# Newton's Law of Universal Gravitation

### Objectives

1. Determine the mathematical relationship between mass and gravitational force.
2. Determine the mathematical relationship between distance of separation and gravitational force.

Created with Geogebra

### Procedure

#### Part I

1. Reset the program by clicking the symbol in the upper right of the simulation window.
2. Set m1 to 10 kg and set G to 0.2 Nm2/kg2.
3. Record the gravitational force on mass 1 in the space provided in data table 1.
4. Change the mass of circle 1 to 20, 30, 40, and 50 kg, recording the gravitational force after each change.
5. Create a graph of gravitational force Fg (y) vs. mass m1 (x) using Excel. Determine the mathematical relationship represented by the data.

#### Part II

1. Set both masses to 10 kg and the separation distance to 2 m. Change G to 46.08 Nm2/kg2.
2. Record the gravitational force Fg for mass 1 in the space provided in table 2.
3. Change the position of mass 2 so that the separation distances are 4, 6, 8, and 10 m, and repeat step 2 after each change.
4. Calculate the "fraction of original force" for each trial and record in the space provided.
5. Construct a graph of gravitational force Fg (y) vs. separation distance r (x) using Excel. Determine the mathematical relationship represented by the data.

#### Part III

1. Set G back to 0.2 Nm2/kg2. Set separation distance to 10 m.
2. Set both masses to 10 kg. What is the magnitude of the force on each?
3. Double both masses to 20 kg. What is the magnitude of the force on each?
4. Set one mass to 20 kg and the other to 30 kg. What is the magnitude of the force on each?
5. What appears to be the mathematical relationship between force of gravity and both masses?

### Data Tables

Table 1 Table 2
Mass of object 2 (kg) Magnitude of Force on Each (N) Separation Distance (m) Magnitude of Force on Each (N) Fraction of original force
10 2
20 4
30 6
40 8
50 10

### Questions

1. How does the gravitational force on mass 1 compare to the gravitational force on mass 2 in each trial? How do you know? What law of physics describes this?
2. What is the mathematical relationship between mass and gravitational force?
3. There is a gravitational force of attraction between two objects. The mass of one of the objects is increased by a factor of 10. What happens to the gravitational force between the two objects?
4. What appears to be the relationship between separation distance and gravitational force?
5. A gravitational force of 10 N exists between two masses that are 100m apart. What would be the gravitational force between the two masses if they are separated by 50 m?
6. Gravitational force is ( proportional / inversely proportional ) to the product of the masses of two objects and ( proportional / inversely proportional ) to the square of the separation distance.