Physics - Classical Mechanics - Weight: The Force of Gravity

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Introduction

Hey it's a me again @drifter1! In this article we will continue with Physics, and more specifically the branch of "Classical Mechanics". Today's article will be about Weight: The Force of Gravity. So, without further ado, let's get straight into it!

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Weight Force w

We already used the weight w of an object in various topics and problems of Physics.

The weight w is equal to the product of an object's mass m and the gravitational acceleration g caused by the force of gravity that attracts the object to the Earth for example.

Thus, mathematically the force of gravity can be described by the following equation:



For Earth we use the accelaration of gravity on the surface of the Earth at sea level, which is: g = 9.8 m/s².

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Gravitational Acceleration g

The gravitational acceleration that an object acts on another object, can be calculated by substituting F with m ⋅ g in Newton's Law of Gravity:



The mass m gets cancelled on both sides giving us an equation for calculating g.

Thinking about planets we can describe the distance d as the radius of a planet r plus the relative height of the object h to the surface of the planet, giving us:

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Gravity on Earth

Let's calculate the value of Earth's gravity at the Earth's surface and some Km's above the surface. Earth's mass is approx. 5.98 × 10²⁴ Kg and the typical radius is 6.38 × 10⁶ m.

Inserting this information in the previous equation we get:




For twice the distance (d = 2 ⋅ r) we get:

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Gravity on Other Planets of the Solar System

From Ref2 remade in quicklatex.

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RESOURCES:

References

1. https://byjus.com/gravitational-acceleration-formula/
2. https://www.physicsclassroom.com/class/circles/Lesson-3/The-Value-of-g
3. https://www.astronomynotes.com/gravappl/s6.htm
4. https://www.khanacademy.org/science/high-school-physics/uniform-circular-motion-and-gravitation-2/newtons-law-of-gravitation/a/newtons-law-of-gravitation-ap1

Images

1. https://iconscout.com/icon/red-apple-fruit-emoj-symbol-food

Mathematical equations used in this article, where made using quicklatex.

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Previous articles of the series

Rectlinear motion

• Velocity and acceleration in a rectlinear motion -> velocity, acceleration and averages of those
• Rectlinear motion with constant acceleration and free falling -> const acceleration motion and free fall
• Rectlinear motion with variable acceleration and velocity relativity -> integrations to calculate pos and velocity, relative velocity
• https://www.grc.nasa.gov/www/k-12/airplane/wteq.html
• Rectlinear motion exercises -> examples and tasks in rectlinear motion

Plane motion

• Position, velocity and acceleration vectors in a plane motion -> position, velocity and acceleration in plane motion
• Projectile motion as a plane motion -> missile/bullet motion as a plane motion
• Smooth Circular motion -> smooth circular motion theory
• Plane motion exercises -> examples and tasks in plane motions

Newton's laws and Applications

• Force and Newton's first law -> force, 1st law
• Mass and Newton's second law -> mass, 2nd law
• Newton's 3rd law and mass vs weight -> mass vs weight, 3rd law, friction
• Applying Newton's Laws -> free-body diagram, point equilibrium and 2nd law applications
• Contact forces and friction -> contact force, friction
• Dynamics of Circular motion -> circular motion dynamics, applications
• Object equilibrium and 2nd law application examples -> examples of object equilibrium and 2nd law applications
• Contact force and friction examples -> exercises in force and friction
• Circular dynamic and vertical circle motion examples -> exercises in circular dynamics
• Advanced Newton law examples -> advanced (more difficult) exercises

Work and Energy

• Work and Kinetic Energy -> Definition of Work, Work by a constant and variable Force, Work and Kinetic Energy, Power, Exercises
• Conservative and Non-Conservative Forces -> Conservation of Energy, Conservative and Non-Conservative Forces and Fields, Calculations and Exercises
• Potential and Mechanical Energy -> Gravitational and Elastic Potential Energy, Conservation of Mechanical Energy, Problem Solving Strategy & Tips
• Force and Potential Energy -> Force as Energy Derivative (1-dim) and Gradient (3-dim)
• Potential Energy Diagrams -> Energy Diagram Interpretation, Steps and Example
• Internal Energy and Work -> Internal Energy, Internal Work

Momentum and Impulse

• Conservation of Momentum -> Momentum, Conservation of Momentum
• Elastic and Inelastic Collisions -> Collision, Elastic Collision, Inelastic Collision
• Collision Examples -> Various Elastic and Inelastic Collision Examples
• Impulse -> Impulse with Example
• Motion of the Center of Mass -> Center of Mass, Motion analysis with examples
• Explaining the Physics behind Rocket Propulsion -> Required Background, Rocket Propulsion Analysis

Angular Motion

• Angular motion basics -> Angular position, velocity and acceleration
• Rotation with constant angular acceleration -> Constant angular acceleration, Example
• Rotational Kinetic Energy & Moment of Inertia -> Rotational kinetic energy, Moment of Inertia
• Parallel Axis Theorem -> Parallel axis theorem with example
• Torque and Angular Acceleration -> Torque, Relation to Angular Acceleration, Example
• Rotation about a moving axis (Rolling motion) -> Fixed and moving axis rotation
• Work and Power in Angular Motion -> Work, Work-Energy Theorem, Power
• Angular Momentum -> Angular Momentum and its conservation
• Explaining the Physics behind Mechanical Gyroscopes -> What they are, History, How they work (Precession, Mathematical Analysis) Difference to Accelerometers
• Exercises around Angular motion -> Angular motion examples

Equilibrium and Elasticity

• Rigid Body Equilibrium -> Equilibrium Conditions of Rigid Bodies, Center of Gravity, Solving Equilibrium Problems
• Force Couple System -> Force Couple System, Example
• Tensile Stress and Strain -> Tensile Stress, Tensile Strain, Young's Modulus, Poisson's Ratio
• Volumetric Stress and Strain -> Volumetric Stress, Volumetric Strain, Bulk's Modulus of Elasticity, Compressibility
• Cross-Sectional Stress and Strain -> Shear Stress, Shear Strain, Shear Modulus
• Elasticity and Plasticity of Common Materials -> Elasticity, Plasticity, Stress-Strain Diagram, Fracture, Common Materials
• Rigid Body Equilibrium Exercises -> Center of Gravity Calculation, Equilibrium Problems
• Exercises on Elasticity and Plasticity -> Young Modulus, Bulk Modulus and Shear Modulus Examples

Gravity

• Newton's Law of Gravitation -> Newton's Law of Gravity, Gravitational Constant G

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Final words | Next up

And this is actually it for today's post!

Next time we will talk about Gravitational Fields....

See ya!

Keep on drifting!