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The MAPs TeamMeaningful Applications Of Physical Sciences

Dr. Michael H. SuckleyMr. Paul A. Klozik

Materials in this manual are based upon the Operation Physics program funded in part by the National Science Foundation. All material in this book not specifically identified as being reprinted from another source is protected by copyright. Permission, in writing, must be obtained from the publisher before any part of this work may be reproduced in any form or by any means.

Participants registered for this workshop have permission to copy limited portions of these materials for their own personal classroom use.

Motion

I. Introduction..................................................3

II. Newton’s First Law.....................................4 A. Motion........................................................5

1. Observing Motion.............................................52. Measuring the Velocity of Various Objects.......6

B. Inertia1. Fundamentals....................................................92. Using Your Marbles....................................10

III. Newton’s Second Law ...............................11A. Acceleration (change in velocity)

1. Observing Acceleration....................................122. Acceleration A More Complete Picture............13

B. Fundamentals of Force1. Observing Forces (using the “Gizmo”) ....................142. Finding The Forces..........................................153. Types of Force.................................................244. Forces in a Collision..........................................265. The Falling Cup................................................27

C. The affect of Mass on Acceleration ............28

IV. Newton’s Third Law..................................29 A. Equal and Opposite.....................................30B. Equal and Opposite Another Look..............31

V. Appendix .....................................................32A. Vendor ListB. Making Formulas Out of Words

Motion ©2004 ScienceScene

An object stays at rest or continues

to move in a straight line at a constant speed

unless acted on by a force.v = d / t

Every action has an equal and opposite

reaction.f1 = f2

When a force acts on a moving object, it will

accelerate in the direction of the force dependent

on its mass and the force. F = m x a

I. IntroductionIsaac 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.


http://encarta.msn.com/find/Concise.asp?z=1&pg=2&ti=761556362

II. 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


Finish Point Starting Point.50-meters

t0t1

Observing Motion

Objective: To measure the speed and velocity of a toy car.Materials: track, stopwatch with electronic sensors, racecar with a magnet attachedPurpose: To collect the data to measure velocity.

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 t1 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 1Sec.

Trial 2Sec.

Trial 3Sec.

AverageSec.

Distancemeters

VelocityMeters/sec

.500

.350


Measuring the Velocity Of Various Object1. 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.

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.


aa

L3=

L2 =

L 1=

L0=

10

9

8

7

6

5

4

3

2

1

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

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.


X1 X2 X2 X3

Linear Motion with Constant Speed/ Velocity

( Record Data in Meters, for example 0.2501-m, and Seconds )

Object Distance Time Speed Average Distance Time Speed Average

1. Toy Cars

Battery Powered Car Pull Back CarTrial 1

Trial 2 Trial 3

2. Flowing Water

400-ml. Beaker 250-ml. BeakerTrial 1

Trial 2 Trial 3

3. Clock HandsWall Clock Wrist Watch With Second Hand

Trial 1

Trial 2

4. Bouncing Ball

Tennis Ball Super BallTrial 1

Trial 2 Trial 3

5. SoundTrial 1

Trial 2 Trial 2

6. Calculate the percentage of error for the speed of sound.

a. air temperature OC b. speed of soundtheo . = m/sec

c. error = m/sec d. % error =


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 Forces1. 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.


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 yardstickPurpose: 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.

Procedure1. 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.


III. 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 = m x a

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.


Observing Acceleration

Objective: To measure the acceleration of a toy car.Materials: track, stopwatch with electronic sensors, racecar with a magnet attached

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 (t0) and the second sensor at the point (t1) or .350-meters 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 = TB - 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 v1 for 0.350-m v2 for 0.150-m

(6) Time (when average velocity occurred)

Position ATA = 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 a = v / t

Acceleration A More Complete PictureMotion ©2004 ScienceScene

Starting PointABt0t1

t2

.350-meter.150-meter.500-meter

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 attachedPurpose: To collect the data to calculate acceleration.

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 trolley6. Describe the calculated accelerations and compare them to the actual trolley track.


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 studentPurpose: To collect the data to observe the direction of force on a moving car.

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


Bubble LevelAccelerometer

Finding The Forces

Materials: 1. set of six arrows 12. graduated cylinder (100 ml)2. clean paper for drawings 13. marble (so fit graduated cylinder)3. 500-gram hooked mass 14. glycerin (to fill graduated cylinder)

4. rubber band 15. paper towels or coffee filters5. wire spring 16. washer6. platform spring scale 17. scissors7. strong laboratory table l8. tape8. sponge or foam rubber 19. string9. two identical books 20. 3x5card

10. meter stick 21. helium-filled balloon (optional) 11. soy car(powered) or air puck 22. skate board (optional)

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 lettered 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 wows 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

A. 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.

What happens to the HM if you push harder with your hand? Which arrow (i.e., force) is affected by pushing 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 on it harder?

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?

B. 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?


C. 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?

D. Please note that the rubber band in part B above and the spring in part C above exert force on the NM by stretching. Hang the hooked mass from a string. While you do this watch the shape of the string. What must be doing the stretching to support the HM now?

What is similar about the items (hand, rubber band, spring and string) supporting the HM in A - D above?

in B (rubber band), and C (spring)?

in B (rubber band), C (spring), and D (string)?

in A (hand), B (rubber band), C (spring), and D (string)?

E. Release the string to drop the HM. (Please catch it.’) Review what happens when an unbalanced force acts on the HM. What force acting on the HM was affected by releasing the string?

F. Place two books about a meter apart so that a meter stick can be placed across them making a bridge. Place the hooked mass in the middle of the meter stick. The meter stick should be visibly deflected. Add arrows to indicate the forces acting on the HM. Remove the NM and you should no longer be able to detect the deflection of the meter stick. Is the meter stick still deflected when the HM is not on it, and you cannot see any deflection? Imagine that the meter stick is a steel beam, with the HM on it. Would you expect to see the beam deflect? Would the beam deflect?

G. 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?

H. This activity is designed to illustrate the deflection of a apparently rigid support such as the steel beam mentioned in activity E. Make a pendulum from a washer and a piece of string. Suspend the pendulum over the edge of a strong table. When the pendulum swings it should just miss hitting the floor. One way to assure this is to place a piece of paper on the floor, and then adjust the length of the string until the washer just touches the paper. When this is accomplished, tape the string in place and remove the paper. Now swing the pendulum. Have someone stand on the table at the point where the pendulum is suspended. Be sure that the pendulum is going back and fourth and not in an oval. Observe the behavior of the pendulum. What does this observation tell you about the table when it is supporting a cylinder? Add arrows to indicate the forces acting on the person standing on the table. Add arrows to the table showing the forces acting on it.

Place the HM on the table. Add arrows to illustrate the forces acting on the cylinder.

What is similar about the items supporting the cylinder in: F (meter stick), 0 (spring scale), and H (table)?

I. 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 alight 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.


J. Remove the sponge from under the HM, and let the HM rest on the table. Repeat activity I above. 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. Push the HM so that it moves with constant speed in a straight line.

Add arrows so the sliding HM to show all the forces acting on ii. How do the arrows on the sliding HM compare with the arrows on the stationary HM in parts H and I? (This is the last activity with the hooked mass.)

K. Run a toy car or a low-friction air puck across the table. It should move at a constant velocity. Add arrows to indicate the forces acting on ii.

L. Attach a suing to a toy car or a low-friction air puck so that it runs in a circle at constant speed on the table. 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]

M. Drop a marble into a graduated cylinder nearly rifled with glycerin. Determine whether the marbles have a constant speed as they fall. Since you can’t attach the arrows to the marble in the graduated cylinder, just make the drawing on the last pages of this activity indicating the names, directions, and relative sizes of all the forces acting on the marble as it falls through the glycerin.

N. Make a parachute from a paper towel. Use a washer or other appropriate item to make a paratrooper. (Or use a basket-type coffee filter, in which case you don’t need a paratrooper.) Drop the parachute and determine if it falls with constant speed. On the last pages of this activity, make the drawing of the forces acting on the parachute.

O. 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 part D you dropped a 500-gram mass. Compare your diagram for that with the one you just made for (iii).

P. 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.


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 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 CF (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.


ID=Inertia Rx=Resultant of Inertia & Center PullCP=Center

IDD IdID

CP direction

R4

ID

ID

ID

ID

ID

ID

ID

CP

CP

CP

CP

R1

=

R2

R3 CP direction

CP direction

Finding The Forces – Teacher Notes

Idea: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 and that objects may move even when one or more forces act.

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 form

Advance Preparation:Check the table intended to be used in part h to make sure it sags enough.The hooked mass can be used here instead of a washer.

Management Tips:The workshop is a set of activities in the format of a self paced tutorial. Instructions for making a low-friction air puck for K and L are found in the appendixFlat-bottomed coffee filters work as well as parachutes.Demonstrate making a free-body diagram before participants begin. Depending on the group of teachers, it may be helpful so stop after every few activities for group discussion.Regarding activity L, avoid using the term centripetal force. “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 (activities Q and R), and more.

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.

Objects can move without a force pushing them along (K and L, especially if an air puck was used).

A few forces (gravity, static electricity and magnetism) act even though they do not touch the object.

Possible Extensions:For activity F, you may graph the observed deflection verses the amount of weight applied using several different masses. This can also be done with a spring balance used to pull down on the meter stick.


Answers For Free Body DiagramsA. At Rest B. At Rest

C. At Rest D. At Rest

E. Acceleration F. At Rest

G. At Rest H. At Rest


I. At Rest J. Moving With Constant Speed

K. Moving With Constant Speed L. Moving With Constant Speed But Accelerating

M. Moving With Constant Speed N. Moving With Constant Speed

O. At Rest and Accelerating P. Accelerating


Q. Accelerating R. Accelerating

S. At Rest T. Moving With Constant Speed


Understanding ForcesFOR 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.


• 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.


Forces in a Collision

Objective: To observe force and its effect.Materials: 2 force scales, 2 bathroom scalesPurpose: 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?


The Falling Cup

Objective: To observe the force of gravity.Materials: stool or chair, foam cup, water, wastebasketPurpose: 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.

The Affect of Mass on Acceleration

Objective: Explore the relationship between force, mass, and accelerationMaterials: battery powered car, C-cell battery, rubber bandPurpose: 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:

Motion ©2004

IV. 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.

Motion ©2004

Equal and Opposite

Objective: Explain how one force produces an equal and opposite forceMaterials: 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.

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:

Motion ©2004

Slippery Plastic

Equal and Opposite, Another Look

Objective: Explain how one force produces an equal and opposite forceMaterials: 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:

Motion ©2004

Appendix A Vendor List Of Materials Used In Physical Science

Operation Physics SupplierArbor ScientificP.O. Box 2750Ann Arbor, Michigan

48106-27501-800-367-6695

Astronomy Learning Technologies, Inc.Project STAR59 Walden StreetCambridge, MA 021401-800-537-8703

The best diffraction grating I've found

ChemistryFlinn Scientific Inc.P.O. Box 219Batavia, IL 605101-708-879-6900

Discount Science Supply (Compass)28475 Greenfield RoadSouthfield, Michigan 48076Phone: 1-800-938-4459Fax: 1-888-258-0220

Educational ToysOriental Trading Company, Inc.P.O. Box 3407Omaha, NE 681031-800-228-2269

Laser glasses

KIPP Brothers, Inc.240-242 So. Meridian St.P.O. Box 157Indianapolis, Indiana 462061-800-832-5477

Rainbow Symphony, Inc. 6860 Canby Ave. #120Reseda, California 913351-818-708-8400

Holographic stuff

Rhode Island Novelty19 Industrial LaneJohnston, RI 029191-800-528-5599

U.S. Toy Company, Inc.1227 East 119th Grandview, MO 640301-800-255-6124

Electronic Kits

Chaney Electronics, Inc.P.O. Box 4116Scottsdale, AZ 852611-800-227-7312

Electronic Kits

Mouser Electronics958 N. MainMansfield, TX 76063-4871-800-346-6873

All Electronics Corp.905 S. Vermont Av.Los Angeles, CA 900061-800-826-5432

Radio ShackSee Local Stores

LasersMetrologicColes Road at Route 42Blackwood, NJ 080121-609-228-6673

laser pointers

MagnetsThe Magnet Source, Inc.607 South GilbertCastle Rock, CO. 801041-888-293-9190

Dowling MagnetsP.O. Box 1829/21600 Eighth StreetSonoma CA 954761-800-624-6381

Science Stuff - General Edmund Scientific101 E. Gloucester PikeBarrington, NJ 08007-13801-609-573-6270

Materials for making telescopes

Marlin P. Jones & Associates, IncP.O. Box 12685Lake Park, Fl 33403-06851-800-652-6733

Flea Markets

Garage Sales

Motion ©2004

Appendix B MAKING FORMULAS OUT OF WORDS

Note: to make the equation simple we place “ “ in place of the word “change”.

Note: The arrow indicates a change in direction

Motion ©2004

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