Gravitation Simulation 4b856

Finding the Universal Gravitational Constant

Name:

Emily Krivak

The simulations used for this activity can be accessed in the any of the following ways.   

and run the Java files from Moodle Follow the links to the PHET website that is posted in Moodle Use these links… http://phet.colorado.edu/sims/html/gravity-force-lab/latest/gravity-force-lab_en.html http://phet.colorado.edu/sims/gravity-and-orbits/gravity-and-orbits_en.jnlp

Introduction The gravitational attraction between any two objects can be found using Newton’s Universal Law of Gravitation:

….if solved for G… This is a very simple, yet accurate, formula that demands a few minimal approximations.  Both masses are treated as point masses (not too far off when compared to the distances involved)  “r” is the distance between the centers of the object (doesn’t matter with point masses)  “G” is not the same as “g”. It is not approximately 9.81 m/s2. “Big G” is called the universal gravitational constant, while “small g” is the acceleration that gravity induces on a freely falling object at the surface of a planet. The purpose of this activity is to use a gravity and orbit simulation to calculate the value of G. Part 1: Finding G with the Gravity Force Lab Change the mass and distance values for a broad mixture of situations, completing the first 4 columns of the chart below. Then use the formula to calculate the value of G for each trial. (Note: you can move the ruler to measure the distances.) Mass Object 1 (kg)

Mass Object 2 (kg)

Distance (m)

Force (N)

Gravitational Constant, G

38

100

5

1.1019x10-8

6.70394737x10-11

11

6

3

4.8x10-10

6.54545455x10-11

16

10

7

2.2x10-10

6.7375x10-11

83

22

6

3.34x10-9

6.58488499x10-11

6.64294673x10-11 Calculate the average value of G from the table………………………………………

Look up the accepted value for G and place it here (including units)

6.67259 x 10-11 N m2/kg2

Now, use the simulation to answer the following questions. (Drag the circle over you answer and resize it.) 1. Gravitational force is always……..

attractive / repulsive.

2. IF a gravitational force exists between two objects, one very massive and one less massive, then the force on the less massive object will be….

greater than / equal to / less than

……the force

on the more massive object. 3. As the distance between masses decreases, force…….

Increases / decreases.

4. Doubling the mass of one object would result in the change in force of ….

4x / 2x

/ no change / (1/2) x / (1/4) x

5. Doubling the distance between two objects will change the force of….

4x / 2x

/ no change / (1/2) x / (1/4) x

Part 2: Gravity and Orbits Simulation This part of the activity uses a different simulation. Be certain you switch to the new simulation or the questions will not make sense. Run several orbit simulations, changing the settings as needed, to answer the following questions. 6. In what direction is the gravitational force of the orbiting object oriented?

Counterclockwise

7. In what direction is the velocity of the orbiting object oriented?

Counter clockwise, away from the sun and Earth

8. If you turn gravity off, what happens? Why does this happen?

Earth goes towards the velocity, it stops revolving around the sun. This happens because Earth revolves around the sun because of gradational force.

9. If you increase the mass of the Sun, what happens to the Earth?

It gets pulled closer to the sun. But if the sun gets too big than the Earth hits it and explodes. 10. If you decrease the mass of the Sun, what happens to the Earth?

Its path is father out than as before.

11. Click on the Earth/satellite button. Increase the speed of the satellite. What happens? Explain. (You can move the satellite or change its velocity by dragging each with the mouse – pause first)

It falls out of orbit. This happens because it goes too fast for how much gravitational attraction it has with Earth.

12. Decrease the speed of the satellite. What happens? Explain.

It hits the Earth. It does this because with less speed, the gravitational force pulls it in more.

13. Move the satellite. Describe what happens. Can you create a stable orbit further from the Earth? How did you do it?

It goes off the screen. Yes, you have to make the Earth bigger and the satellite smaller.

14. Change the mass of the satellite only. Will this change the orbit of the satellite? Why or Why not? Explain what happens. (Use the slider at the bottom right.)

It does not change the orbit of the satellite. What happens is that the satellite follows the same path no matter what size. This happens because the big G is the same (6.673x10-11 Nm2/kg2) no matter the size of the object.

15. The mass of the moon is 7.35x1022kg and the mass of the earth is 5.97x1024kg. The moon’s orbit distance is 3.84x108m. What is the gravitational force on the moon by the earth? What is the gravitational force of the earth on the moon? (Calculate it using the equation)

F=[Gm1m2]/d2 F= [(6.673x10-11)(5.97x1024)(7.35x1022)]/(3.84x108)2 =1.99x1020N

16. What is the centripetal acceleration of the moon around the earth, realizing that the gravitational force is the centripetal force? (Assume the orbit is circular and calculate it… Fc=mac)

Fc=mac 1.99x1020=(7.35x1022)ac ac=.002707483m/s2

17. What is the speed of the moon as it travels around the Earth? (Calculate it… ac=vt2/r)

ac=(Vt2)/r .002707483=(Vt2)/1.738x106 4705.605454=Vt2 Vt=68.5974158m/s