newton’s law of gravitation states that any two bodies attract each other with a force that is inversely proportional to the square of the distance between them. The force of attraction between two bodies is 460 * 10^-12 newtons when they are 6 cm apart. What is the force on the bodies when they are 23 cm apart?
Since the force is k/r^2
Then if r is multiplied by a factor of a, the new force is
k/(ar)^2 = k/r^2 / a^2
So, you have multiplied the distance r by a factor of 23/6. Consequently, the force is reduced by a factor of (23/6)^2.
To determine the force between two bodies when they are 23 cm apart using Newton's Law of Gravitation, we can follow these steps:
1. Identify the given information:
- Force (F1) = 460 * 10^-12 newtons (when the bodies are 6 cm apart)
- Distance (r1) = 6 cm
- Distance (r2) = 23 cm
2. Understand the inverse square law:
According to Newton's Law of Gravitation, the force of attraction (F) between two bodies is inversely proportional to the square of the distance (r) between them. Mathematically, it can be represented as:
F ∝ 1/r^2
3. Use the inverse square law equation:
To find the force (F2) when the distance (r2) increases to 23 cm, we can set up the following equation using the inverse square law:
F1 / F2 = (r2^2) / (r1^2)
4. Substitute the given values:
Plugging in the values we know:
460 * 10^-12 / F2 = (23^2) / (6^2)
5. Solve for F2:
Rearrange the equation to solve for F2:
F2 = (460 * 10^-12 * (6^2)) / (23^2)
Calculating this expression will give us the force (F2) between the bodies at a distance of 23 cm.
Note: It's important to ensure the unit of distance is consistent throughout the calculation, so either convert the given values to meters or use inches instead of centimeters.