Math Problem Statement
Solution
The problem in the image asks for the gravitational force between two objects. We can calculate this using Newton's Law of Universal Gravitation:
Where:
- is the gravitational force.
- is the gravitational constant, given as .
- (mass of object A).
- (mass of object B).
- (distance between the two bodies).
Let's calculate the force:
- Calculate the masses' product:
- Calculate the square of the distance:
- Plug values into the formula:
- Simplify:
- Now multiply by the gravitational constant:
- Convert to micronewtons ():
Thus, the gravitational force between the two objects is approximately 108.5 µN.
Let me know if you'd like more details on any of these steps!
Here are some related questions to explore:
- How does the force change if the distance between the objects is doubled?
- What would happen to the force if the mass of object A is halved?
- How does the gravitational force compare to other fundamental forces?
- Why is the gravitational constant so small?
- What are the real-world applications of calculating gravitational forces?
Tip: The force of gravity decreases rapidly with distance, as it is inversely proportional to the square of the distance between the two masses.
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Math Problem Analysis
Mathematical Concepts
Gravitational Force
Newton's Law of Universal Gravitation
Unit Conversion
Formulas
F = G * (m1 * m2) / r^2
Theorems
Newton's Law of Universal Gravitation
Suitable Grade Level
High School, College
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