Gravitational force is a key concept that most people know as the force that keeps us on Earth. But did you know it affects much more than just keeping us grounded? This article will help you understand how gravitational attraction works between objects with mass and how to calculate it.
Gravitational force isn’t just something that happens between you and the Earth. It actually acts between any two objects that have mass. For example, a table and a chair are gravitationally attracted to each other. This means that everything around you is pulling on you, and you are pulling on them, even if you don’t notice it. The reason we don’t feel this attraction is that the force is usually very small.
To figure out the gravitational attraction between two objects, we use a formula from Newton’s law of universal gravitation. The gravitational force (F) between two masses is given by:
$$ F = G frac{m_1 times m_2}{r^2} $$
Where:
The formula shows us that:
Let’s see how this works with an example. Imagine two people, each weighing 70 kg, standing 1.5 meters apart.
Substitute the values:
$$ F = 6.67 times 10^{-11} frac{70 times 70}{(1.5)^2} $$
This calculation shows that there is a gravitational force of about ( 1.45 times 10^{-7} ) Newtons pulling the two people towards each other. This force is very small, which is why we don’t notice it in everyday life.
Gravitational force is a universal phenomenon that affects all objects with mass. Learning how to calculate this force helps us understand the subtle yet important interactions between objects in our universe. Even though the force is small in everyday situations, gravitational attraction is crucial for the structure and behavior of the cosmos.
Gather a variety of small objects like a pencil, eraser, and a small ball. Predict which pairs of objects will have the strongest gravitational attraction based on their masses. Use a sensitive scale to measure the masses and calculate the gravitational force between them using the formula $$ F = G frac{m_1 times m_2}{r^2} $$. Discuss why the forces are too small to feel.
Use an online simulation tool to visualize how gravitational forces change with different masses and distances. Adjust the masses and distances to see how the gravitational force varies. Record your observations and explain how the simulation demonstrates the proportional and inversely proportional relationships in the gravitational force formula.
In pairs, identify and list objects around your school that exert gravitational forces on each other. For each pair, estimate their masses and the distance between them. Calculate the gravitational force using the formula $$ F = G frac{m_1 times m_2}{r^2} $$ and present your findings to the class.
Write a short story from the perspective of a gravitational force between two objects. Describe how the force changes as the objects move closer or farther apart, and how it feels to be stronger or weaker. Share your story with the class and discuss the scientific concepts illustrated in your narrative.
Solve a series of puzzles that involve calculating gravitational forces between various objects. Each puzzle will provide different masses and distances. Work in groups to solve the puzzles and explain the steps you took to find the solutions. Reflect on how changing different variables affects the gravitational force.
Gravitational – Relating to the force that attracts two bodies toward each other, typically due to their masses. – The gravitational pull of the Earth keeps the Moon in orbit around it.
Force – A push or pull upon an object resulting from the object’s interaction with another object. – The force applied to the car made it accelerate down the road.
Mass – A measure of the amount of matter in an object, typically measured in kilograms or grams. – The mass of the textbook is about $1.5$ kilograms.
Calculate – To determine the value of something using mathematical processes. – We can calculate the speed of the car using the formula $v = frac{d}{t}$, where $d$ is distance and $t$ is time.
Distance – The amount of space between two points, usually measured in meters or kilometers. – The distance between the two cities is approximately $150$ kilometers.
Proportional – Having a constant ratio or relationship with another quantity. – The force of gravity is proportional to the product of the masses of two objects.
Attraction – The action or power of drawing objects toward each other, especially due to gravitational or magnetic forces. – The attraction between the magnets was strong enough to hold them together.
Objects – Things that can be seen and touched, which may have mass and occupy space. – In physics, we often study how forces affect the motion of objects.
Universal – Applicable everywhere or in all cases; general. – Newton’s law of universal gravitation explains how every mass attracts every other mass in the universe.
Newton – The SI unit of force, named after Sir Isaac Newton, defined as the force required to accelerate a one-kilogram mass by one meter per second squared. – A force of $5$ newtons was needed to move the box across the floor.
