Moment and forces for a person standing on tiptoe

In summary: Why not?" The table isn't accelerating, so the force exerted by the ground is the same as the weight of the table.
  • #36
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).
 
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  • #37
Tusike said:
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.)
 
  • #38
Tusike said:
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 :smile:.

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? :biggrin:

regards
 
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  • #39
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).
 
  • #40
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 said:
@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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  • #41
Tusike said:
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 :smile:

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

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? :biggrin:

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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  • #42
hikaru1221 said:
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
 
  • #43
arkofnoah said:
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.

[tex]\Sigma \vec \tau = 0[/tex] implies [tex]R\cdot D_R = T \cdot D_T \cos {(11^0)}[/tex]
 
  • #44
Bartek said:
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.
 
  • #45
hikaru1221 said:
The pendulum has one-point basement too, but that's stable equilibrium.
Which one?

99px-Stable_unstable_pendulum.svg.png


Men on tiptoe is in unstable equilibrium too.
 
  • #46
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.
 
  • #47
@hikaru: yeah, and if you push a person on tiptoe a little, he/she will fall:)
 
  • #48
hikaru1221 said:
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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  • #49
Nice picture! Human pendulum? :biggrin:
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.
 
  • #50
Okay I'm now convinced that friction must be present for this problem to be solvable. Kudos to the first person who mentioned friction :)
 
<h2>1. What is the moment for a person standing on tiptoe?</h2><p>The moment for a person standing on tiptoe is the product of the force applied and the distance from the pivot point. It is a measure of the tendency of the force to cause rotation.</p><h2>2. How does the moment change when a person stands on tiptoe?</h2><p>The moment increases when a person stands on tiptoe because the distance from the pivot point increases, resulting in a greater lever arm and therefore a greater moment.</p><h2>3. What is the relationship between moment and forces for a person standing on tiptoe?</h2><p>The moment is directly proportional to the force applied and the distance from the pivot point. This means that as the force or distance increases, the moment also increases.</p><h2>4. Why is the pivot point important when considering moments and forces for a person standing on tiptoe?</h2><p>The pivot point is important because it determines the distance from which the force is applied and affects the resulting moment. A change in the pivot point can greatly alter the moment and the stability of a person standing on tiptoe.</p><h2>5. How does the moment affect a person's balance when standing on tiptoe?</h2><p>The moment plays a crucial role in a person's balance when standing on tiptoe. A greater moment results in a greater tendency for the person to fall over, while a smaller moment allows for better balance and stability.</p>

1. What is the moment for a person standing on tiptoe?

The moment for a person standing on tiptoe is the product of the force applied and the distance from the pivot point. It is a measure of the tendency of the force to cause rotation.

2. How does the moment change when a person stands on tiptoe?

The moment increases when a person stands on tiptoe because the distance from the pivot point increases, resulting in a greater lever arm and therefore a greater moment.

3. What is the relationship between moment and forces for a person standing on tiptoe?

The moment is directly proportional to the force applied and the distance from the pivot point. This means that as the force or distance increases, the moment also increases.

4. Why is the pivot point important when considering moments and forces for a person standing on tiptoe?

The pivot point is important because it determines the distance from which the force is applied and affects the resulting moment. A change in the pivot point can greatly alter the moment and the stability of a person standing on tiptoe.

5. How does the moment affect a person's balance when standing on tiptoe?

The moment plays a crucial role in a person's balance when standing on tiptoe. A greater moment results in a greater tendency for the person to fall over, while a smaller moment allows for better balance and stability.

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