# Settle a bet:

If Two objects, both traveling in a vacuum, go from point A to B, but one object travels twice as fast - does that take more, less or the same amount of energy?

## Answers and Replies

nbo10
more

JMD

More?

Thanks, but could you tell me what logical theory, equation, or reference material your response is based up?

MrCaN
The speed at which a object moves is dependent on the energy applied to it.

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As I said in your other thread (argh) -- it takes no work to move an object from one point to another in a vacuum. The energy you invest in initially accelerating the object can be (in principle) reclaimed as you slow it back down. There are no dissipative forces in a vacuum, and there are no fields in which you must invest potential energy. The energy thus consumed is zero.

- Warren

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Originally posted by MrCaN
The speed at which a object moves is dependent on the energy applied to it.
You don't apply energy to things. You apply forces.

- Warren

MMkay...

Ah yes good point. So UNLESS you have a resistant force such as air to provide drag, then the amount of 'force' necessary to propel an object in a vacuum from point A to B is the same despite the speed of these objects?

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You can't determine force that way. If someone tells you how rapidly they want to accelerate an object, and how much mass it has, you can calculate the requisite force.

If someone tells you they want to move a body from A to B in a vacuum in a certain amount of time, you are free to choose any force you want.

You could select a very very large force that acts over only a very short time at the beginning and the end of the motion, so that the body's velocity while in transit is more or less always constant, and no force is applied at all during the majority of its trip.

Or you could select a very mild force and apply it in one direction all the way to the half-way point -- at which point you begin applying it in the opposite direction to slow the body back down so that it stops at B.

- Warren

it depends on the mass, and also the question wasn't phrased exactly in a physical sense. it would be better to ask "what are the objects kinetic energies?" is this what you meant?

maximus
Originally posted by ando
If Two objects, both traveling in a vacuum, go from point A to B, but one object travels twice as fast - does that take more, less or the same amount of energy?

as i said in the other thread, more, but only by an increadible small amount. the effects of E=mc2 do not come into play unless these two objects are very close to the speed of light.

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Bah. I give up.

- Warren

J-Man
If Two objects, both traveling in a vacuum, go from point A to B, but one object travels twice as fast - does that take more, less or the same amount of energy?
The statement "both traveling in a vacuum" implies that both objects have a nonzero starting velocity at point A. Therefore it requires no energy for either to get to point B, assuming that point B is along a direct line from point A coincidental to both trajectories. See Newton's 1st law - inertia: particle in motion will remain in motion unless there is a force acting upon it.
The correct answer, as I see it, is they take the same amount of energy, which is zero.

P.S. The answer is different if they both start with zero velocity at point A, but we will need to know the mass of both objects.

poop

Basically I don't know what I'm talking about and I really didn't know what I was asking. I really just wanted to know if walking a mile on planet Earth burns more, less, or the same amount of energy as running a mile. My intuition says walking a mile burns less energy, but I have read an article that suggests otherwise here:

http://content.health.msn.com/content/pages/1/3079_883.htm?lastselectedguid= [Broken]{B7F18B8A-5BA8-43FC-B950-5FA349C6A692}

I'm still not convinced however. My friend says that if you take a step, it doesn't matter wether you do it fast or slowly, it burns the same amount of energy. The above article says that walking a mile burns slightly more energy than running, but only because you are exposed to the natural elements for a longer perioed of time and thus your body has to work longer to keep itself cool and keep the heart and lungs working.

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J-Man
That's an entirely different question.
K = 0.5 * m * v^2, where K is kinetic energy, m is mass, and v is velocity.
So technically, a person running has more kinetic energy than a person walking, however, that doesn't necessarily mean he/she is expending more energy, just that they turned more potential energy into kinetic for an equal time running/walking.

I too would think it would require more energy to run a distance than to walk it, especially as the distance increases. But I think it would be hard to prove one way or the other.

Originally posted by ando
If Two objects, both traveling in a vacuum, go from point A to B, but one object travels twice as fast - does that take more, less or the same amount of energy?

No. In the first place it doesn't take any energy whatsoever to go from one place to another unless there is a force acting on the object. In an inertial frame of referance in the absence of an applied force the energy required to go from one place to another is zero. That means that one does not have to expend at non-zero net amount of energy to make this happen.

For example: If there is no net force acting on the object then that object has the exact same amount of energy when it left point A as when it arrived at point B.

Now as the amount of energy a moving body has - that's another thing. In the absence of a net force the total energy of a body is the kinetic energy. Here I'm defining the kinetic energy as the energy required to cause the object to change it's speed from zero to v. The kinetic energy is a function of both speed and mass. So while a bodies energy depends on its speed and will increase if the speed is faster - the energy might be less than the energh of a larger object which is moving slower.

Hope that helps - sorry if I repeated what someone said

Pete

To the revised question, you have to move your limbs faster when running than walking, so your muscles are producing more force than if you're walking. When you're walking or running, you only have to overcome friction and air resistance (you don't have to accelerate your whole body with every step except to overcome these forces). So KE = mv2/2 will be the energy required only for the INITIAL acceleration. You can see that one will be greater. Force and energy are related fundamentally (energy = integral of force if force is a function of distance), so my guess is that it would indeed take more energy in this particular situation for the faster runner, even if they begin from point A at full velocity.

For the first question, they will both require zero energy, almost: the momentum of virtual particles impacting on the object will require a small amount of energy to overcome. This energy is homogeneous througout space so far as anyone knows, so the net energy of the virt particles will be equal. But the POWER (E/time) impacting the higher velocity particle will be greater than for the small vel. part.

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Staff Emeritus
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Originally posted by ando
Basically I don't know what I'm talking about and I really didn't know what I was asking. I really just wanted to know if walking a mile on planet Earth burns more, less, or the same amount of energy as running a mile.

My friend says that if you take a step, it doesn't matter wether you do it fast or slowly, it burns the same amount of energy.]

To answer this question, you really have to examine the mechanism behind walking and running. In both, one leg swings forward, while the other pushes backwards, until the forward leg hits the ground, then it starts moving backward, and the backward leg starts moving forward. Each leg has to come to a complete stop(if even for an instant) before it can reverse direction.

This means the muscles must accelerate the leg back up to speed with each stride. For running, this takes more force, because the leg has to be accelerated to a higher speed. this equates to a greater energy output by the muscles.

So if you isolate to just the energy expended by the legs, you will use more energy running.

Of course, as the article points out, the total energy expended by the body can be a factor if you bring it into consideration.