Why is force mass times acceleration? Specifically, why acceleration? What’s the difference between force and momentum?
In: Physics
First, let’s start with position. Position is pretty straightforward – it’s where you are in space. If you’re moving, then your position is changing. A changing position over time is known as velocity, and velocity does not change unless something causes it to. This is why a stationary object stays stationary and a moving object moves until something stops it.
Now, when an object gains velocity, it doesn’t do it instantly. Think about when you floor the gas pedal in a car – your velocity (think: speed) increases but not instantly. This means that your car is accelerating.
A heavier car is harder to accelerate – it has more mass. So, you need to push harder to squeeze the same acceleration out of it. You need more force to achieve the same acceleration. This gives us an equation relating force, mass, and acceleration. a=f/m. It is more commonly written as f=ma, but I find that a=f/m is often more intuitive.
However, we know that an object pushing on another object will also be pushed on itself. So, for every force that is exerted by an object, an equal and opposite force is exerted *on* that object.
Logically, we know that the force lasts the same amount of time on both objects. So, we know that the forces are opposite and the durations are the same. Thus, -f•t=f•t. We know that f•t for these two objects must be opposite, and add up to zero. Thus, the f•t for both objects together is 0. This applies to any number of objects. As long as no external forces are applied, all of their f•t’s add up to 0. So, we can compare the f•t’s of different objects this way. For instance, when a gun fires a bullet, the gun and bullet experience the same f•t. We named this very useful quantity f•t “momentum”, and as I have shown, momentum is conserved (does not change) unless an external force is applied.
Additionally, by comparing our two equations f=ma and momentum=ft, as well as an additional equation v=at, we can create a fourth equation relating momentum to mass and velocity. f•t=momentum=mass•velocity. So, momentum=mass•velocity. Through clever use of these equations, we can solve a lot of problems in physics.
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