Stability & Balance of rigid bodies

[M_G]

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..

 

[tiny-tim]

Hi M_G!

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? where will the girder actually rotate around if the man is too heavy?

 

[M_G]

you mean it will not rotate? so what will happen when this person walk on it?
topple on the other side, right?

 

[tiny-tim]

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.​

 

[M_G]

ok..but there will be a torque..?

 

[tiny-tim]

Ok...but there will be a torque..?

uhh? there's always torque.

What point does the girder rotate around?

 

[M_G]

I'm sorry...I'm confused a little bit, I'll try to think about it again...

 

[M_G]

uhh? there's always torque.

What point does the girder rotate around?

The right end of slab?

 

[tiny-tim]

oh sorry, I've just realized I've misread the original question

let me start again …

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.

 

[M_G]

Thanx!