# Newton's Law of Universal Gravitation

### Objectives

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

### Procedure

#### Part I

- Reset the program by clicking the symbol in the upper right of the simulation window.
- Set m
_{1}to 10 kg and set G to 0.2 Nm^{2}/kg^{2}. - Record the gravitational force on mass 1 in the space provided in data table 1.
- Change the mass of circle 1 to 20, 30, 40, and 50 kg, recording the gravitational force after each change.
- Create a graph of gravitational force
*F*(y) vs. mass_{g}*m*(x) using Excel. Determine the mathematical relationship represented by the data._{1}

#### Part II

- Set both masses to 10 kg and the separation distance to 2 m. Change G to 46.08 Nm
^{2}/kg^{2}. - Record the gravitational force Fg for mass 1 in the space provided in table 2.
- 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.
- Calculate the "fraction of original force" for each trial and record in the space provided.
- Construct a graph of gravitational force
*F*(y) vs. separation distance_{g}*r*(x) using Excel. Determine the mathematical relationship represented by the data.

#### Part III

- Set G back to 0.2 Nm
^{2}/kg^{2}. Set separation distance to 10 m. - Set both masses to 10 kg. What is the magnitude of the force on each?
- Double both masses to 20 kg. What is the magnitude of the force on each?
- Set one mass to 20 kg and the other to 30 kg. What is the magnitude of the force on each?
- 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

- 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?
- What is the mathematical relationship between mass and gravitational force?
- 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?
- What appears to be the relationship between separation distance and gravitational force?
- 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?
- 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.