### How do you determine how much force you need to create a particular acceleration?

The answer to that question is Newton’s second law of motion. That law relates the force you exert on an object, divided by the object’s mass, to the resulting acceleration of the object. For example, if I take this baseball, and I neglect all the other forces except for my force on it. So, for example, if we went out into deep space where there wasn’t gravity and there wasn’t air and life was simple, if I exert a force on the baseball. Well, we take that force, my force on the baseball, and divide it by the baseball’s mass, that ratio will tell us exactly how the baseball will accelerate. The baseball will undergo an acceleration that’s in the same direction as the force and that has the amount equal to the force I exert divided by the baseball’s mass.

The baseball has very little mass, so even gentle forces will cause significant accelerations in the baseball. If I double the force I exert on the baseball, I’ll consequently double the acceleration of the baseball. In contrast, my lead brick has a huge mass. Now, if I exert the same forces I did on the baseball, I’m going to be dividing those forces by a much larger mass and the brick’s acceleration will consequently be much smaller. It’ll still be proportional to my force, if I double my force I will double the acceleration, but it’ll be on a much smaller scale.

If you have a particular acceleration in mind, and you want to achieve it by exerting the right amount of force on the object, you just take that relationship between the force divided by the mass gives you acceleration, and you rearrange it algebraically so that you know what acceleration you want, a certain amount, multiply it by the mass of the object and that will tell you what force you need to achieve the acceleration you have in mind.