You fill up a wagon so much that you expend lots of energy to just move it. But if you get it going and keep momentum up it get easier to pull and lets say you run a 100 feet with it. What was the hardest part? The initial getting the inertia moving.
Now think instead of pulling it the whole hundred feet in one shot you pull it a foot and have to start off the inertia energy expenditure again. Now it takes a hundred of those hard pulls.
But both wagons only went a 100 feet; but you spent way more energy one wagon. Where does the hidden energy missing off the ledger reside?
BingAI:
Copilot
The “hidden” energy you’re referring to is actually the energy required to overcome inertia. Inertia is the resistance of any physical object to any change in its velocity, which includes changes to both speed and direction. It is directly proportional to the object’s mass.
In your first scenario, the hardest part is indeed getting the wagon moving from rest, i.e., overcoming its inertia. This requires a force to accelerate it from rest to a certain velocity, and this force application results in an energy expenditure, known as work done1. Once the wagon is in motion, it’s easier to keep it moving due to the principle of momentum (mass times velocity). If there’s no opposing force (like friction or air resistance), theoretically, no extra energy is needed to keep the wagon moving at a constant speed1.
In your second scenario, you’re repeatedly overcoming the wagon’s inertia, i.e., you’re repeatedly doing the “hardest part”. Each stop-and-start requires you to expend energy to overcome inertia and get the wagon moving again. Hence, you end up doing more work overall compared to the first scenario1.
So, the “missing” energy in the second scenario isn’t really missing; it’s just that more energy is expended in repeatedly overcoming inertia. This illustrates the principle of energy conservation: energy cannot be created or destroyed, only transferred or transformed. In this case, the extra energy you expend is transformed into kinetic energy of the wagon each time you start moving it2.
You
But I expended more energy in the same distance and it is not tied up in kinetic energy anymore.
I don't believe a word of it. It is just fancy accounting because they don't know where the energy goes. They can't say it went to inertia so suddenly something is made up called Static Friction to take the energy in the form of heat.Copilot:
That’s correct. The extra energy you expended in the second scenario isn’t stored as kinetic energy in the wagon. Instead, it’s dissipated as heat due to the work done against friction.
When you stop and start the wagon repeatedly, each time you start, you have to overcome both the inertia of the wagon and the friction between the wagon and the ground. This requires more force, and hence more energy. When you apply this force, some of the energy is transferred to the wagon as kinetic energy, but some is also lost as heat due to the friction.
This is why you feel more tired in the second scenario: you’re not just moving the wagon, you’re also generating heat! This is a manifestation of the law of energy conservation: the total energy in a closed system (you + the wagon + the Earth) remains constant. If you’re using more energy to move the wagon, that energy has to come from somewhere (your body), and it has to go somewhere (the kinetic energy of the wagon and heat).
I can guarantee my car tires get hotter at high speed than starting and coasting repeatedly.