# Keeping an object from gaining or losing altitude

How can I find the thrust, $t$, needed to keep an object with $m$ mass, in the influence of an object with $g$ gravity, from gaining or losing any altitude?

Forces cause acceleration, or changes in speed. If your speed is constant, the total force on you must be 0.

Gravity is one force acting on you. The force of gravity is equal to your weight. It pulls you down.

To make the total force add up to 0, you need another force equal to your weight in the upward direction. Often this upward force is provided by the floor you are standing on. You could also get it by standing on a rocket. Either way, the same force is needed.

If the total force is 0, your speed will not change. If that speed happens to be 0, you will not gain or lose altitude.

If your mass is $m$, then your weight is $mg$. So the thrust must also be this much. $t = mg$

Take a simple example of an everyday situation where an object is kept from gaining or losing amplitude: Put the object on a shelf and let it sit there.

Now think about this situation. What is the force applied by the shelf to the object to keep it from gaining or losing amplitude?