In high school physics, I learned that the equation for energy from moving something is a factor of force and displacement. So if an object remains stationary, then no matter how much force is put into it, no energy is expended.
So how come if I hold a heavy box filled with dumbbells, I get tired? I’m obviously putting a lot of newtons into it to keep it from falling, but it’s not moving. So how is the weight of the object causing Me to expend energy?
That is a good question!
The answer is that there are two concepts here!
When you hold a heavy box filled with dumbbells it absolutely takes energy to stand there holding it not moving, it is evident in your body and the exertion it takes.
You expend energy when you stand there with a box of heavy dumbbells not moving but you do not do any work while doing so.
Work is a specific physics concept and it refers to this idea that even though you may expend energy by doing something that is a different measurement than how much the system was changed by an input of energy.
The reason I think this is a good question is because it is a really natural question to ask and many times people just assume the answer isn’t intuitive and they are just too stupid to understand it (they aren’t) but in asking your question now you know there is another thing called “Work” that describes the part of the thing that was confusing you!
The question is also a rabbit hole because of how gravity is always accelerating us (unless we are in free fall such as when orbiting the earth) and yet intuitively we of course see that as a steady state and in a sense it is, work is not being done on us by gravity but that does not mean we are not experiencing a constant force upon our bodies from it.
Imagine you are in deep space in a spacesuit holding the box of heavy dumbbells, in this case it would take no energy to simply stay in that state with your hands on the box right? Now, if you went to try to lift the box and push yourself down away from it you would need to expend energy. When you add gravity into the context the reason the difference between the amount of energy something takes and the amount of work is accomplished can feel so mismatched is that we are in a constantly accelerating context and the bones and chemical bonds within us keep us from crumpling… which takes energy to maintain!
edit okay one more intuitive real world example, unfortunately a common hazard with helicopters landing in random places during emergencies is people don’t intuitively connect a massive heavy object relatively motionless in the air with an absolutely huge amount of force needed to maintain that state, and the immense air flow downwash from the rotors can send objects hurtling into people or knock them over and hurt them in a way that catches people by surprise because our brains see the helicopter not moving and think -> not a violent amount of force. A helicopter expends an immense amount of energy to hover, but it does not do any work with its engines to maintain a hover from a gravitational potential/kinetic energy context.
The effect of gravity is the same as movement. We are all “falling” towards the center of the Earth, at all times. You holding onto something heavy, is preventing it from falling…so the force needed to keep it stationary is equal to the force of gravity pulling it down.
Energy is not movement. Kinetic energy comes from movement (half mv squared!)
You need to account for thermal, chemical, potential, elastic potential, electric, etc. energies
Energy is being expended as your muscles are working against the force of gravity to hold the object up!
There is force being applied and you are resisting it. If you weren’t resisting it, movement would occur, but only in an entropic fashion.
Net movement is zero. But there is equal and opposite force (gravity and your arms) making net force zero. The force exerted by your arms is what makes you tired.
Look at energy = force, not only movement (one type of force, kinetic force). There are other types of forces, like gravity. In your example, you’re constantly providing a counter-force to gravity.
But energy isn’t force. Energy is force times distance. There’s no distance.
The distance is to the ground (technically to the centre of the nearest gravity well, but generally the ground gets in the way of that). The box would move towards the ground in order to expend potential kinetic energy and reach a lower energy state, but the counter force you’re providing cancels it out, keeping it in place.
It has potential energy it wants to make into kinetic, and you are the force holding that back
