Where Does a Bar on a Fulcrum First Tip When a Person Walks Across It?

  • Thread starter Thread starter JohnnyLaws
  • Start date Start date
  • Tags Tags
    Forces Torque
AI Thread Summary
The discussion centers on the mechanics of a bar on a fulcrum and the conditions for tipping when a person walks across it. Key points include the necessity of accounting for all forces acting on the bar, particularly the reaction forces at the fulcrum and the implications of the tipping point. Participants emphasize the importance of drawing a complete Free Body Diagram to represent known and unknown forces accurately. The conversation also highlights the roles of supports A and C, with support A preventing downward movement and support C acting as a pivot. Understanding these dynamics is crucial for determining the maximum distance a person can walk on the bar without tipping it.
JohnnyLaws
Messages
10
Reaction score
0
Homework Statement
We have a 4-meter-long uniform bar weighing 100 kg, and a person weighing 75 kg is walking across it. The statement specifies a stationary point C situated 2.5 meters away from the origin where the bar can rotate. The question is: 'What distance can this person move away while keeping the bar in equilibrium?'
Relevant Equations
I believe that I should set all torques equal to 0 and forces too but I don't know How to draw this specific Free body Diagram. On the other hand I don't know why I need point C.
So here is my equations:
Ra = reaction in A
Rx = reaction in person
Wb = bar's weight
Wp = Person's weight

Forces:
Ra+Rx+Wb+Wp = 0
Ra+Rx-100-75 = 0

Torques:

0*Ra+x*Rx-2*100-x*75 = 0
I think that explained all in "Relevant equations".
Here is the image of this exercise:
a.JPG

This is my Free Body Diagram:
b.JPG
 
Last edited by a moderator:
Physics news on Phys.org
You have not accounted for all the forces. Doesn't the fulcrum exert a force at point C?
Also, you need an additional equation. What is so special about the point of tipping? In other words what condition must hold for the bar to tip?
 
  • Like
Likes MatinSAR, JohnnyLaws and Lnewqban
JohnnyLaws said:
... but I don't know How to draw this specific Free body Diagram.
Simply represent all the known and unknown possible forces acting on the bar.
For example,
Rx = reaction in person
is a real force, but it is not acting on the bar; therefore, it is not interesting regarding resolving the balance of the beam.

Please, see:
https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/5-7-drawing-free-body-diagrams/

Balance bar.png


JohnnyLaws said:
On the other hand I don't know why I need point C.
Please note that:

*The support A only restrains the bar end from moving downwards, but it lets the end go upwards.

*The support C is a pivot, which retrains any movement of the point C, except rotation on the plane of the paper.

*The problem is asking you about the maximum distance that the man can move his weight to the right without inducing the above rorartion.
 
  • Like
Likes MatinSAR and JohnnyLaws
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top