And one of the complex equations that Hawking wished to include? In other words, the force F acting on an object is equal to the mass m of the object multiplied by the acceleration experienced by the object.
This states N2 in terms of momentum, where momentum is the product of mass m multiplied by the velocity v. This is the version of N2 stated in most dictionaries of Physics. For example, the Oxford Dictionary of Physics p. Imagine my consternation and horror when I found that I was wrong. Actually, not that much consternation and horror: I am fairly inured to being wrong as it happens fairly often…. Richard Feynman wrote along similar lines in his justly famous Lectures on Physics :.
Thus at the beginning we take several things for granted. These ideas were of course implied by Newton when he wrote his equation, for otherwise it is meaningless. For example, suppose the mass varied inversely as the velocity; then the momentum would never change in any circumstance, so the law means nothing unless you know how the mass changes with velocity.
At first we say, it does not change. However, I think Feynman is considerably oversimplifying what Newton said here. Most objects don't come stamped with an "m" value on them. Space and time aren't laid out with a labeled grid of coordinates, so we aren't just given the " a " values for objects.
Worst of all, what's F? Let's say we ignore the question of how to determine a , by assuming that somehow we have a common-sense set of space-time coordinates that we're happy with. We can bounce objects off each other, and by measuring their velocities before and after the bounce, figure out the ratios of their m's. Pick one object to call the unit mass, and now we have a set of m's. Now we get to the hard part. What are the F 's?
Let's say we see some m with an a. So we must insist on some rules about the F 's. The third law says that there needs to be an opposite F on something else, and we can insist that the something else is fairly nearby. More generally, we can insist that the rules for when there should be an F shouldn't be too weird or complicated. Up to a point, that program works. That's a very compressed version of a long discussion.
Feel free to follow up. It seems like this is what Mr. Newton did while experimenting on accelerating objects before he came up with this law, but since he was the head of the British Royal Society of science, no one dared question him.
U is energy measured in joules. V is energy per coulomb of charge, measured in volts. They are similar, but say you were asked about the potential energy of an electron.
In Physics, various symbols or notations are used to denote different quantities. The denotations make the representation of the quantities easier. The body might speed up, slow down or change direction, after which, the body will continue moving at a new constant velocity unless, of course, the impulse causes the body to stop. There is one situation, however, in which we do encounter a constant force — the force due to gravitational acceleration, which causes massive bodies to exert a downward force on the Earth.
Notice that in this case, F and g are not conventionally written as vectors, because they are always pointing in the same direction, down. The product of mass times gravitational acceleration, mg , is known as weight , which is just another kind of force. Without gravity, a massive body has no weight, and without a massive body, gravity cannot produce a force. In order to overcome gravity and lift a massive body, you must produce an upward force m a that is greater than the downward gravitational force mg.
If the rocket needs to slow down, speed up, or change direction, a force is used to give it a push, typically coming from the engine.
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