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Universal Gravitation Test

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Universal Gravitation
Objectives
* Compare and contrast gravitational force vectors as mass and distance are changed. (Explorations 1, 2, and 3) * Discover how changes in the distance between two objects affects the gravitational force between them. (Explorations 1, 2, and 3) * Describe how changes in the masses of two objects affects the gravitational force between them. (Explorations 1, 2, and 3)
Description of Activity
In this activity, you will explore how distance and mass affect the gravitational force between two objects. You will select one of three locations to work within: a 9 m2 room, a 9 × 104 m2 city block, or a 9 × 1022 m2 region of space. You will also change the mass of each object as well as manipulate the positions of both objects. For purposes of this simulation, masses will be represented as spheres and the distance between them will be the distance between their centers.
Jump Start 1. What is mass?
Mass is the amount of matter an object has.

2. Describe gravitational force.
Gravitational force is the force of attraction between all masses in the universe; especially the attraction of the earth's mass for bodies near its surface. 3. How can you tell if one variable is directly proportional to another variable?
Two variables are said to be directly proportional if an increase or decrease in one variable causes simultaneous increase or decrease in another variable.

4. How can you tell if one variable is inversely proportional to another variable?
If one goes up as the other goes down (or vice versa) they are inversely proportional.

5. Write Newton’s law of universal gravitation as an equation.
Solving for gravitational force exerted between two objects.
F = G (m1 * m2) / d2

Exploration 1: Gravitational Interactions in a Room
Procedure
1. Spend several minutes exploring the laboratory and manipulating the variables. Select Scenario 1. Set both m1 and m2 to 10.0 kg, the approximate mass of a one-year-old child. Place the objects 1.50 m apart. 2. Observe the gravitational force vectors on the masses. Sketch these as observations. 3. Move the objects to 2.00 m apart, and sketch the gravitational force vectors again. 4. Change the distance to 2.50 m apart, and sketch the gravitational force vectors again. 5. Repeat steps 1–4, but increase m1 or m2 to 40.0 kg, roughly the mass of a sixth grader.

Observations and Analysis 1. In what direction do the gravitational forces act?
The force is stronger when the objects are closer and smaller when they are farther. 2. Describe the relationship between gravitational force and distance.
The gravitational force is directly proportional to the mass of the bodies and is inversely proportional to the square of the distance between them. 3. Did replacing one of the 10.0−kg masses with a 40.0−kg mass have any effect?
Yes…. The force of gravity improved to 40.3

Exploration 2: Interaction of Masses on a City Block
Procedure
1. Select Scenario 2. Study the gravitational force acting between two 2.0 × 107−kg objects (each represents the approximate mass of a house). Set the two “houses” 100 m, 150 m, and 200 m apart. Sketch the gravitational force vectors each time. 2. Investigate the gravitational force acting between a 2.5 × 107- kg “house” and a 2.0 ×
108−kg “house” with the same distances as step 1. Sketch the gravitational force vectors each time.

Observations and Analysis 1. In what direction do the gravitational forces act?
The force is stronger when the objects are at 100m.

2. When one of the masses was increased, what happened to the gravitational force?
The gravitational force decreased. 3. When the distance was doubled, what happened to the gravitational force?
The force is smaller when they are farther away.

4. Describe the relationship between the mass of an object and the gravitational forces that object experiences.
The more massive, the more they attract, the more distant, the even less they attract.
Exploration 3: Forces Between Planets
Procedure
1. Select Scenario 3. 2. Set m1 to 1.0 × 1026 kg (which represents the mass of Neptune). Set m2 to 5.7 × 1026 kg (which represents the mass of Saturn). Place the two planets 1.5 × 1011 m apart, the approximate distance between Earth and the Sun. Sketch the gravitational force vectors for each planet. 3. Move Neptune and Saturn closer to each other, so that they are only 5.7 × 1010 m apart, the approximate distance between Mercury and the Sun. Once more, sketch the gravitational force vectors for each planet.

Observations and Analysis 1. Which direction do the gravitational force vectors point?
Along the line of the accelerating force

2. How are the gravitational force vectors affected by moving the planets closer together?
Gravity is the only force affecting the motion of the planet, and it obeys Newton’s universal law of gravitation.
Conclusions
In complete sentences, describe all the ways that one can increase or decrease the gravitational force between two objects.
Whenever something gets closer to each other (distance decreasing) and when something gets bigger (mass increases).

Inquiry Extension
Consider the Moon and Earth. Which pulls harder gravitationally, the Moon on Earth or Earth on the Moon? Which has the larger acceleration?
The moon has the harder gravitationally while Earth has the large acceleration.

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