Energy to hold an object for a given time

[h1a8]

Let's say an object is held at rest by a force opposite of gravity for a given amount of time. Since it takes energy to hold the object then how can one calculate the energy needed to hold the object for x amount of time?

Assume near 100% efficiency, or most of the force is used to hold the book and not create heat or anything else.

The reason why I ask this is because I notice how tired I get holding things for a long time. Obviously I'm expending energy. Just wanted to know how much if my muscles were theoretically very efficient.

 

[xAxis]

if your muscles were 100% efficient, no energy would be required to hold an object at the same hight, because no work has been done

 

[h1a8]

if your muscles were 100% efficient, no energy would be required to hold an object at the same hight, because no work has been done

We know that's not true since indeed I am still applying a force and will still get tired after a while. Also I'm saying close to 100% efficient, not exactly 100%.

 

[azizlwl]

It depends on how you hold the object.
Try 3 positions with your hand fully stretch. Down, horizontally and up.
Surely you can't hold long if it is hold with the hand in horizontal position.
Use ladder to make the object at equal height.

 

[h1a8]

It depends on how you hold the object.
Try 3 positions with your hand fully stretch. Down, horizontally and up.
Surely you can't hold long if it is hold with the hand in horizontal position.

True. But assuming just a random force is holding the object (not me).

 

[azizlwl]

Energy is conserved.
If you put an object on a spring, it will be compressed and remained compressed. without outside energy to keep it in compressed state.

 

[h1a8]

Nevermind I think I know how to calculate it. All I have to do is calculated the distance the object will move if gravity wasn't acting on it. Let's say I hold a m kg object for t seconds. Then I would need to apply a force of mg netwons. Now the distance an object at rest will travel if mg force was applied to it over t seconds is d=1/2at^2 = 1/2gt^2
So the work done or energy used would be W=mg x 1/2gt^2 = 1/2mgt^2

So the energy required to hold an object with weight w for t time is
E=1/2wt^2.

Is this correct?

 

[azizlwl]

The object is not moving, so a=0

 

[h1a8]

The object is not moving, so a=0

lol it doesn't matter. If gravity was suddenly cut off then the object will move. Read my post above it solves the question completely.

 

[azizlwl]

If there is any energy to hold the object, what do you think that supplying the energy?

 

[h1a8]

If there is any energy to hold the object, what do you think that supplying the energy?

It doesn't matter what is supplying the energy since it is a hypothetical question and can be applied to any situation.

The fact is without energy forces can't exist. In space, where gravity is negligible, if the same force holding the object was applied then the object will now accelerate and move a distance. You can easily calculate the energy by the product of the force and the distance it moved. But on Earth the object remains at rest because gravity is opposing the force. That doesn't mean energy isn't being used since it was being used in space.

In summary, the fact that an object isn't moving doesn't imply that energy is not being used.

 

[azizlwl]

Now you hold an object on your hand AND another object hold by a string.
Will you hold it for a long time without eating?
Will the string hold the object for a long time too.
Do we need to feed the string?

You received your energy from food to keep the muscle in contract position from relax position. How about without food for days and try to lift a heavy object. Will the object weighs more, equal or less.

Where do the string gets its energy.
Or do the string need energy to hold the object.

If the string gets energy to hold the object, then why you can't receive that energy.
You have to resort to food for the energy.

 

[Drakkith]

Let's say an object is held at rest by a force opposite of gravity for a given amount of time. Since it takes energy to hold the object then how can one calculate the energy needed to hold the object for x amount of time?

It does not take energy to hold an object as long as you are not using a machine or other mechanism that performs work (such as your muscles) to do it. For example a string holding up an object does not require energy to do so. The fundamental forces of nature, such as the electromagnetic force that keeps the atoms and molecules of the string together, do not require energy to function.

 

[nvir477]

1. Two equal amount of forces in opposite direction at a given time may not move the OBJECT as per third law of Newton. This is horizontal pull like Tug-of-War. Here 'x' amount of energy is released at one end, and as OBJECT is not moved in either direction opposite end may also have released equal amount of energy i.e. 'x'.
OBJECT is not moved and total release of energy is 'x'+'x'='2x'.

2. Now let you hold an OBJECT at one meter height having `X`kgs of weight for a given period of time this is a vertical position comparing to the tug-of-war. You are constantly releasing your energy with passing of time.
As time increases you release more energy and another person could replace you to hold the OBJECT in the same state of position, he would also release energy with passing of time...Now as per (1.) above OBJECT is not moved and equal amount of energy is released from opposite ends. If we measure amount of energy 'x' used to hold the OBJECT at given height during given time then it would be same amount of energy used from other end i.e. Earth due to effect of GRAVITY.

 

[Drakkith]

Now as per (1.) above OBJECT is not moved and equal amount of energy is released from opposite ends. If we measure amount of energy 'x' used to hold the OBJECT at given height during given time then it would be same amount of energy used from other end i.e. Earth due to effect of GRAVITY.

There is no energy released or used from the Earth as a result of you holding up an object.

 

[xAxis]

We know that's not true since indeed I am still applying a force and will still get tired after a while. Also I'm saying close to 100% efficient, not exactly 100%.

Biologists (or anatomists) have an explanation for this. I think it's because many different muscles act when we hold object and they continuously strain and relax, and we get tired. Phisicaly, as long as the object is at the same hight, no energy is required. Otherwise, the law of conservation of energy would be violated.

 

[mfb]

Biologists (or anatomists) have an explanation for this. I think it's because many different muscles act when we hold object and they continuously strain and relax, and we get tired. Phisicaly, as long as the object is at the same hight, no energy is required. Otherwise, the law of conservation of energy would be violated.

This.

If you want to find the required energy, ask a biologist. This is a purely biological thing, a robot (or a table...) would not require any energy.

 

[HallsofIvy]

Let's say an object is held at rest by a force opposite of gravity for a given amount of time.

Since it takes energy to hold the object

As a general statement this is not true. For example, if you place a weight on a table, the weight "holds" the weight up without doing any work. That does not require any energy. If you suspend an iron weight from a permanent magnet, no energy is required.

then how can one calculate the energy needed to hold the object for x amount of time?

Assume near 100% efficiency, or most of the force is used to hold the book and not create heat or anything else.

The reason why I ask this is because I notice how tired I get holding things for a long time. Obviously I'm expending energy. Just wanted to know how much if my muscles were theoretically very efficient.

This is more a physiology question than a physics question. "A" muscle consists of many separate fibers that contract for a moment, then relax. As a result, the weight you are holding is constantly dropping slightly, then being pulled back up. Since your muscles do not recover energy from the work done by the weight when it drops down, you lose energy in the work done in moving the weight back up.

 

[256bits]

Nevermind I think I know how to calculate it. All I have to do is calculated the distance the object will move if gravity wasn't acting on it. Let's say I hold a m kg object for t seconds. Then I would need to apply a force of mg netwons. Now the distance an object at rest will travel if mg force was applied to it over t seconds is d=1/2at^2 = 1/2gt^2
So the work done or energy used would be W=mg x 1/2gt^2 = 1/2mgt^2

So the energy required to hold an object with weight w for t time is
E=1/2wt^2.

Is this correct?

Or you could try the calculation if a rocket or helicopter iis holding up the object. and perhaps a frictional belt attached to the object and running over a rotating drum. And see if you get the same result just for fun.

Yes you will become tired holding up an object with your muscles and the tiredness depends on how you are holding it. you might take note that in certain countries it is common practise to carry a heavy load on top of the head for very long distances, and some people are so adept that they need not balance it with their hands. The reason being is that the load is supported more through the skeleton and less through muscle action.

 

[h1a8]

As a general statement this is not true. For example, if you place a weight on a table, the weight "holds" the weight up without doing any work. That does not require any energy. If you suspend an iron weight from a permanent magnet, no energy is required.


This is more a physiology question than a physics question. "A" muscle consists of many separate fibers that contract for a moment, then relax. As a result, the weight you are holding is constantly dropping slightly, then being pulled back up. Since your muscles do not recover energy from the work done by the weight when it drops down, you lose energy in the work done in moving the weight back up.

Thanks I didn't know that about how the muscles work.

Well I'll go the theoretical route and not talk about muscles or tables or strings but actual forces that are pushing (not holding) the object upward against gravity. So if gravity was suddenly cut off then the object will accelerate upward and move a distance and thus work is done. Now just because the object moved in the direction of the force when gravity was cut off vs. it not moving when gravity is acting shouldn't not change the fact that energy is still being used in both situations and that my calculation is indeed correct (E=1/2mgt^2) Right?

 

[willem2]

So if gravity was suddenly cut off then the object will accelerate upward and move a distance and thus work is done. Now just because the object moved in the direction of the force when gravity was cut off vs. it not moving when gravity is acting shouldn't not change the fact that energy is still being used in both situations and that my calculation is indeed correct (E=1/2mgt^2) Right?

It's actually $E = \frac {1}{2} m g^2t^2$

Using the fact that the speed v = gt and kinetic energy = (1/2)mv^2

The power needed to push an object away with a force F, depends on the speed of the opject v, in the direction of the force. It is equal to vF. If v = 0, the power needed is 0.

From your equation for kinetic energy, you can easily see that the power can't be constant. After 1 second, the kinetic energy would be (1/2)mg, so the average power would be (1/2)mg, but after 2 seconds the energy would be 2mg, and the avergage power over 2 seconds would be mg.

The instantaneous power needed is the derivative of the kinetic energy with respect to time. The derivative of (1/2) mg^2 t^2 is m g^2 t, and this is equal to (gt) (mg), so it's equal to vF.

 

[Nobelian]

You are exerting a force (force normal) upwards, but there is no work done because the object has not traveled a distance. The energy of muscular contraction requires a constant change in tension of the muscle fibres, so while the object is not moving, your body is consistently doing work on the muscle fibres, and that is how they expend energy. This energy dissipates because it is not effective, and turns into heat. So no energy is actually applied on the object itself-- it is the muscle fibres that require constant energy to contract.

 

[h1a8]

You are exerting a force (force normal) upwards, but there is no work done because the object has not traveled a distance. The energy of muscular contraction requires a constant change in tension of the muscle fibres, so while the object is not moving, your body is consistently doing work on the muscle fibres, and that is how they expend energy. This energy dissipates because it is not effective, and turns into heat. So no energy is actually applied on the object itself-- it is the muscle fibres that require constant energy to contract.

Thanks but I already changed the question into one where a true upward force (not a holding one) is equal but opposite to gravity. The result is
E=1/2mg^2t^2

 

[Dale]

Now just because the object moved in the direction of the force when gravity was cut off vs. it not moving when gravity is acting shouldn't not change the fact that energy is still being used in both situations and that my calculation is indeed correct (E=1/2mgt^2) Right?

Wrong, it completely changes the facts. In the no-gravity case the force is applied over a distance, so work is done, the object accelerates so kinetic energy increases. In the gravity case the force is applied over 0 distance, so no work is done, and the object does not move so kinetic energy is zero and potential energy is unchanged. If you were right then energy would not be conserved.

You have had consistent feedback from several knowledgeable people. If you don't like the answers then you are always welcome to try and find another universe that has laws of physics more to your liking.

 

[sophiecentaur]

Work involves a force and a distance moved. Work on a stationary object (sitting, supported on a shelf) is zero. Hence there is no transfer of energy.
Muscle fibres actually switch on and off in sequence and there are finite movements as they switch on and off. There is your work done but it's internal to your body but not done ON the object you are supporting.
The only useful measures of the energy of an object sitting on a shelf would be, either its potential energy wrt an arbitrary ground height (mgh) or its absolute potential related to its energy at infinity (out in space) (mMG/r).

 

[HallsofIvy]

You generally seem to be confusing "force" and "energy". The fact that you apply a force to something does NOT neccesarily mean you are doing work (using energy). As others have said "work= force times distance". If a table is holding up a weight, it is applying force but not doing in work so that requires no energy.

 

[Lsos]

We know that's not true since indeed I am still applying a force and will still get tired after a while. Also I'm saying close to 100% efficient, not exactly 100%.

I will join into reinforce the concept that energy = force x distance. If distance is 0, then so is energy. You cannot argue the math here, it is non-negotiable. You DO NOT need energy to apply a force. If you die, your dead body will continue to apply a force to the cold ground for as long as it remains.

The reason you get tired holding things up is because you are NOT 100% efficient. In fact, you are 0% efficient. You are expending energy to do NOTHING (of value). You could use you hand and spend a few watts to hold the thing up, you could use a helicopter with thousands of horsepower or a space shuttle with millons. Or you could use a table with 0 power (or a cart if you want to be able to move it around...it's why they invented the wheel). The reason a space shuttle, helicopter, and you are wasting energy, is because they are putting it all into everything BUT whatever they are holding up. A helicopter and rocket, for example, need to pump around tons of air or propellant to stay up. YOU need to pump blood and twitch your muscles and generate heat and breathe etc. A table doesn't need to do anything.

Point is, if all you want to do is hold something up, chances are you don't need a human to do it. In most cases, a rock will suffice.

 

[h1a8]

I will join into reinforce the concept that energy = force x distance. If distance is 0, then so is energy. You cannot argue the math here, it is non-negotiable. You DO NOT need energy to apply a force. If you die, your dead body will continue to apply a force to the cold ground for as long as it remains.

The reason you get tired holding things up is because you are NOT 100% efficient. In fact, you are 0% efficient. You are expending energy to do NOTHING (of value). You could use you hand and spend a few watts to hold the thing up, you could use a helicopter with thousands of horsepower or a space shuttle with millons. Or you could use a table with 0 power (or a cart if you want to be able to move it around...it's why they invented the wheel). The reason a space shuttle, helicopter, and you are wasting energy, is because they are putting it all into everything BUT whatever they are holding up. A helicopter and rocket, for example, need to pump around tons of air or propellant to stay up. YOU need to pump blood and twitch your muscles and generate heat and breathe etc. A table doesn't need to do anything.

Point is, if all you want to do is hold something up, chances are you don't need a human to do it. In most cases, a rock will suffice.

lol correct. But now I'm not talking about holding forces anymore or forces supplied by the human body.

You generally seem to be confusing "force" and "energy". The fact that you apply a force to something does NOT neccesarily mean you are doing work (using energy). As others have said "work= force times distance". If a table is holding up a weight, it is applying force but not doing in work so that requires no energy.

Work involves a force and a distance moved. Work on a stationary object (sitting, supported on a shelf) is zero. Hence there is no transfer of energy.
Muscle fibres actually switch on and off in sequence and there are finite movements as they switch on and off. There is your work done but it's internal to your body but not done ON the object you are supporting.
The only useful measures of the energy of an object sitting on a shelf would be, either its potential energy wrt an arbitrary ground height (mgh) or its absolute potential related to its energy at infinity (out in space) (mMG/r).

Wrong, it completely changes the facts. In the no-gravity case the force is applied over a distance, so work is done, the object accelerates so kinetic energy increases. In the gravity case the force is applied over 0 distance, so no work is done, and the object does not move so kinetic energy is zero and potential energy is unchanged. If you were right then energy would not be conserved.

You have had consistent feedback from several knowledgeable people. If you don't like the answers then you are always welcome to try and find another universe that has laws of physics more to your liking.

The laws of physics are not being violated in any way in the scenario I'm thinking of but not explaining correctly. It's my fault and not others. I'm talking about the minimum energy needed to fuel the force, not the energy the force creates. And I'm talking about forces that actually create movement if no opposing forces existed (not holding forces). And I'm not talking about forces from the human body anymore.

I see the problem. It's my scenario. I'll revise it:

"Let's say an object is at rest in the vacuum of space. Then simultaneously two equal but opposite opposing forces were applied to the object. Both forces are such that each will accelerate the object in it's direction if it weren't for the opposite force (no holding forces here)."

Discussion:

Although the object is still at rest doesn't mean there is no energy fueling the forces. To prove this let's say that one force was suddenly cut off. The object will now accelerate and move in the direction of the acting force. Minimum energy fueling the force during the motion can now be easily calculated by the product FORCE x DISTANCE. But that same energy was also fueling the force when the object was being opposed by the other force. The moment that one force was released doesn't mean that energy is NOW fueling the acting force, when before it wasn't.

In other words, We all can simply calculate the minimum Energy that it will take to generate a force of magnitude 'mg' in order to move an object of mass m over the distance X. This is because energy generated the force that did work on the object. But since we know the object's acceleration over the distance X (it was g) we can calculate the time t it took to travel X distance by using the equation Energy= mgX=1/2m(gt)^2. Now in the scenario where both opposite forces are acting on the object and the object isn't moving, this same equation can also be used to calculate the minimum energy that's fueling each force over time t, since it is a function of time only.

 

[azizlwl]

If a block rests a horizontal plane and no forces acting on it horizontally, then what energy is consumed. You say no energy(horizontally) since no forces(horizontally) involved.

Now you see only the centre of the block, the rest you can't see. Then if 2 horizontal opposite and equal forces applied to it. It does not move and to you the situation is as above. Not moving and no forces seen by you.

How do you know that energy is consumed in case 2 but not case 1.

 

[willem2]

Now in the scenario where both opposite forces are acting on the object and the object isn't moving, this same equation can also be used to calculate the minimum energy that's fueling each force over time t, since it is a function of time only.

No, it can't. And with that, I mean that if you actually try to calculate it, you get more than 1 answer.

If you use a force of 1N on a 1Kg object for 1 second, it will move at 1 m/s and gets a kinetic energy of 0.5J
If you use a force of 1N on a 2Kg object for 1 second, it will move at 0.5 m/s and gets a kinetic energy of 0.25 J.

How can this be? which of these energies is the minimum energy needed to "fuel the force" for 1 second?

I'll stick with power = force * speed.

 

[Drakkith]

In other words, We all can simply calculate the minimum Energy that it will take to generate a force of magnitude 'mg' in order to move an object of mass m over the distance X. This is because energy generated the force that did work on the object. But since we know the object's acceleration over the distance X (it was g) we can calculate the time t it took to travel X distance by using the equation Energy= mgX=1/2m(gt)^2. Now in the scenario where both opposite forces are acting on the object and the object isn't moving, this same equation can also be used to calculate the minimum energy that's fueling each force over time t, since it is a function of time only.

Energy does not create force, instead it is force that creates energy. If I place an electron near another electron, the two will experience a repulsive force and be accelerated away from each other and in the process they will gain kinetic energy. The force is why the electrons gained energy, and it does not require energy to function.

Now, the situation is much more complicated if we get into things like rocket engines which have to go through chemical reactions to generate their thrust, but the basics are still the same. A force is what accelerates something and gives it energy.

 

[Dale]

The moment that one force was released doesn't mean that energy is NOW fueling the acting force, when before it wasn't.

Actually, it does. The minimum amount of energy required is equal to the work done on the object, by conservation of energy. If the work done is 0 then the minimum energy is 0.

Consider your example where the forces are provided by a pair of springs at equilibrium under a compression force F. If one spring is used the object accelerates, but if both springs are used the object does not. Use the standard spring formulas to calculate the energy used in each case.

 

[Lsos]

The laws of physics are not being violated in any way in the scenario I'm thinking of but not explaining correctly. It's my fault and not others. I'm talking about the minimum energy needed to fuel the force, not the energy the force creates. And I'm talking about forces that actually create movement if no opposing forces existed (not holding forces). And I'm not talking about forces from the human body anymore.

I'm trying to understand what you're asking...

Is it this: How much minimum energy would it take to, for instance, keep a spaceship motionless in one point above the earth?

Or, How much minimum energy would it take, for instance, to keep a helicopter hovering motionless?

If that's what you're asking, then that is no different a question than asking how much energy would it take for a human or table to hold the object in place. Whether on the ground, on a rock, or in space fighting against a black hole's gravity (outside of the event horizon), as long as there is no acceleration the answer is ZERO. All you have to do is break up the problem into a simple free-body diagram. You will notice that all these examples have two equal but opposite forces acting on an object. Whatever is is that applies those forces is irrelevant. As long as the forces are balanced, the energy requirement is none.

Now, realistically if we want a helicopter to hover we need a lot of energy. But that's just a limitation of our technology. The fact is that theoreticaly we shouldn't need any energy. For example, if we made the rotor blades longer (thereby moving more air), they would be more efficient at providing lift, and the energy requirement would drop. Make them infinitely long and perfect blades, and we need no energy. Obviously we don't know how to do that, but physics doesn't prevent us from accomplishing an equivalent thing.

A spacehip hovering in space: obviously we need to fire a rocket to keep it from falling, requiring lots of energy. But again, depending on the rocket we could use more or less fuel. An ion engine, firing a little mass but very quickly requires much more energy than a chemical rocket engine firing lots of mass but slower. The more mass we expel, the less energy we need, so we could always use bigger engines to fire more and more mass and require less and less fuel. The minimum is, again, zero. Of course no reasonable rocket we can build could fire mountains of mass, but that's just an engineering limitation of rocket engines. There's no reason, for example, why we couldn't place a great big magnet on the Earth that keeps the spaceship hovering. Or place another Earth behind it, balancing out the forces and, again, keeping it hovering. These are all just technological limitations. The theoretical limitations and the answer to your question is, to reiterate, zero.

 

[ronaldleemhui]

To hover, a helicopter needs to provide a thrust by accelerating air downward. The thrust is proportional to the mass of downdraft per unit time times the velocity of the flow. If the rotors are extremely long and wide, the volume of downflow can be great. This allows the velocity to be low and still achieve the same thrust. In the extreme, the work required would approach zero, apart from parasitic drag of the rotors, the effects of turbulence, friction and the inefficiencies inherent in the need for a tail rotor.

Another way to look at things is to view the rotors just like wings on an airplane. In this case, however, the wings move while the helicopter stays put. One can think of a glide ratio for a glider, or of an airplane without power. Typical ratios can run from 1:8 for a small plane to 1:50 for a highly efficient glider. Now let us assume that the rotors are safely subsonic at the tips and perhaps 100 mph somewhere near the effective middle. A 1:8 glide ratio for the airfoil would therefore lead to a natural sink rate of 100/8 mph without power. The sink rate times the weight of the helicopter becomes the power consumption required to hover. (That is, if that amount is applied to the rotors, the natural sink rate will be neutralized.) As an order of magnitude,

weight of helicopter 1800 lb
sink rate as estimated above = 12.5 mph = roughly 18 ft/sec

so power requirement = 1800 * 18 / 550 hp or about 60 hp.

Power requirement would be less, perhaps by 50% close to the ground.

Just order of magnitude estimates.

 

[K^2]

Nevermind I think I know how to calculate it. All I have to do is calculated the distance the object will move if gravity wasn't acting on it. Let's say I hold a m kg object for t seconds. Then I would need to apply a force of mg netwons. Now the distance an object at rest will travel if mg force was applied to it over t seconds is d=1/2at^2 = 1/2gt^2
So the work done or energy used would be W=mg x 1/2gt^2 = 1/2mgt^2

So the energy required to hold an object with weight w for t time is
E=1/2wt^2.

Is this correct?

If you put an object on the table, all of the above logic still applies. Yet, a table doesn't use up any energy to support an object. The above logic is, therefore, flawed.

The amount of energy required to support an object by a person has everything to do with biology of a muscle and cannot be resolved from physics considerations alone.