What is the difference between energy, force and momentum?
In: Physics
Energy and momentum are the same thing, in different forms. Momentum is the energy of motion, and energy is the energy of position (potential).
When you throw a ball straight up, you impart it with momentum, which is converted to potential energy while it slows down as it approaches the peak of its height, where potential energy is max, and momentum is absent. Then the process reverses, converting that stored potential energy back into momentum, returning the ball to you at precisely the same speed that you threw it at.
Because potential energy is explicitly a phenomenon associated with position (location in a gravitational field, location of charged particles relative to one another, compression or extension of a spring), then for there to be a change in the energy, there must be a corresponding change in position.
When you measure the rate of change of energy with respect to the change in position, the value that comes out of that is force.
Conversely, because momentum is explicitly a phenomenon associated with time (time derivatives, really), then for there to be a change in momentum, there must be a corresponding change in time.
When you measure the rate of change of momentum with respect to the change in time, the value that comes out of that is force.
So, in reverse direction now –
If you apply a force over a distance (compress a spring), you have done *work*, which is the transference of energy over a given distance.
if you apply a force for a given amount of time, you have provided an *impulse*, which is the transference of momentum over a given time.
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