Where force is equal to the derivative of m, defined as the object's momentum, in relation to time, t. Have you ever watched a SpaceX rocket launch? Besides being one of the most incredible spectacles of our time, Newton's Second Law of Motion is essential to understanding how we can move a rocket as massive as the Falcon 9 against the pull of Earth's gravity to get it into orbit.
There are many other practical circumstances where we need to use Newton's Second Law of Motion to determine how objects are going to behave when a certain amount of force is applied. Probably the most direct application of Newton's Second Law of Motion is in ballistics, which makes it possible to actually calculate the trajectory of a projectile with a high degree of accuracy.
The cannon had been in use for centuries before Newton was even born, perhaps the most famous early use of cannon was when the Ottomans used them to blow open the walls of Constantinople in But without Newton's Second Law of Motion, artillery officers pretty much pointed the cannon in the general direction of the target and performed ad hoc estimates, based on where projectiles landed, to narrow down their aim.
Newton's Second Law of Motion made more precise calculations of trajectories possible, making artillery far more lethal in the following centuries as officers could calculate where a cannonball or shell would land before it was even fired. With the introduction of the steam engine and with it, locomotives, steamboats, and industrial factories how to power an engine and how to use the force an engine produced to turn systems of gears through acceleration became just as important as the development of modern accounting practices to a factory owner.
While the factory owners may not have known how to do all that math, they had engineers who did, because they had Newton's Second Law of Motion and the math that it provided them. In a preindustrial world, it took time to circulate this material outside of the academy, but circulate it did.
Those who studied and learned the classical mechanics that the Second Law of Motion inspired wasted no time using it to transform the world through machinery. So that leads to the natural question, how does a net force affect the constant velocity? Or how does it affect of the state of an object? And that's what Newton's Second Law gives us. So Newton's Second Law of Motion. And this one is maybe the most famous.
They're all kind of famous, actually. I won't pick favorites here. But this one gives us the famous formula force is equal to mass times acceleration. And acceleration is a vector quantity, and force is a vector quantity.
And what it tells us-- because we're saying, OK, if you apply a force it might change that constant velocity. But how does it change that constant velocity?
Well, let's say I have a brick right here, and it is floating in space. And it's pretty nice for us that the laws of the universe-- or at least in the classical sense, before Einstein showed up-- the laws of the universe actually dealt with pretty simple mathematics.
What it tells us is if you apply a net force, let's say, on this side of the object-- and we talk about net force, because if you apply two forces that cancel out and that have zero net force, then the object won't change its constant velocity. But if you have a net force applied to one side of this object, then you're going to have a net acceleration going in the same direction.
So you're going to have a net acceleration going in that same direction. And what Newton's Second Law of Motion tells us is that acceleration is proportional to the force applied, or the force applied is proportional to that acceleration.
And the constant of proportionality, or to figure out what you have to multiply the acceleration by to get the force, or what you have to divide the force by to get the acceleration, is called mass. That is an object's mass. And I'll make a whole video on this. You should not confuse mass with weight. And I'll make a whole video on the difference between mass and weight.
Mass is a measure of how much stuff there is. Now, that we'll see in the future. For a constant mass, force equals mass times acceleration. F is force, m is mass and a is acceleration. The math behind this is quite simple. If you double the force, you double the acceleration, but if you double the mass, you cut the acceleration in half. Newton expanded upon the earlier work of Galileo Galilei , who developed the first accurate laws of motion for masses, according to Greg Bothun, a physics professor at the University of Oregon.
Galileo's experiments showed that all bodies accelerate at the same rate regardless of size or mass. Newton also critiqued and expanded on the work of Rene Descartes, who also published a set of laws of nature in , two years after Newton was born. Forces belong to a category of physical properties, which includes momentum and velocity, known as vectors. These contrast with scalars, which have a size but no direction, for example temperature or mass.
The F in Newton's second law refers to the net force acting on an object. Working out what happens to an object that has several forces acting on it, therefore, requires you to take account of both the directions and sizes of each force.
Two forces might have the same sizes but, if they are pointed directly opposite one another, they will cancel to zero. A game of tug-of-war is a good way to think about this. When two teams are pulling in opposite directions, the movement of the rope as calculated by Newton's second law will be determined by the net force on the rope.
The size of that net force is the difference in the sizes of the forces being exerted by the two teams. The direction of the net force will be in the direction of whichever team is pulling harder.
To describe atoms, and even smaller things, physicists use versions of force and momentum in the equations that include quantum-mechanical descriptions of time as well as space.
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