(455) Gravitational fields and force [IB Physics SL/HL]

Gravitational Fields

• Definition: Gravitational field lines represent the direction a test mass would move under the influence of gravity.

  • A test mass shows where it would go when placed in a gravitational field.

• Drawing Gravitational Field Lines:

  • Arrows are drawn pointing towards the center of a mass (e.g., Earth).

  • The number of field lines indicates the strength of the gravitational field: more lines = stronger field.

  • Field lines radiate inwards toward the center of the mass.

Newton's Universal Law of Gravitation

• Fundamental Principle: Every object with mass attracts every other object with mass.

• Gravitational Force Equation: F = G (M1 M2) / R²

  • F: Force of attraction (in Newtons)

  • M1, M2: Masses (in kilograms)

  • R: Distance between the centers of the masses (in meters)

  • G: Gravitational constant (6.67 x 10⁻¹¹ N(m²/kg²))

• Interpretation of the Equation:

  • Force is directly proportional to the product of the two masses.

  • Force is inversely proportional to the square of the distance between the masses.

Example Problem

• Situation: Two planets are separated by distance R; determine new force when distance increases to 4R.

  • Using the Equation (Brute Force):

    • F2 = G (M1 M2) / (4R)² = G (M1 M2) / 16R²

    • F2 / F = (G M1 M2 / 16R²) / (G M1 M2 / R²) = 1/16.

  • Simplified Approach: The force is proportional to 1/R², thus:

    • For 4R: F ∝ 1/(4)² = 1/16.

• Conclusion: The new force is 1/16th of the original force.

Summary

• Gravitational field lines point inward towards the center of mass and indicate strength by the number of lines drawn.

• Newton's law explains how objects with mass attract each other based on mass and distance.