stuff - General
Edmund Scientific
101 E. Gloucester Pike
Barrington, NJ 08007-1380
1-609-573-6270
Materials for making telescopes
Marlin P. Jones & Associates, Inc
P.O. Box 12685
Lake Park, Fl 33403-0685
1-800-652-6733
Flea Markets
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Garage Sales
Motion
©2004
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Appendix 2
Making Formulas Out of Words
SPEED 
CHANGE IN DISTANCE
CHANGE IN TIME
VELOCITY 
CHANGE IN DISTANCE & DIRECTION
CHANGE IN TIME
ACCELERATION 
CHANGE IN SPEED
CHANGE IN TIME
ACCELERATION 
CHANGE IN VELOCITY
CHANGE IN TIME
Note: to make the equation simple we place “  “ in place of the word “change”.
SPEED ( s) 
d
t

s or d
VELOCITY (v ) 
t
ACCELERATION (a ) 
s
t
ACCELERATION (a ) 
v
t
Note: The arrow indicates a change in direction
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Appendix 3
Physical Science Grade Level Content Expectations
K-7 Standard Science Processes
Inquiry Process
S.IP:
S.IP.M.1
S.IP.05.11
S.IP.05.12
S.IP.05.13
S.IP.05.14
S.IP.05.15
S.IP.05.16
Develop an understanding that scientific inquiry and reasoning involves observing, questioning,
investigating, recording, and developing solutions to problems.
Inquiry involves generating questions, conducting investigations, and developing solutions to problems
through reasoning and observation.
Generate scientific questions about motion based on observations, investigations, and research
Design and conduct scientific investigations on motion and changes in motion.
Use tools and equipment (stop watches, meter sticks and tapes, models, balances) appropriate to
scientific investigation of motion.
Use metric measurement devices in the investigation of motion.
Construct charts and graphs from data and observations dealing with motion and changes in motion.
Identify patterns in data regarding motion.
Inquiry Analysis and Communication
S.IA:
S.IA.M.1
S.IA.05.11
S.IA.05.12
S.IA.05.13
S.IA.05.14
S.IA.05.15
Develop an understanding that scientific inquiry and investigations require analysis and communication
of findings, using appropriate technology.
Inquiry includes an analysis and presentation of findings that lead to future questions, research, and
investigations.
Analyze information from data tables and graphs to answer scientific questions on motion.
Evaluate data, claims, and personal knowledge through collaborative science discourse about motion.
Communicate and defend findings of observations and investigations about motion using evidence.
Draw conclusions from sets of data from multiple trials of a scientific investigation on motion and
changes in motion.
Use multiple sources of information on motion and changes in motion to evaluate strengths and
weaknesses of claims, arguments, or data.
Reflection and Social Implications
S.RS:
S.RS.M.1
S.RS.05.11
S.RS.05.12
S.RS.05.13
S.RS.05.15
S.RS.05.16
S.RS.05.17
S.RS.05.19
Develop an understanding that claims and evidence for their scientific merit should be analyzed.
Understand how scientists decide what constitutes scientific knowledge. Develop an understanding of
the importance of reflection on scientific knowledge and its application to new situations to better
understand the role of science in society and technology.
Reflecting on knowledge is the application of scientific knowledge to new and different situations.
Reflecting on knowledge requires careful analysis of evidence that guides decision-making and the
application of science throughout history and within society.
Evaluate the strengths and weaknesses of claims, arguments, and data regarding motion and changes in
motion.
Describe limitations in personal and scientific knowledge regarding motion and changes in motion.
Identify the need for evidence in making scientific decisions about motion.
Demonstrate scientific concepts about motion through various illustrations, performances, models,
exhibits, and activities.
Design solutions to problems concerning the motion of objects using technology.
Describe the effect humans and other organisms have on the balance in the natural world when force is
applied to an object.
Describe how science and technology of motion have advanced because of the contributions of many
people throughout history and across cultures.
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Appendix 4
Physical Science Grade Level Content Expectations
Grade 5 Science Standards, Statements, and Expectations
Students participate in an in-depth study of motion as related to a point of reference, distance, time, and direction.
Their exploration into motion also presents high interest content for students to hone their skills in metric
measurement and the use of tools and equipment appropriate to scientific investigations. The middle school
experiences of investigating balanced and unbalanced forces, and their relationship to the size of change in
motion, provide concrete experiences on which a more comprehensive understanding of force can be based at the
high school level. Students can move from qualitative descriptions of moving objects in the elementary to
quantitative descriptions of moving objects and the identification of the forces acting on the objects. The
completion of the study in motion involves the exploration and identification of contact and non-contact forces
and how they change the motion of objects. Students’ everyday experiences in motion lead them to believe that
friction causes all moving objects to slow down and stop. In-depth explorations into reducing the force of friction
can help the students understand and demonstrate that a moving object requires friction to keep it moving. The
understanding of objects at rest requires the students recognize that there are balanced forces in equilibrium, such
as a book on a table or chair on the floor.
Force and Motion
P.FM:
P.FM.05.21
P.FM.05.22
P.FM.M.3
P.FM.05.31
P.FM.05.32
P.FM.05.33
P.FM.05.34
P.FM.M.4
P.FM.05.41
P.FM.05.42
P.FM.05.43
Force Interactions - Some forces between objects act when the objects are in direct contact
(touching), such as friction and air resistance, or when they are not in direct contact (not
touching), such as magnetic force, electrical force, and gravitational force..
Distinguish between contact forces and non-contact forces.
Demonstrate contact and non-contact forces to change the motion of an object.
Force- Forces have a magnitude and direction. Forces can be added. The net force on an
object is the sum of all of the forces acting on the object. The speed and/or direction of
motion of an object changes when a non-zero net force is applied. A balanced force on an
object does not change the motion of the object (the object either remains at rest or continues
to move at a constant speed in a straight line).
Describe what happens when two forces act on an object in the same or opposing directions.
Describe how constant motion is the result of balanced (zero net) forces.
Describe how changes in the motion of objects are caused by a non-zero net (unbalanced)
force.
Relate the size of change in motion to the strength of unbalanced forces and the mass of the
object.
Speed- Motion can be described by a change in position relative to a point of reference. The
motion of an object can be described by its speed and the direction it is moving. The position
and tempo of an object can be measured and graphed as a function of time.
Explain the motion of an object relative to its point of reference.
Describe the motion of an object in terms of distance, time and direction, as the object
moves, and in relationship to other objects.
Demonstrate how motion can be measured and represented on a graph.
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Appendix 5
Grade 5 Grade Level Mathematics Expectations
Measurement
N.ME.05.08 Understand the relative magnitude of ones, tenths, and hundredths and the relationship of each
place value to the place to its right.
N.ME.05.15
N.FL.05.16
Multiply a whole number by powers of 10: 0.01, 0.1, 1, 10, 100, 1000, and identity patterns.
Divide numbers by 10’s,100’s, 1000’s using mental strategies.
M.UN.05.03
Compare the relative sizes of one cubic inch to one cubic foot, and one cubic centimeter to one
cubic meter.
M.UN.05.04
Convert measurements of length and weight within a given system using easily manipulated
numbers.
D.RE.05.01
Read and interpret line graphs, e.g., distance-time graphs.
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