Stability & Balance of rigid bodies

In summary, the problem involves determining how far a 100kg man can walk on a 10m steel girder resting on a concrete slab with 4m overhanging the edge. Using the law of equilibrium of rigid bodies, the sum of torques around a fulcrum point is set to zero. The equation used to solve for the maximum distance the person can walk is 100kg * X m = 1000Kg * 1 m, where X represents the distance the person can walk and 1m is the distance between the center of gravity of the girder and the fulcrum point. It is determined that the man can walk the full 4m without the girder losing balance.
  • #1
M_G
14
0

Homework Statement



A steel girder with a mass of 1000kg and a length of 10m rests on a concrete slab, with 4m overhanging the edge. How far can a 100kg man walk on the girder?

The Attempt at a Solution



I supposed that the right end of the slab is the fulcrum (rotating point), and according to the law of equilibrium of rigid bodies, the sum of torques around that point will be zero,
If the maximum distance the person could walk is X, then the eqn. will be:
100kg * X m = 1000Kg * 1 m (segma tao = 0)
Where:
1 m is the distance between the point of center of gravity of the steel girder (length/2 m)& the fulcrum...

But...X=10m ! I missed something, but I don't know what? am I proceeding right from the begining??
Thanks in advance for your help..
 
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  • #2
Hi M_G! :smile:
M_G said:
A steel girder with a mass of 1000kg and a length of 10m rests on a concrete slab, with 4m overhanging the edge. How far can a 100kg man walk on the girder?
…
I supposed that the right end of the slab is the fulcrum (rotating point),

uhh? :confused: where will the girder actually rotate around if the man is too heavy? :wink:
 
  • #3
you mean it will not rotate? so what will happen when this person walk on it?
topple on the other side, right?
 
  • #4
M_G said:
you mean it will not rotate? so what will happen when this person walk on it?
topple on the other side, right?

Of course it will rotate …

I asked where it will rotate round.​
 
  • #5
ok..but there will be a torque..?
 
Last edited:
  • #6
M_G said:
Ok...but there will be a torque..?

uhh? :confused: there's always torque.

What point does the girder rotate around?
 
  • #7
I'm sorry...I'm confused a little bit:frown:, I'll try to think about it again...
 
  • #8
tiny-tim said:
uhh? :confused: there's always torque.

What point does the girder rotate around?
The right end of slab?
 
  • #9
oh sorry, I've just realized I've misread the original question :redface:

let me start again …
M_G said:
A steel girder with a mass of 1000kg and a length of 10m rests on a concrete slab, with 4m overhanging the edge. How far can a 100kg man walk on the girder?
…
I supposed that the right end of the slab is the fulcrum (rotating point), and according to the law of equilibrium of rigid bodies, the sum of torques around that point will be zero,
If the maximum distance the person could walk is X, then the eqn. will be:
100kg * X m = 1000Kg * 1 m (segma tao = 0)
Where:
1 m is the distance between the point of center of gravity of the steel girder (length/2 m)& the fulcrum...

But...X=10m ! I missed something, but I don't know what? am I proceeding right from the begining??

Yes, your method of torques is correct …

if the man could walk 10m, the girder would still just balance …

but he can't …

so the answer is that he can walk the full 4m. :smile:
 
  • #10
Thanx!
 

FAQ: Stability & Balance of rigid bodies

1. How is the stability of a rigid body determined?

The stability of a rigid body is determined by its center of gravity and the location of its support or pivot point. If the center of gravity is above the support point, the body is stable. If the center of gravity is outside the support point, the body is unstable and may tip over.

2. Can the stability of a rigid body be changed?

Yes, the stability of a rigid body can be changed by altering its mass distribution or its support point. For example, adding weight to the bottom of the body or widening its base of support can increase its stability.

3. What is the difference between stability and balance of a rigid body?

Stability refers to the ability of a rigid body to resist tipping over, while balance refers to the distribution of forces acting on the body to keep it in a steady position. A body can be stable but not balanced if it is tilted on its support point, and vice versa.

4. How does the shape of a rigid body affect its stability?

The shape of a rigid body can affect its stability by altering its center of gravity and base of support. For example, a wider base of support and a lower center of gravity can increase stability, while a narrow base and a higher center of gravity can decrease stability.

5. What factors can cause a rigid body to lose its stability?

A rigid body can lose its stability due to external forces such as wind, uneven surfaces, or changes in its mass distribution. Additionally, if the support point of the body is moved or removed, it can also cause the body to lose its stability.

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