# Moment and forces for a person standing on tiptoe

#### hikaru1221

Now I'm very happy with this and I'm hope it's right and everything, I just don't see why there would be friction taking care of the horizontal components... Because with these values, (3) wouldn't be true...
I think that's because the arrangement of T and R in this problem implies the existence of friction (oh yes, the problem gives us the values 21 degrees and 10 degrees without showing us why!). There certainly is a case where friction = 0, but with other angles of T and R. Static friction is somewhat "inactive" - it only appears to balance everything.

#### Tusike

Yeah, but what about my problem with the whole body? Let's not look at the ankle. The only forces acting on the body would be N, mg, and the friction. These are the "outside" forces. The inner forces (like R, T and many other ones that keep you're head held and arms bent and everything) don't matter, they're canceled out, if we think of the whole body as a closed system, which it is. The outer forces are the ones that cause the acceleration of a closed system, N and mg cancel each other out, but nothing cancels out the friction (if there's any); which would mean we're accelerating!

Please tell me why, if it is, wrong.

#### hikaru1221

Yeah, but what about my problem with the whole body? Let's not look at the ankle. The only forces acting on the body would be N, mg, and the friction. These are the "outside" forces. The inner forces (like R, T and many other ones that keep you're head held and arms bent and everything) don't matter, they're canceled out, if we think of the whole body as a closed system, which it is. The outer forces are the ones that cause the acceleration of a closed system, N and mg cancel each other out, but nothing cancels out the friction (if there's any); which would mean we're accelerating!

Please tell me why, if it is, wrong.
So again, you assume that there is no other force acting on the body beside N, mg and friction?
Again, the arrangement of T and R implies that isn't true.

#### kuruman

Homework Helper
Gold Member
Yeah, but what about my problem with the whole body? Let's not look at the ankle. The only forces acting on the body would be N, mg, and the friction. These are the "outside" forces. The inner forces (like R, T and many other ones that keep you're head held and arms bent and everything) don't matter, they're canceled out, if we think of the whole body as a closed system, which it is. The outer forces are the ones that cause the acceleration of a closed system, N and mg cancel each other out, but nothing cancels out the friction (if there's any); which would mean we're accelerating!

Please tell me why, if it is, wrong.
For the problem as initially stated, you do need friction. If you change the problem to one where friction is not needed, then you don't need friction.

#### Tusike

"So again, you assume that there is no other force acting on the body beside N, mg and friction?
Again, the arrangement of T and R implies that isn't true. "

Oh I see. So the only way this is possible (with this arrangement) is if I'm like holding on to something on a wall to make sure I don't fall. Sorry for all that then, I was always imagining a person standing in the middle of nowhere on tip-toe:)

#### RoyalCat

"So again, you assume that there is no other force acting on the body beside N, mg and friction?
Again, the arrangement of T and R implies that isn't true. "

Oh I see. So the only way this is possible (with this arrangement) is if I'm like holding on to something on a wall to make sure I don't fall. Sorry for all that then, I was always imagining a person standing in the middle of nowhere on tip-toe:)
Exactly, since friction is a requirement for the equilibrium of the foot, we find that the equilibrium of the whole body is impossible without another external force, acting to the left.

I'm not much an indicator, considering I have poor balance, but I can't stand on tip-toe without leaning on anything.

#### Tusike

Now see that may have been my problem:) I could, in any angle.

#### Bartek

For the problem as initially stated, you do need friction.
Do you mean that person standing on tiptoe will generated horizontal force?? So, on frictionless surface he/she will be accelerated!

You mean we have perpetuum mobile?

#### RoyalCat

Do you mean that person standing on tiptoe will generated horizontal force?? So, on frictionless surface he/she will be accelerated!

You mean we have perpetuum mobile?
As the problem is stated, it is impossible to be in equilibrium without an external force. Should an external force not be there, the normal force and friction would change as the center of mass accelerates and shifts position relative to the foot, with the friction eventually changing directions with the end result being you, flat on your face. :p

#### Bartek

Should an external force not be there, the normal force and friction would change as the center of mass accelerates and shifts position relative to the foot, with the friction eventually changing directions with the end result being you, flat on your face. :p
Not exactly. "When a person stands on tiptoe" doesn't mean that before that "person stands on feet". He/she can be leave down (by the rope for instance).

It will be unstable equilibrium - but equilibrium .

Problem is stated as a static situation. The rest is our assumption.

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#### Tusike

Bartek, I think what we both got wrong is that the angles they gave us in the problem probably never happen in real life. So a person standing on tip-toe won't generate frictional force, but R and T won't look like that either. So actually we are right, but the problem isn't close to reality. For example, say that 21 degree angle is 35; does it really matter? I think we overthinked this problem a bit; I'd really like to know what kind of book it was from (to see what level solution it might expect from us).

#### RoyalCat

Bartek, I think what we both got wrong is that the angles they gave us in the problem probably never happen in real life. So a person standing on tip-toe won't generate frictional force, but R and T won't look like that either. So actually we are right, but the problem isn't close to reality. For example, say that 21 degree angle is 35; does it really matter? I think we overthinked this problem a bit; I'd really like to know what kind of book it was from (to see what level solution it might expect from us).
The problem here isn't the specific angle that it is, but the specific angle that it is not.

There are only a handful (If not just one, I didn't do the math on this) of angles for which there is no frictional force required for the equilibrium of the foot. As the problem was stated, there are two additional forces we -must- add in order for the foot, and the whole body to be in equilibrium, they are the frictional force and an external horizontal force, respectively.

Our assumptions in this case are necessary for the problem to make sense, otherwise we're claiming equilibrium for the foot where there is none (In the case of no friction) and equilibrium for the whole body where there is none (In the case of no additional external force.)

#### Bartek

I think we overthinked this problem a bit; I'd really like to know what kind of book it was from (to see what level solution it might expect from us).
Well... my proposition to solve I show in https://www.physicsforums.com/showpost.php?p=2793199&postcount=3". There were no word about friction .

I think there are many problems with no chance to happen. Do you remember https://www.physicsforums.com/showthread.php?t=412600" which flying 13 hours with speed equal 120km/h?

regards

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#### Tusike

I think that no matter what angle your foot is, there's no frictional force. However, no matter the angle of your foot, R and T are NEVER in those angle's specified; they're always in a way that require no friction; since there isn't any friction (in real life. in the problem, yes, it's needed).

#### arkofnoah

Wow I didn't expect this question to be so... controversial. Anyway this is taken from an A level physics book so it should be just about plain and simple torque and forces. The answer given is 1.77kN and 2.42kN, and I got it rather easily by just considering the torque. I believe that the most straight-forward and intuitive answer. I'm still confused over the inconsistency when I use the vector-sum method because by right I should get the same answer.

Anyway from reading the comments I've decided that these two are the most possible explanations:
1. There is an external force acting on it, like for example:
So the only way this is possible (with this arrangement) is if I'm like holding on to something on a wall to make sure I don't fall.
and therefore friction balances this external force out.
2. The angles for R and T could never be that value without friction.

My problem with one is that there should not be any "invisible" forces because I would figure that all the external forces, i.e. weight of the body, any normal forces and friction from holding on to any support, etc will be included in the R and T, AND THEREFORE resulting in that combination of angles for R and T. Then friction is needed to balance things out.

BUT:

@kuruman: here are two equations:
Sum of torques is 0, which would mean:
(1) 18*R = 25 * T*cos(11)

Sum of forces is 0, son vertically:
(2) T*cos(21) - R*cos(10) + N = 0
and horizontally:
(3) T*sin(21) - R*sin(10) = 0

Divide (1)/(3), you get nonsense. If we somehow manage to solve the friction thing, and say there is friction so (3) doesn't apply, from (1) and (2) we get:
T=1678,65N
R=2288.63N

Now I'm very happy with this and I'm hope it's right and everything, I just don't see why there would be friction taking care of the horizontal components... Because with these values, (3) wouldn't be true...
I agree with your values for R and T. Now for the third equation. If you introduce friction, you get

T*sin(21) - R*sin(10) + f= 0

Knowing the values for R and T, you can find (if you wish) how much f is needed and in what direction to keep this thing in equilibrium in the horizontal direction too. Although the problem does not ask for it, friction is there. Static friction, like the normal force, is a contact force that is whatever is necessary to provide the observed acceleration, in this case zero.
If you figure in friction, then you need to change (1) as well to include the torque due to friction (or at least if we take R as the pivot point instead of N, we can't leave out the moment due to friction anymore). Then the R and T value will be different and you cannot use it to calculate friction.

So based on my assumption (and a quite reasonable one I think) that R and T already take into account all the external forces acting (weight of body, compression of the bone due to holding onto support, whatever), we need to add in friction to balanced the forces. But then if we add in friction then the torque will be different.

This stupid foot is inconsistent with itself :s

A third possibility:
3. There is a typo in the question regarding the angle :uhh:

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#### hikaru1221

Bartek, I think what we both got wrong is that the angles they gave us in the problem probably never happen in real life. So a person standing on tip-toe won't generate frictional force, but R and T won't look like that either. So actually we are right, but the problem isn't close to reality. For example, say that 21 degree angle is 35; does it really matter? I think we overthinked this problem a bit; I'd really like to know what kind of book it was from (to see what level solution it might expect from us).
So you mean "real life" here is standing on tiptoe without holding or leaning on anything?
Maybe, yes, maybe the problem wants you to figure out yourself that your "real life" is not the case of this problem

Well... my proposition to solve I show in https://www.physicsforums.com/showpost.php?p=2793199&postcount=3". There were no word about friction .

I think there are many problems with no chance to happen. Do you remember https://www.physicsforums.com/showthread.php?t=412600" which flying 13 hours with speed equal 120km/h?

regards
If there were no friction, there would be no equilibrium in this problem particularly, and the problem would be unsolvable both theoretically and practically. It's different from the unrealistic assumptions such as the bird flying at 120km/h, whose problems are still solvable theoretically.

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#### Bartek

If there were no friction, there would be no equilibrium in this problem particularly, and the problem would be unsolvable both theoretically and practically. It's different from the unrealistic assumptions such as the bird flying at 120km/h, whose problems are still solvable theoretically.
Why unresolvable theoretically? Body is in equilibrium when center of mass is preciselly above point of footing. THEORETICALLY.

IF basement is one point, body is in unstable equilibrium. Accepted in physics. THEORETICALLY.

regards

#### RoyalCat

Wow I didn't expect this question to be so... controversial. Anyway this is taken from an A level physics book so it should be just about plain and simple torque and forces. The answer given is 1.77kN and 2.42kN, and I got it rather easily by just considering the torque. I believe that the most straight-forward and intuitive answer. I'm still confused over the inconsistency when I use the vector-sum method because by right I should get the same answer.

Anyway from reading the comments I've decided that these two are the most possible explanations:
1. There is an external force acting on it, like for example:

and therefore friction balances this external force out.
2. The angles for R and T could never be that value without friction.

My problem with one is that there should not be any "invisible" forces because I would figure that all the external forces, i.e. weight of the body, any normal forces and friction from holding on to any support, etc will be included in the R and T, AND THEREFORE resulting in that combination of angles for R and T. Then friction is needed to balance things out.

BUT:

If you figure in friction, then you need to change (1) as well to include the torque due to friction (or at least if we take R as the pivot point instead of N, we can't leave out the moment due to friction anymore). Then the R and T value will be different and you cannot use it to calculate friction.

So based on my assumption (and a quite reasonable one I think) that R and T already take into account all the external forces acting (weight of body, compression of the bone due to holding onto support, whatever), we need to add in friction to balanced the forces. But then if we add in friction then the torque will be different.

This stupid foot is inconsistent with itself :s

A third possibility:
3. There is a typo in the question regarding the angle :uhh:
If you take the torques about the point of contact of R, you'll have a completely different torque equation. The solution will still be the same, though, it would just require a bit more algebraic legwork.

If you take the torques about the pivot point, friction has no torque there, and the equations are particularly simple.

$$\Sigma \vec \tau = 0$$ implies $$R\cdot D_R = T \cdot D_T \cos {(11^0)}$$

#### hikaru1221

Why unresolvable theoretically? Body is in equilibrium when center of mass is preciselly above point of footing. THEORETICALLY.

IF basement is one point, body is in unstable equilibrium. Accepted in physics. THEORETICALLY.

regards
Do you think that with only T, R and N (no friction) given in the problem, the toe can be in equilibrium? Calculations throughout this thread show that if we consider the torque = 0 condition only, the result will not satisfy the condition of zero net force on the toe.

IF basement is one point, body is in unstable equilibrium.
The fact that the system has one-point basement has nothing to do with its equilibrium. Only the total force and total torque do. The pendulum has one-point basement too, but that's stable equilibrium. The pen, whose one end touches the ground, inclined at some angle not 90 degrees to the horizontal, has one-point basement too, but that's even not equilibrium.

#### Bartek

The pendulum has one-point basement too, but that's stable equilibrium.
Which one?

Men on tiptoe is in unstable equilibrium too.

#### hikaru1221

Okay that's not the pendulum I meant to say. It's the one with a string, not a solid rod.
Not every man on his tiptoe or anything on its one-point basement is in equilibrium. Only when the conditions, which are: 1- zero net force and 2- zero torque, are satisfied does equilibrium form. To find whether the equilibrium is stable or not, we must consider the 3rd condition: if the system returns to its equilibrium position after small disturbance, it's stable.

#### Tusike

@hikaru: yeah, and if you push a person on tiptoe a little, he/she will fall:)

#### Bartek

To find whether the equilibrium is stable or not, we must consider the 3rd condition: if the system returns to its equilibrium position after small disturbance, it's stable.
Absolutely right!

As the problem is stated I can't find there any word about type of equilibrium.

I believe, that this:
[PLAIN]http://img267.imageshack.us/img267/1874/foot2v.jpg [Broken]

can be in unstable equilibrium as well as pendulum.

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#### hikaru1221

Nice picture! Human pendulum?
I think you digress a bit from the initial problem. In the initial question of the OP, we don't have to care about what type of equilibrium it is, as it isn't asked! The problem is that whether equilibrium can be formed (which means we have to deal with the first 2 conditions) with T and R as given and without friction. And my answer is no. Of course, there is a case where friction is zero but equilibrium is still formed, but T and R are different.
In short, the correct solution for the problem of the OP must have something to do with friction.

#### arkofnoah

Okay I'm now convinced that friction must be present for this problem to be solvable. Kudos to the first person who mentioned friction :)

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