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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!
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.
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:
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:
Gravity on Other Planets of the Solar System
From Ref2 remade in quicklatex.
RESOURCES:
References
- https://byjus.com/gravitational-acceleration-formula/
- https://www.physicsclassroom.com/class/circles/Lesson-3/The-Value-of-g
- https://www.astronomynotes.com/gravappl/s6.htm
- 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
Mathematical equations used in this article, where made using quicklatex.
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
Final words | Next up
And this is actually it for today's post!Next time we will talk about Gravitational Fields....
See ya!
