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Think Conceptually: Grasp the relationships between gravitational forces and field strength.

Writer's picture: Broken PencilBroken Pencil

The following section is tailored for A level Physics students who are finding it challenging to achieve higher grades in their exams. It addresses some common reasons why they may be losing marks or struggling to understand certain questions in the gravitational field topic.


One of the reason might be that they do not udnerstant the relationship between the concepts of the formulas.




 Gravitational Field Strength, g

The formula for gravitational field strength at a distance r from the center of a mass M is:

  • What it Represents: Gravitational field strength g tells us the acceleration experienced by a unit mass at a distance r from a mass M. It is a measure of how strong the gravitational field is at that point.

  • Units: g is measured in N/kg or m/s2

  • When to Use: Use this formula when you are asked to find the gravitational field strength or the acceleration due to gravity at a specific point in the field created by a mass M. For example:

    • Calculating the gravitational field strength at the surface of a planet.

    • Determining how gravity changes with distance from a celestial body.

2. Gravitational Force, F

The formula for the gravitational force between two masses, M and m, separated by a distance r is:

  • What it Represents: Gravitational force F is the force of attraction between two masses M and m separated by a distance r. It describes the actual pulling force that the masses exert on each other due to gravity.

  • Units: F is measured in newtons N.

  • When to Use: Use this formula when you need to calculate the force of gravity between two specific masses. For example:

    • Finding the gravitational pull between the Earth and the Moon.

    • Calculating the force of gravity between a satellite and the Earth.

Understanding the Relationship Between the Two

The gravitational field strength g can be thought of as the force per unit mass:


where:

  • F is the gravitational force experienced by a mass mmm,

  • g gives the acceleration or field strength at that point.

How They are Derived from Each Other

  1. From Gravitational Force to Gravitational Field Strength:

    This gives the gravitational field strength, which is independent of the smaller mass m.

  2. Key Differences in Application:

    • Use ​

      when dealing with the strength of the gravitational field at a distance r from a mass M. This is useful when discussing how gravity affects an object, regardless of the object's mass.Use when calculating how strong gravity is at a specific location.

    • Use ​

      when dealing with the actual gravitational force between two masses. This accounts for the interaction between both masses and gives the total force acting on each mass.Use when calculating the actual force between two masses.





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