### Physics Problem: Gravitational Force Calculation#### Task Description:**Problem 10:** Find the resultant force on:- (a) the 0.100 kg mass- (b) the 0.200 kg mass in Fig. 6-15 (the masses are isolated from the earth).#### Diagram Explanation:**Figure 6-15:** This figure displays three masses aligned in a straight line and isolated from any external gravitational influences, including Earth.- The mass on the left is **0.400 kg**.- The mass in the center is **0.200 kg**.- The mass on the right is **0.100 kg**.The distances between the masses are as follows:- The distance between the 0.400 kg and the 0.200 kg masses is **10.0 cm**.- The distance between the 0.200 kg and the 0.100 kg masses is also **10.0 cm**.### Further Problem:**Problem 11:** Three isolated particles, each having a mass of 2.00 kg, are at the vertices of an equilateral triangle with 1.00 m sides. Find the magnitude and direction of...(NOTE: The rest of Problem 11 is cut off in the image.)### Educational Context:This problem requires students to apply their knowledge of gravitational forces between masses, including the use of Newton's Law of Universal Gravitation, which states:\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]where:- \(F\) is the gravitational force,- \(G\) is the gravitational constant (\(6.67430 \times 10^{-11} \ \mathrm{m^3 \cdot kg^{-1} \cdot s^{-2}}\)),- \(m_1\) and \(m_2\) are the masses of the two objects,- \(r\) is the distance between the centers of the two masses.### Solution Strategy:1. **Calculate the gravitational force** between the 0.400 kg and 0.200 kg masses and the 0.200 kg and 0.100 kg masses.2. **Consider the directions** of these forces to determine the resultant force on each mass.3. **Account for the Vector Addition** of forces when summing the gravitational influences on each specific mass.Understanding

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Description: ### Physics Problem: Gravitational Force Calculation#### Task Description:**Problem 10:** Find the resultant force on:- (a) the 0.100 kg mass- (b) the 0.200 kg mass in Fig. 6-15 (the masses are isolated from the earth).#### Diagram Explanation:**Fig

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away and has a mass of 60. kg. 10 Find the resultant force on (a) the 0.100 kg mass and (b) the 0.200 kg mass in Fig. 6-15 (the masses are iso- lated from the earth). 0.400 kg 0.200 kg 0.100 kg 10.0 cm 10.0 cm Fig. 6-15

away and has a mass of 60. kg. 10 Find the resultant force on (a) the 0.100 kg mass and (b) the 0.200 kg mass in Fig. 6-15 (the masses are iso- lated from the earth). 0.400 kg 0.200 kg 0.100 kg 10.0 cm 10.0 cm Fig. 6-15

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### Physics Problem: Gravitational Force Calculation

#### Task Description:
**Problem 10:** Find the resultant force on:
- (a) the 0.100 kg mass
- (b) the 0.200 kg mass in Fig. 6-15 (the masses are isolated from the earth).

#### Diagram Explanation:
**Figure 6-15:** This figure displays three masses aligned in a straight line and isolated from any external gravitational influences, including Earth.

- The mass on the left is **0.400 kg**.
- The mass in the center is **0.200 kg**.
- The mass on the right is **0.100 kg**.

The distances between the masses are as follows:
- The distance between the 0.400 kg and the 0.200 kg masses is **10.0 cm**.
- The distance between the 0.200 kg and the 0.100 kg masses is also **10.0 cm**.

### Further Problem:
**Problem 11:** Three isolated particles, each having a mass of 2.00 kg, are at the vertices of an equilateral triangle with 1.00 m sides. Find the magnitude and direction of...

(NOTE: The rest of Problem 11 is cut off in the image.)

### Educational Context:
This problem requires students to apply their knowledge of gravitational forces between masses, including the use of Newton's Law of Universal Gravitation, which states:

\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]

where:
- \(F\) is the gravitational force,
- \(G\) is the gravitational constant (\(6.67430 \times 10^{-11} \ \mathrm{m^3 \cdot kg^{-1} \cdot s^{-2}}\)),
- \(m_1\) and \(m_2\) are the masses of the two objects,
- \(r\) is the distance between the centers of the two masses.

### Solution Strategy:
1. **Calculate the gravitational force** between the 0.400 kg and 0.200 kg masses and the 0.200 kg and 0.100 kg masses.
2. **Consider the directions** of these forces to determine the resultant force on each mass.
3. **Account for the Vector Addition** of forces when summing the gravitational influences on each specific mass.

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