Activity 2 Newton’s Law of Universal Gravitation€¦ · · 2011-11-03with your small group and the class. For You To Do 1.Place a projector 0.5 m from the ... 1 25 1 52 1 32

258Active Physics

Patterns and Predictions

What Do You Think?Astronauts on many Shuttle flights studythe effects of zero-gravity. Fish taken aboardthe Shuttle react to “zero-gravity” byswimming in circles.

• How would a fish's life be different without gravity?

• Does gravity hold a fish “down” on Earth?

Record your ideas about these questions in your Active Physics log. Be prepared to discuss your responseswith your small group and the class.

For You To Do1. Place a projector 0.5 m from the

chalkboard. Insert a blank slide. Turn onthe projector.

2. Use chalk to trace around the square oflight on the board.

GOALSIn this activity you will:

• Explore the relationshipbetween distance of a lightsource and intensity of light.

• Graph and analyze therelationship between distanceof a light source and intensityof light.

• Describe the inverse squarepattern.

• Graph and analyze gravitydata.

• State Newton’s Law ofUniversal Gravitation.

• Express Newton’s Law ofUniversal Gravitation as amathematical formula.

• Describe dowsing and statewhy the practice is notconsidered scientific.

Activity 2 Newton’s Law of Universal Gravitation

CS_Ch5_Predictions 2/24/05 8:08 PM Page 258

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3. Place the photocell in one corner of the light square. Attach it to the galvanometer as directed by your teacher.The photocell and galvanometer measure light intensity. The more light that strikes the cell, the greater the currentreading on the galvanometer.

a) Copy the table below in your log. Record the distance tothe board, current in galvanometer, and length of a side of the square.

4. Move the projector to a position 1 m from the board. Adjustthe projector so that the original square of light sits in onecorner of the new square of light.

a) Enter the data into the table in your log.

5. Repeat Step 4 with the projectorat distances of 1.5 m, 2 m, 2.5 m,and 3 m.

a) Enter the data into the table inyour log.

6. Graph the current in thegalvanometer versus distance.Label this graph Graph 1.

a) Is Graph 1 a straight line? b) What does a straight line on

the graph tell you?

First square of light

Second square of light

Galvanometer

Photocell

Distance to Distance Current in Side of Area ofboard (m) squared galvanometers (A) square (cm) 2square (cm )


260Active Physics


7. Light intensity decreases with distance as the light from thesource spreads out over larger areas. The light is literallyspread thin. The light intensity at any one spot increases asthe area gets smaller and decreases as it gets larger. Thisobservation is an example of a pattern called the inversesquare relation. In an inverse square relation, if you double thedistance the light becomes or as bright. If you triple the distance, the light becomes or as bright. If you increase the distance by 5 times, the light becomes

, or as bright. If you increase the distance by 10 times,the light becomes , or times as bright.

a) How closely does your data reflect an inverse squarerelation?

8. Compute the distances from the center of the Earth (6400 km below sea level). Plot these distances vs.acceleration in a graph. Draw the best possible curve throughthe points on the graph. Label this graph Graph 2.

a) Does the data form a pattern?

b) Is the pattern familiar to you? Give evidence for yourconclusion.

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19

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Acceleration Due tothe Earth’s Gravitational Field at Different Heights

Height above Acceleration due Sea Level (km) to Gravity (m/s2)

0 9.813.1 9.7611 9.74160 9.30400 (Shuttle orbit) 8.651600 6.248000 1.9216,000 0.7936,000 (geosynchronous orbit for 0.23

communications satellite)385,000 (orbit of the Moon) 0.003

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Physics Wordsacceleration: the changein velocity per unit time.

gravity: the force ofattraction between twobodies due to theirmasses.

Inverse square relation:the relationship of a forceto the inverse square ofthe distance from themass (for gravitationalforces) or the charge (forelectrostatic forces).




FOR YOU TO READ

An Important Pattern

You’ve seen one pattern in this activity.But you’ve seen it in two different ways. InSteps 1 through 8 you found that light intensitybecomes less as the light source is movedfurther away. In Step 7, you’ve seen thatacceleration due to gravity becomes less asan object moves further from the surface of theEarth. Both are examples of the inversesquare relation. Although light is not a force,the effect of distance on its behavior in thisactivity is like that of the effect of distance onthe force of gravity.That is, the behavior of lightin this activity is analogous to the behavior ofgravity. In simple terms for gravity, the inversesquare relation says that the force of gravitybetween two objects decreases by the square ofthe distance between them.

Mapping the Earth’s GravitationalField

In Activity 1, you mapped the magnetic fieldaround a bar magnet using a compass as aprobe.You also read about electric fields. In thisactivity, you used data on acceleration due togravity to map the Earth’s gravitational field.Theprobe is the acceleration of a falling mass.To seethe pattern of Earth’s gravitational field, youneeded data from satellites. The gravitationalfield changes very slowly near the surface of theEarth.The pattern is very difficult to see usingsurface data.

Newton’s Law of Universal Gravitationdescribes the gravitational attraction of objectsfor one another. Isaac Newton first recognizedthat all objects with mass attract all otherobjects with mass.

Experiments show that objects have mass andthat the Earth attracts all objects. Newtonreasoned that the Moon must have mass, andthat the Earth must also attract the Moon. Hecalculated the acceleration of the Moon in itsorbit and saw that the Earth’s gravity obeyedthe inverse square relation. It is a tribute toNewton’s genius that he then guessed that notonly the Earth but all bodies with mass attracteach other.

Almost 100 years passed before Newton’s idea that all bodies with mass attract all other bodies with mass was supported byexperiments.To do so, the very smallgravitational force that small bodies exert onone another had to be measured. Because thisforce is very small compared to the force ofthe massive Earth, the experiments were verydifficult. But in 1798, Henry Cavendish, aBritish physicist, finally measured thegravitational force between two masses of afew kilograms each. He used the tiny twist of aquartz fiber caused by the force between twomasses to detect and measure the forcebetween them.

Newton’s Law of Universal Gravitationstates:

All bodies with mass attract all otherbodies with mass.

The force is proportional to the productof the two masses and gets stronger aseither mass gets larger.

The force decreases as the square of the distances between the two bodiesincreases.

➔


262Active Physics


Physics and Dowsing: ComparingForces

Dowsing is a way some people use to locateunderground water. It is claimed to work on anapparent “attraction” between running waterand a dowsing rod carried by a person.Alldowsers claim to feel a force pulling the rodtowards water, and many claim to feel unusualsensations when they cross running water. Inthe 19th century, many dowsers described the force on the rod as an electric force. Noevidence supports this idea. In fact, there is no scientific theory to explain any attractionbetween running water and a dowsing rod.

Despite the skepticism of the scientificcommunity about dowsing, it is widely used in the United States. Even a national scientificlaboratory has used dowsers! But the UnitedStates Geological Survey has investigateddowsing and finds no experimental evidencefor it. Statistics show that the success ratecould be a result of random events. Even ifexperimental evidence supported the successof dowsing, there is no theory to predict itsoperation. In order to be accepted as scientific,a phenomenon must be reproducible in carefulexperiments. Its effects must be predictable bya theory.Also, the theory must give rise toother predictions that can be tested byexperiments.

PHYSICS TALK

Newton’s Law of Universal Gravitation inMathematical Form

Complex laws like Newton’s Law of Universal Gravitationmay look easier in mathematical form. Let FG be the forcebetween the bodies, d be the distance between them, m1 and m2 the masses of the bodies and G be a universalconstant equal to 6.67 � 10-11 N•m2/kg2.

You can express Newton’s Law of Universal Gravitation as

FG =

You can see that the equation says exactly the same thingas the words in a much smaller package.

G m1m2

d2



Reflecting on the Activity and the ChallengeIn this activity you determined experimentally how lightintensity varies with distance. By plotting measured data, youfound that gravity follows an identical pattern. You detectgravity by measuring the acceleration of objects falling atspecific locations. Patterns help you understand the worldaround you. Light follows the inverse square relation and sodoes gravity. You can detect gravity with masses. You can detectmagnetic fields with compasses. But you cannot detect the“attraction” claimed by dowsers. There are no detectors for that!You will be required in the Chapter Challenge to differentiatebetween the measured gravity and its inverse square nature andthe dowser’s claim of measurement. This activity helped you tounderstand one difference between science and pseudoscience.

Physics To Go1. How would the light intensity of a beam from a projector

1 m from a wall change if the projector was moved 50 cmcloser to the wall?

2. The gravitational force between two asteroids is 500 N. Whatwould the force be if the distance between them doubled?

3. A satellite sitting on the launch pad is one Earth radiusaway from the center of the Earth (6.4 � 106 m).

a) How would the gravitational force between them bechanged after launch when the satellite was two Earthradii (1.28 � 107 m) from the center of the Earth?

b) What would the gravitational force be if it was 1.92 � 107 mfrom the center of the Earth?

c) What would the gravitational force be if it was 2.56 � 107 mfrom the center of the Earth?

4. Why does everyone trust in gravity?

5. Why doesn’t everyone trust in dowsing?




264Active Physics

6.

a) Which is closer to the Moon, the middle of the Earth or thewater on the side of Earth facing the Moon?

b) Use your answer to a) to propose an explanation for theuneven distribution of water on Earth’s surface, as shownin the diagram.

c) Suggest an explanation for high tides on the side of theEarth facing the Moon.

Stretching Exercises1. To locate underground water, a dowser uses a Y-shaped stick

or a coat hanger bent into a Y. The dowser holds the Y by itstwo equal legs with the palms up and elbows close to his orher sides. The long leg of the Y is held horizontal. The dowserwalks back and forth across the area he or she is searching.When he or she crosses water, the stick jerks convulsively and twists so hard that it may break off in the dowser’shands. Dowsers claim to be unaware of putting any force onthe stick. Most observers think that the motion of the stick is probably due to the unconscious action of the dowser.

According to records of those who believe in dowsing,approximately 1 in 10 people should have the ability to dowse. Do you have dowsing ability? Try this activity to findout. Can you prove that you’re a dowser to a classmate? Whatwould constitute proof?

2. Does the inverse square relation apply to magnetic force?Work with your group to plan an experiment to find out. State your hypothesis, and describe the method to test it.If your teacher approves your experimental design, try it.Report your results to the class.


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Activity 2 Newton’s Law of Universal Gravitation€¦ · · 2011-11-03with your small group and the class. For You To Do 1.Place a projector 0.5 m from the ... 1 25 1 52 1 32