## Physics Tutorial

*Motion of objects under gravity*

#### Intro

Have you wondered why an apple hits the ground when it falls from a tree but why the moon does not hit the earth? In this tutorial, we will look at different types of motion under gravity.

#### Sample Problem

When an apple falls from a tree, it hits the ground because of gravitational attraction. Why doesn’t the moon hit the earth under gravity? Explain the difference between these two types of motion.

#### Solution

When an apple falls from a tree, it does not have any initial velocity. The direction of gravitational pull is in vertical direction. Therefore, the apple accelerates along the vertical direction and eventually hits the ground.

Before we talk about the motion of the moon, first, let’s talk about the motion of the apple if we throw it horizontally. Now, the apple has an initial horizontal velocity. If there were no gravity, according to Newton’s First Law, once the apple leaves our hand, there would be no unbalanced force and the apple would move horizontally at a constant speed. When gravity is present, gravitational attraction pulls the apple downwards. Since we throw the apple horizontally, the apple will hit the ground at a certain distance from us. The trajectory of the motion is a parabola. This motion is called a projectile. Please note that in any projectile motion, we need to throw an object in a way that it has a horizontal component of velocity. If we throw an object vertically upward, the object moves along the vertical direction and the motion is not a projectile motion.

If we throw the apple harder, the apple will have a larger horizontal velocity and it will hit the ground at a distance farther away from us. If we throw it harder and harder, it will stop at a distance farther and farther away from us. If the horizontal velocity is large enough, the apple will eventually move around the earth. Therefore, at the right horizontal velocity, the apple will actually move around the earth and will never fall. This motion is a circular motion. In this situation, gravitational attraction keeps the object moving around the earth. The force required to keep an object moving along a circular path is called centripetal force. This is also how a satellite is placed on a circular orbit. We need to provide a tangential velocity at the right magnitude to keep it moving around the earth.

To conclude, motion under gravity depends on the initial velocity. For free falling, an object moves vertically under gravity. Similarly for an object that is thrown vertically (i.e. no tangential component of velocity). If an object is thrown horizontally, the motion is a projectile if the velocity is not large enough. If the velocity is large enough, the object will follow a circular path under gravity and will never fall.

The moon does not hit the earth because its motion is a circular motion. Gravitational force provides the required centripetal force for the moon to keep moving around the earth.

# About The Author

Math And Science |

I have a Ph.D. in Chemical Engineering specialized in process optimization. In my full-time job, I have been applying mathematical techniques to solving engineering problems in oil industry for more than 10 years. I know very well what level of understanding students should have in mathematics and s... |