# Energy to hold an object for a given time

1. Jul 4, 2012

### 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.

2. Jul 4, 2012

### 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

3. Jul 4, 2012

### h1a8

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%.

4. Jul 4, 2012

### 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.

5. Jul 4, 2012

### h1a8

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

6. Jul 4, 2012

### 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.

7. Jul 4, 2012

### 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?

8. Jul 4, 2012

### azizlwl

The object is not moving, so a=0

9. Jul 4, 2012

### h1a8

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.

10. Jul 4, 2012

### azizlwl

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

11. Jul 4, 2012

### h1a8

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.

12. Jul 4, 2012

### 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.

Last edited: Jul 4, 2012
13. Jul 5, 2012

### Drakkith

Staff Emeritus
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.

14. Jul 5, 2012

### 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 Xkgs 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.

Last edited by a moderator: Jul 5, 2012
15. Jul 5, 2012

### Drakkith

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

16. Jul 5, 2012

### xAxis

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.

17. Jul 5, 2012

### Staff: Mentor

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.

18. Jul 5, 2012

### HallsofIvy

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.

19. Jul 5, 2012

### 256bits

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.

20. Jul 5, 2012

### h1a8

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?

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