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Physics · 05 / 12

Gravitation, weight and distant interaction

High school foundations · Worked example and 4 exercises with solutions, at your pace.

Need a foundation?Units: numbers have dimensionsEquations: keep the balance level
UnderstandSee an exampleGuided exercise3 progressive challenges

The principle, simply

Masses attract gravitationally. For point masses, or externally viewed spherically symmetric bodies, F=Gm₁m₂/r² uses centre-to-centre distance. Forces are equal, opposite and act on different objects. Near the ground, weight P=mg uses approximately constant local g.

F=G*m_1*m_2/r^2
THE PICTURE TO REMEMBERGravitation, weight and distant interaction
  1. 01Two masses
  2. 02Centre distance
  3. 03Inverse-square law
  4. 04System and direction

WORKED EXAMPLE

From principle to reasoning

2 kg at g=9.8 N/kg weighs 19.6 N. Doubling distance quarters gravitational force. Changing planet changes weight rather than mass.

Solve a problem in this subject

  1. Draw the system

    Define the studied object, reference frame and positive axis. A force diagram shows external interactions acting on the system.

  2. Sort quantities

    Separate data and unknowns; convert units before substitution. 36 km/h = 10 m/s, so never insert 36 into a formula expecting SI speed.

  3. Write the model

    Choose a law matching assumptions: constant acceleration, thin lens, ohmic resistor. Isolate the unknown symbolically before rounding.

  4. Interpret

    Check dimensions and signs. Negative velocity gives direction on the chosen axis. Discuss scale and model limitations.

YOUR TURN

01 · Try before checking

What happens if distance triples at fixed masses?

One hint

Distance is squared in the denominator.

Reveal and understand the solution

Force multiplies by 1/9, using centre-to-centre distance.

Compare method, conditions and answer; identify the exact part to revisit.

IMPROVE THROUGH PRACTICE

Three additional challenges with solutions

Start with the first challenge. Write your method before opening a hint; use the solution to find the first step that needs work.

Reflect after practising
02 · Recognise and understandLink to this exercise

If two masses double their separation, what happens to gravitational force?

A hint to get started

Distance is squared in the denominator.

Step-by-step solution
  1. F = Gm₁m₂/r².
  2. Replacing r by 2r multiplies the denominator by 4.
  3. The force becomes one quarter, with masses unchanged.

Which step did you miss? Retry without help, then explain why the method works.

03 · Apply the methodLink to this exercise

Find the weight of 3 kg with g = 9.8 N/kg.

A hint to get started

Mass and weight are different quantities.

Step-by-step solution
  1. P = mg.
  2. P = 3 × 9.8 = 29.4 N.
  3. Mass remains 3 kg; weight is a force.

Which step did you miss? Retry without help, then explain why the method works.

04 · Go furtherLink to this exercise

Does a satellite attract its planet less strongly than the planet attracts it?

A hint to get started

Use Newton’s third law.

Step-by-step solution
  1. The forces have equal magnitude and opposite directions.
  2. They act on different bodies, so they do not cancel on one body.
  3. The accelerations differ because the masses differ.

Which step did you miss? Retry without help, then explain why the method works.

The trap to avoid

Equal opposite forces on different objects do not cancel in one object’s force balance.

Without notes, can you…

  • Explain the principle in your own words?
  • Rebuild the diagram and its connections?
  • Solve the exercise and justify the method?

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