I’ve always struggled to conceptualize the difference between the two. I understand their equations are different and KE being a scalar and Momentum is a vector, but to me they seem to describe the same thing … a mass moving with some velocity.
How are they different and why are they not interchangeable. Whats the best way to conceptualize their differences
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Just because two things can be used to describe the same thing in some way, that doesn’t mean they are identical. Your size can be described in terms of your height in metres and your mass in kg, but those are not the same quantity.
Perhaps one way to look at this is the classic “billiard ball” problem. Imagine two identical air hockey pucks with mass m, moving towards each other at equal but opposite speeds v. They both have momentum mv and kinetic energy 0.5*m*v^2 [more or less… let’s ignore irrelevant effects like relativity]. Since energy is a scalar it just adds – the total kinetic energy in the system is m*v^2 – but since momentum is a vector quantity, we add them vectorially. In 3 dimensions, the momenta are (mv, 0, 0) and (-mv, 0, 0) if we choose our axes to line up nicely, thus the overall momentum is zero. This is how gas temperature works – the average kinetic energy of the gas molecules is related to the temperature, there’s a whole lot of buzzing around going on, but there’s no overall momentum unless the gas a whole is moving (eg there’s some wind)
Maybe another approach to get some sort of feel for their difference using just words: the change in momentum is given by a force exerted over some time, while the change in energy is given by the force exerted over some distance. When a ball bounces off a wall there is very little energy transfer as there’s very little distance the force is exerted over, but the momentum is completely reversed as there is some a mount of time involved as the ball smushes up against the wall then rebounds. When a ball crashes into a wall and crunches a hole into it, the energy is all dissipated into crunching the wall – moving it some distance – but there is actually less momentum transfer (the ball just stops, rather than rebounding in the other direction, and the collision takes less time at high force as the wall gives way). Alternatively, if you push a very heavy thing to get it to accelerate very slowly – think strongman pulling a bus or something – then lots of momentum is imparted but not all that much energy comparatively.
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