Three objects of equal mass  m1 = m2 = m3 = 2.50 kg  are located on the vertices of an equilateral triangle of length  d = 3.60 m.  A fourth mass  m4 = 15.5 kg  is at the center of the triangle. What is the net gravitational force on the mass  m1  that is at the origin? Express your answer in vector form.

College Physics
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Chapter1: Units, Trigonometry. And Vectors
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Three objects of equal mass 

m1 = m2 = m3 = 2.50 kg

 are located on the vertices of an equilateral triangle of length 

d = 3.60 m.

 A fourth mass 

m4 = 15.5 kg

 is at the center of the triangle. What is the net gravitational force on the mass 

m1

 that is at the origin? Express your answer in vector form.

The diagram depicts an equilateral triangle formed by three masses, \( m_1 \), \( m_2 \), and \( m_3 \), each represented as a blue sphere. A fourth mass, \( m_4 \), shown as a gray sphere, is located at the centroid of the triangle.

### Key Features:

- **Triangle Configuration**: 
  - The triangle is equilateral, meaning all sides are of equal length and all internal angles are \(60^\circ\).
  - The side labeled as \( d \) indicates the equal distance between each pair of masses \( m_1 \), \( m_2 \), and \( m_3 \).

- **Coordinate Axes**:
  - The \( x \)- and \( y \)-axes are represented with dashed lines, forming a standard Cartesian coordinate system.
  - Mass \( m_1 \) is positioned along the negative \( y \)-axis, while \( m_2 \) is on the positive \( x \)-axis.

- **Centroid**:
  - Mass \( m_4 \) is positioned at the centroid of the triangle, which is the point where the medians intersect and is equidistant from all vertices in an equilateral triangle.

This configuration is commonly used in physics to analyze systems of particles, balancing forces, and center of mass calculations.
Transcribed Image Text:The diagram depicts an equilateral triangle formed by three masses, \( m_1 \), \( m_2 \), and \( m_3 \), each represented as a blue sphere. A fourth mass, \( m_4 \), shown as a gray sphere, is located at the centroid of the triangle. ### Key Features: - **Triangle Configuration**: - The triangle is equilateral, meaning all sides are of equal length and all internal angles are \(60^\circ\). - The side labeled as \( d \) indicates the equal distance between each pair of masses \( m_1 \), \( m_2 \), and \( m_3 \). - **Coordinate Axes**: - The \( x \)- and \( y \)-axes are represented with dashed lines, forming a standard Cartesian coordinate system. - Mass \( m_1 \) is positioned along the negative \( y \)-axis, while \( m_2 \) is on the positive \( x \)-axis. - **Centroid**: - Mass \( m_4 \) is positioned at the centroid of the triangle, which is the point where the medians intersect and is equidistant from all vertices in an equilateral triangle. This configuration is commonly used in physics to analyze systems of particles, balancing forces, and center of mass calculations.
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