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.
Kinetic energy is from a force applied over a given distance (J = Nm)
Momentum is from a force applied over a given time (kgm/s = Ns)
These might sound similar, and they can both be used to describe how something is moving, but that distance or time thing results in them having wildly different applications
The big difference is that energy is proportional to velocity squared, while momentum is only proportional to velocity.
Lets say you sit on a skateboard, and fire a gun. You and the bullet both end up with the same amount of momentum, but the bullet gets the vast majority of the kinetic energy, because it’s moving faster.
Another way of looking at it is that momentum = force * time, while energy = force * distance. A less massive object will move farther when the same force is applied for the same amount of time.
The big difference is that kinetic energy can be converted to other forms of energy, but momentum will always be momentum.
When two billiard balls collide, you can approximate their final kinetic energy as about the same as the kinetic energy going in.
When two cars collide, crumple, and stick together afterward they’ve converted the most possible kinetic energy into other forms like heat.
Initial and final total momentum are the same in both cases, but the collisions are very different
Momentum and kinetic energy differ in their fundamental properties and what they describe. Momentum is a vector quantity determined by an object’s mass and velocity, with direction being crucial. In contrast, kinetic energy is a scalar quantity solely dependent on mass and the square of velocity, with no directional component. Momentum characterizes an object’s motion and direction, while kinetic energy quantifies its capacity to do work due to that motion.
Imagine a car and a truck moving down the highway.
Momentum: The car is small, and the truck is much larger. They are both moving at the same speed, say 60 miles per hour (mph). Momentum takes into account both their size (mass) and how fast they are going. So, even though they have the same speed, the truck has more momentum because it’s heavier. It’s like a big boulder rolling downhill; it’s hard to stop because it has a lot of momentum.
Kinetic Energy: Now, think of kinetic energy as the “oomph” or power these vehicles have because they are moving. The car and the truck both have kinetic energy because they are going at 60 mph. However, the car has less kinetic energy than the truck because it’s smaller and has less mass. It’s like comparing a small firecracker to a big fireworks display – the big fireworks have more kinetic energy and can do more exciting things.
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