# The question no one seems to know average force

1. Feb 25, 2010

### waynexk8

Hi all,

Question 1,
If my 1RM {RM is the most I can lift, repetition maximum} is 200 pounds, and if I accelerate 160 pounds {80%} with a force of 200 pounds 80% of a mile or metre, or any distance, {it’s a weightlifting rep if you would like to know} and use the other 20% to decelerate and immediately reverse the direction, what is the average force please ???

As I am accelerating for the whole distance of 80% I would have thought it had to be 200.

As I find averages out like this, 200 divided by 1 = 200. Alternatively, 200 and zero {as there is zero acceleration but only deceleration} = 200 thus again divided by 1 = 200.

Question 2,
Here is where it gets a little tricky.

Above I have moved 200 pounds up and then down in .5/.5 and I can do this 6 times in 6 seconds. In addition, 5 more times the distance as in the one time I lifted it up and down.

So have I not in some way used my average force {strength} 5 more times ??? And used more power {work energy} ???

As if you shot a putt at .5 of a second to a very slow 6 seconds, it is going to go further, thus using more force {strength} power {work energy} ???

Wayne

2. Feb 25, 2010

### waynexk8

1 rep at 2/4 = 6 seconds, distance 1m each way, weight moved once, for 2m.

5 reps at .5/.5 = 6 seconds, distance 1m each way, weight moved 6 times, for 12m.

Thus, it must take more force {strength} and more average force {strength} on the .5/.5 rep speed rep.

As if you move something faster for the same distance you must you more force {strength} and energy {calories} and if you move something the same distance 5 times faster and for 5 times the distance, you must use more force {strength} and power {work energy]

Wayne

3. Feb 26, 2010

### waynexk8

Hi there,

I am quite surprised that no one can tell me question 1, the average force ???

Wayne

4. Feb 26, 2010

### Staff: Mentor

Question 1 was a little vague and the answer probably depends on some specifics, but let me try some numbers for you:

Your 40lb additional force gives you 1/4g of acceleration upward, so you can cover 2 feet in half a second, at 4 fps final speed. 2 feet if 80% of 2.5 feet, so then you'd have to decelerate in .5 feet. That would be 2 fps average speed for 1/4 second, or 16fps/s of deceleration...which is .5g or 80lb (and 160-80=80).

So the average force over time is 160lb, over the .75 seconds total time.

5. Feb 26, 2010

### Gokul43201

Staff Emeritus
Irrespective of any of the details along the way (acceleration, deceleration, fraction of time spent accelerating, force exerted during each phase, etc.), the average force is always equal to the weight of the object, so long as you start and finish at rest.

Reason: You start from rest, accelerate, then decelerate to rest. The net change in momentum is therefore zero, which is equal to the net impulse delivered. Therefore, the average net force on the object is also zero. But since the net force is equal to the vector sum of your upward force and the downward weight of the object, the average upward force should equal the average downward force, i.e., the weight.

$$\Delta \mathbf{p} = \mathbf{I} = \mathbf{F}_{av}(net)\Delta t = 0$$

$$\implies \mathbf{F}_{av}(net)=0=\mathbf{F}_{av}(up)-\mathbf{F}_{av}(down) = \mathbf{F}_{av}(up) - \mathbf{W}$$

$$\implies \mathbf{F}_{av}(up) = \mathbf{W} = 160lb$$

Last edited: Feb 26, 2010
6. Feb 26, 2010

### waynexk8

Ok thx.

Right here is where it gets a little more interesting and difficult.

Above I have moved 160 pounds up and then down in .5/.5 {.5s concentric .5s eccentric} thus you have told me the average force is 160 pounds. And I have moved the 160 pounds up and down in 2/4,{2s concentric 4s eccentric} and you have told me the average force is 160 pounds.

But what is the average force if I move the same 160 pounds up and down 6 times in 6 seconds at the .5/.5

As it’s being moved 5 times the distance, and it’s moving at 5 times the speed, as it was the one time it was lifted up and down.

So have I not in some way used my average force {strength} 5 more times ??? And used more power {work energy} ???

As just shove a penny on the table with small force {strength} and then shove a coin with a BIG force {strength} and you will see the BIG shove force {strength} the penny goes far further. Thus, I must be using more force and more average force and power {work energy}.

Wayne

7. Feb 26, 2010

### Staff: Mentor

If the deceleration exceeds the acceleration due to gravity, then you'd have to pull the weight down.

8. Feb 26, 2010

### waynexk8

Not sure what you are saying there.

However, what I am saying is we found both the .5/.5 and the 2/4 to be of the same average force. But what happens to this average force when we add 5 more .5/.5

As you will be able to rep a weight up, and down, 6 times in the same time frame as you can do 1 rep up and down at 2/4

Thus if the average force is the same on both one of each reps, the 1 rep at .5/.5 and the one rep at 2/4, adding 5 more reps at .5/.5 must up the force and average force.

As it will take more force {strength} to do 6 reps {repetitions} rather than 1 rep. {at any speed]

Wayne

Last edited: Feb 26, 2010
9. Feb 27, 2010

### waynexk8

Rep means repetitions, as in weightlifting up and down, or the concentric and eccentric.

.5/.5 means reps, .5 concentric and .5 eccentric.

Still nobody on this one ???

Basically, all I want to do, is find out how much more force {strength} and more average force {strength} I used doing 6 reps at .5/.5 to one rep .5/.5 and one rep at 2/4.

We have worked out that one .5/.5 rep accelerated for 80% of the concentric, using 200 pounds of force {strength} and one 2/4 rep at a constant speed using 160 pounds for 100% of the concentric, using 160 pounds of force {strength}

As there must be more force {strength} and more average force {strength} used on doing 6 reps at .5/.5 to 1 rep at .5/.5 as we have used 5 times more time, 5 times more reps, and covered 5 times more distance.

BUT HOW DO WE WORK OUT HOW MUCH MORE FORCE IS USED ???

Wayne

Last edited: Feb 27, 2010
10. Feb 27, 2010

### waynexk8

Cant not we use f/p or n/m ??? as when multiplying feet and pounds, the resulting unit of measurement is foot-pounds. In the metric system, the unit of measurement used to express work is normally netwon-meters.

As one foot-pound force is the amount of energy expended when one pound-force acts through a distance of one foot along the direction of the force.

In my example it could be better to usde the metric system, as each rep is 1m by 1m.

Wayne

11. Feb 27, 2010

### Gokul43201

Staff Emeritus
It's still the same as the weight (160lb). The argument used above continues to apply, since the initial and final states are still rest.

Push a penny gradually along a table for 1sec. Then, using the same force, push the penny along the table for 6 seconds. Clearly, the penny travels a greater distance the second time, but the extra work done does not come from a greater force, it simply comes from applying the same force for longer.

12. Feb 28, 2010

### waynexk8

I think I said that a little wrong.

You shove the penny with a force of 200 pounds for 1m that takes .5 of a second, then immediately when you stop shoving the penny at 80% of 1m {0.8m} how far would the penny go. Let’s say the penny weights 160 pounds. {Yup I want to too ROL}

You then shove the penny with a force of 160 pounds for 1m that takes 2 seconds, then immediately when you stop shoving the penny at 1m how far would the penny go.

Wayne

13. Feb 28, 2010

### waynexk8

Can not we work the force out like this ???

As in the 6 reps at .5/.5 you move the weight 6 times, thus 6 times the disstance as to the 2/4.

Power = Force x velocity,

Slow rep shorter distance.

Work = 100Ib x 1ft
Work = force x distance = 100ft-lb.

Fast reps, same time frame, but far longer distance.

Work = 100 x 6ft
Work = force x distance = 600ft-lb.

Take of 20% for the deceleration and the transition from positive to negative = 480ft-lb

A STAGGERING 380% MORE FORCE USED.

Wayne

14. Feb 28, 2010

### Gokul43201

Staff Emeritus
No, that's 380% more work done (not force used).

15. Feb 28, 2010

### waynexk8

But is not power {work} part of force ???

Ok how can I work out how much force and average force was used, as it has to be more ??? As this is driving me mad.

What force is required to accelerate a body with a mass of 15 kilograms at a rate of 8 ms?

Slower speed,
a force of 25kg is required to accelerate a body with a mass of 50 kilograms at a rate of .5 ms
F=ma
Force = Mass x Acceleration
50 x .5 = 25kg

Faster speed,
And a force of 150kg is required to accelerate a body with a mass of 50 kilograms at a rate of 3ms
50 x 3 = 150kg

But that does not seem to work out, as how can 25kg move 50kg ???

Wayne

16. Feb 28, 2010

### Gokul43201

Staff Emeritus
Work, power and force are three completely different things. They are all related to each other, but that doesn't mean anything here.

No, the average force is not any greater for a million reps as it is for one rep. You've seen the proof, and if you're asking this question again it means you did not understand the proof.

17. Mar 1, 2010

### waynexk8

Hmm, ok sorry,

However surely I must be using more force to do 1 rep at .5/.5 to 2 reps or in my case 6 ??? Thus how do we work that out please ??? As I am not using the same force each time I lift, I am using a new/different force each time.

What about the F=ma, Force = Mass x Acceleration ??? Can not we use that.

Wayne

18. Mar 1, 2010

### waynexk8

I still can not belive no on e can help me with this ??? Surely there is a way to work out how much force is used ???

Wayne

19. Mar 1, 2010

### waynexk8

One Slow rep at 2/4 = 6 seconds = 160 pounds of average force {strength} and 160 pounds of gross overall force {strength}

Six fast reps at .5/.5 = 6 seconds = 160 + 160 +160 +160 +160 +160 = 160 pounds of average force {strength} BUT 960 pounds of gross overall force {strength}

This = 500% MORE OVERALL GROSS FORCE {STRENGTH}

Wayne

20. Mar 2, 2010

### Gokul43201

Staff Emeritus
As I've mentioned before, this is wrong. You do not use more force to do more reps. You do more work, but you do not use more force.

Yes, there is a way, and I showed you how to calculate it. Unfortunately, you do not want to accept that answer. And it appears you are instead looking for someone to provide a solution that fits in with your preconceived - but incorrect - ideas about force and work.

The only thing I can suggest is to start over from the beginning, and work your way up from the definitions. You have some deep seated misconceptions about what a force is, and you need to fix them.

If on the other hand, you believe you are correct, and that my answer is wrong, then you must try to show me the mistake in my proof. If there is such a mistake, then fixing it will likely lead us to a correct answer.

21. Mar 2, 2010

### waynexk8

Hi Gokul, and thx for helping me.

Maybe be I am either confusing force, or explaining it wrong, shall I try again.

When I lift 100 pounds for 1 set, and for 1 rep at .5/.5
I have to use a force {strength} but when I lift a 100 pounds for 1 set, but for 6 reps at .5/.5 I have to use more force {strength} As I have lifted the 100 pounds 5 more times, and 5 more times the distance, and it took 5 times more time.

As if you go pick up a 100 pounds onto a wall, you will know its far harder to pick it up 6 times rather than 1 time, thus I have used more force {strength}

I also know the power {work energy calories} is more, and know how to work this out, but I want the extra force {strength} used.

I tried using Force = Mass x Acceleration, but that did not seem to work ???

I think you only showed me how to calculate the average force {strength} however I wanted the overall force {strength}

It’s like I have £100 and you have £50 to find the average we add 100 + 50 = 150 and divided by 2 = 75. But that not our full/overall amount, as its 100 + 50 = 150. This if I lifted a 100 pounds 6 times would I x 100 by 6 = 600 pounds of full/overall force {strength} used.

Wayne

22. Mar 10, 2010

### Gokul43201

Staff Emeritus
Wayne, the terms force, work, power, etc. have very specific definitions in Physics. Just because you have to put in more "effort" on 6 reps than on 1 rep does not mean you are using more force. The work done is 6 times greater, and the impulse delivered by you is 6 times greater, but the force applied is the same.

And terms like "overall force" and "strength" do not exist in Physics. If you wish to calculate something, it needs to have a definition, or you need to define it in terms of already well-defined quantities.

23. Mar 11, 2010

### waynexk8

Ok thx. Yes think you hit the nail on the head there, as I am using more strength, or more of the same strength or force, or as you say effort, but do not exist in Physics.

F=MA. One Newton is defined as the amount of force required to give a 1-kg mass an acceleration of 1 m/s/s. 1 kg exerts a force of approximately 9.8 N.

MANY Ns WOULD YOU NEED TO ACCELERATE 50kg MASS 1 M/S/S,
AND HOW MANY Ns WOULD YOU NEED TO ACCELERATE 50KG MASS 6 M/S/S,

Slow rep is moving 50kg at a constant 2 seconds for 1 metre. It takes 2 seconds to travel 1m. Fast rep is accelerating 50kg 1 metre every .5 of a second. And does this 4 times in the same time frame as the slow rep. Thus, it has moved 50kg 3 times the distance in the same time frame as the 2-second slow rep.

As 2 seconds is 4 times slower than .5 I divided .5 by 2.

Slow rep, moving at 2s per 1m
F=50kg x .125 = 6.25N

Fast rep, moving at .5s per 1m
F=50 kg x .5m = 25N.

Thus I need and have used {lets take off the 20% for the deceleration phase on the faster reps} N18.75 = 1.875kg MORE force {strength} on the fast reps to accelerate if faster in the same time frame !!!

So for doing 12 reps = 22.5kg

SO ON MY FAST REPS ACCELERATING AT .5/.5 {THAT’S .5 OF A SECOND FOR THE CONCENTRIC AND .5 SECOND FOR THE ECCENTRIC} AND SLOW REPS AT 2/4 USING A 100 POUNDS FOR 12 REPS, I HAVE USED 49.5 POUNDS MORE FORCE {STRENGTH} NOT COUNTING THE ECCENTRIC.

???

Wayne

24. Mar 11, 2010

### waynexk8

In simple terms.

I cannot see in my none physics way of looking at how two people of the same strength, or say clones, and one moves a 100 pounds 6m in 6 seconds, and then the other clone move 100 pounds only 1m in 6 seconds.

I cannot see how the clone that moved the 100 pounds further, 5m further in the same time frame did not use more force {strength} ??? Some might then say, but the clone who moved it further used more work, however you need more force {strength} to do more work in the same time frame.

If you and me were the same strength, and we both tried to move the 100 pounds, and I moved it 6m and you 1m in the same time frame, I would say to you, you just did NOT use as much force {strength} effort as I did.

Wayne

25. Mar 11, 2010

### Staff: Mentor

Hi waynexk8,

I verified Gokul43201's statements numerically. He is completely correct (as his math showed that he would be). As long as the initial and final velocity is 0 then the time averaged force is equal to the weight. It does not matter how much time is taken nor does it matter how far up or down the weight is moved, the average force is constant.

For example, let's say for simplicity that you are using maneuvers where you lift up at one constant force for the first part of the maneuver and then a second force constant force for the remainder. If you want to lift a 160 lb weight a distance of 3 ft in 1 s with an initial force of 200 lb then you have to use 200 lb for .75 s and 40 lb for .25 s. That averages out to (200 lb .75 s + 40 lb .25 s)/1s = 160 lb. Now, if you instead want to use an initial force of 220 lb then you have to use 220 lb for .5 s and 100 lb for .5 s. That averages out to (220 lb .5 s + 100 lb .5 s)/1s = 160 lb.

I think the problem is that average force is simply not a quantity that you are really interested in, because Gokul43201 is correct that over any maneuver where the weight begins and ends at rest the average force always equals the weight.