- Home/
- GATE MECHANICAL/
- GATE ME/
- Article

# Motion Under Gravity

By BYJU'S Exam Prep

Updated on: September 25th, 2023

A** motion under gravity** occurs when an item moves due to the application of gravity. When an object is raised or moved away from the ground, a downward force is applied to the object. This force is referred to as gravity. The earth’s gravity pushes the object towards itself with an acceleration known as acceleration due to gravity. This force results from the earth’s gravitational attraction and is related to the idea of gravitational forces.

Here, we provide a quick explanation of the concept of motion under gravity. It covers topics including vertical motion under gravity, the equation of motion under gravity, the formula, and a few examples.

Download Formulas for GATE Mechanical Engineering-Engineering Mechanics

Table of content

## Define Motion Under Gravity

The movement of an item whose vertical motion is altered by the presence of gravity is referred to as motion under gravity. GRAVITY is the force that pulls things downward.

### Motion Under Gravity PDF

In actuality, gravity pulls objects toward the Earth’s center. The gravitational force’s strength is determined by the object’s mass and the gravitational constant.

### Motion Under Gravity Formula

The basic formula of the body with some weight experiencing some gravitation force as:

**Weight = Mass×Gravity**

**(w=mg)**

Weight is a force that is measured in Newtons. Gravity is measured in meters per second (m/s^{2}) and mass in kilograms (kg). Gravity is estimated to be 9.8 m/s^{2} for objects relatively close to the Earth’s surface.

Download Formulas for GATE Mechanical Engineering – TOM & Vibrations

## Equation of Motion Under Gravity

When an object moves owing to the influence of gravity, there are certain standard equations of motion that are used to analyze the motion of the object. The equation of motion for normal horizontal forces is the same as the equation of motion for gravity, which is shown below.

v = u + gt

h = ut + (1/2)gt^{2}

v^{2} = u^{2} + 2gh

There is a sign convention for the acceleration due to gravity that is followed in all of the given equations relating to the concept of equations of motion under gravity. It is interpreted as suitable for downward movement and negative for upward movement.

## The velocity of a Body Having Motion Under Gravity

When an object is dropped from a given height, it is referred to as “h.” Since the object is initially at rest before being dropped from that height, its initial velocity is zero. There must be some final body velocity when the object reaches the ground.

As a result, the equation of motion that is being discussed is as follows:

v^{2} = u^{2} + 2gh

The value of “g” will be interpreted as positive, which represents an item moving downward.

v^{2} = (0)^{2} + 2gh

v^{2} = 2gh

v = √2gh

## Motion Under Gravity Forces Examples

Check out a few examples of the body having motion under Gravity:

- Every time a ball is thrown upward, gravity causes the ball to fall back to the ground.
- The person’s movement on the ground will be caused solely by the gravitational force that holds the person in place.
- Gravitational forces regulate tides in terms of their short-term periodic movement caused by the rise and fall of water in bodies of water.
- Jumping, sliding, walking, jogging, dancing, and other common daily actions are all governed by the forces of gravity.
- Gravitational forces govern the motion of celestial bodies around the sun to ensure appropriate alignment and rotation around their axes.

Download Formulas for GATE Mechanical Engineering – Fluid Mechanics and Machinery