Helium balloon tied to a backpack

Question

I recently saw a video where a man was walking with a heavy backpack tied to a large helium balloon. The balloon made the backpack feel much lighter and helped him walk more easily.

It got me wondering - how is the principle of conservation of energy applying here?

Imagine the balloon is perfect and doesn’t lose any helium, and the person walks a 100kms distance with it. The helium buoyancy reduces the 10kg backpack to just 1kg. Now, if the man walked the same distance without the balloon, he'd have to spend far more energy. How is the ballon able to provide the seemingly free energy?

I get that the balloon provides buoyancy, like floating in water, but I still can’t fully wrap my head around how the energy savings is achieved in this scenario and where is it coming from?

Answer 1

The buoyancy of the balloon doesn't supply any energy for propelling the walker foward.

To understand why, one first needs to understand the forces and work required for walking (and running, for that matter).

When a person walks each foot needs to exert both a downward and backward force on the ground. The ground in turn exerts an upward and forward force on the person's foot per Newton's 3rd law propelling the person forward.

The vertical forces involved with walking enable each foot to leave the ground while the static friction force acting forward on the grounded foot enables the person to be propelled forward without slipping. It would be impossible for the person to move forward if both feet were always in contact with the ground.

But the vertical forces involved in walking do not accelerate the person forward since they are perpendicular to the horizontal displacement of the person during walking. Only the components of forces that act in the direction of the displacement of an object accelerate the walker horizontally. Thus the upward buoyant force of the balloon on the person does not supply energy needed to propel the person forward.

On the other hand, the upward buoyant force does reduce the effort of the walkers muscles that support the persons weight while walking or, for that matter, while simply standing! (Think of the reduced effort required of the muscles of astronauts in a zero gravity environment). So overall the walker becomes less fatigued due to the buoyancy of the balloon.

It's analogous to the requiring less effort to simply hold (without lifting ) a light weight versus a heavy weight. For further discussion of the difference between physiological work associated with “effort” and physics work, see my answer here: Energy Conservation in Holding Weights

Hope this helps.

Answer 2

This is more of an extended comment than an actual answer because the question is not really a physics question.

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Q: How much energy is required, in theory, to move a 10kg weight from point A to point B on the surface of the Earth if both points are at the same elevation above sea level, and if the two points are separated by 100km?

A: None! No energy at all. You will need to supply some energy to start the weight moving along the path from A to B, but in theory, you can recover all of that energy when you bring the weight to rest at B. You may need to supply some energy to climb to the top of a hill that's somewhere along your way from A to B, but in theory, you can recover all of that energy when you descend the other side of the hill.

If a human being spends energy by working their leg muscles all along the way, and if that energy cannot be recovered, that's a biology problem, not a physics problem. It's a question about the biochemical mechanism by which muscle tissue generates force. A metal spring can exert a continuous force on an object forever without using any energy at all. So why, does a human, skeletal muscle require a continuous supply of chemical energy to exert the same force? Maybe the folks at https://biology.stackexchange.com/ would like to answer that one.

Answer 3

Conservation of energy is like a bank account. Money can move from one bank account to the other, but it can't be destroyed. What conservation of energy doesn't say is how much money can be transferred and to what account.

By walking, the man is converting his stored chemical energy to kinetic energy, heat and sound. The heat and sound energy are wasted. By using a balloon, less of the chemical energy is converted into heat.

As mentioned in the other answers, in theory you only need an infinitessimal amount of energy to move from A to B if they are at the same height. Which you can achieve by moving in a vacuum on a low friction surface. A lot of energy is wasted inside your muscles. A bicycle is way more efficient for example. If you are planking you are also wasting energy without doing any useful work (in the physics sense).

If we go back to the bank accounts analogy, you are paying 100 € for shoes, but the shoes cost only 15 € to make. Physics does not forbid you to pay less. It only forbids money disappearing.

Answer 4

The comments about buoyancy are close. The energy comes from Gravity. The air surrounding the balloon is subject to gravity and falls down towards the Earth. This air displaces the balloon which, as others have said, is more buoyant. So the energy is the air pushing inwards and upwards on the balloon. And this energy is purely gravitational. It would be no different than if rocks were falling off the cliff and displacing water in a lake and causing a stick floating on the water to rise. Purely gravitational energy.

Here is a photo of an air bubble trapped inside water on the international space station. Although the air is more buoyant that the water, it remains in the middle because gravity is neutralized on the ISS. If the ISS returned to earth, the air bubble would obviously shoot to the top of the water. Your helium baloon is eactly the same. It is gravity that holds the air down and thus causes the baloon to rise.

Here is another example. A big kid and a small kid are sitting on either end of a see-saw. Every time the big kid jumps up, he falls back down again. So what energy is causing the little kid to rise up in the air? Gravity! Gravity causes the big kid to fall down and thus causes the little kid to rise up. It is the same thing with buoyancy. Gravity causes the air to fall and thus causes the baloon to rise.