Equilibrium of Two People Holding Uniform Beam

[nameVoid]

two people are holding a unifrom beam of length 7.6m and weight 450N. the first person is holding the beam 1 m from the left end the second is holding the beam 2m from the right end determine the force the each person exerts on the beam.

choosing the axis as the left most person who exerts F1

sum F = F1 + F2 -450=0
sum torque = 4.6F2-2.8*450 =0

 

[tiny-tim]

hi nameVoid!

that looks ok …

what's worrying you about it? ​

 

[nameVoid]

thanks i was unsure where to take the axis

 

[tiny-tim]

it doesn't matter …

take the axis anywhere (even somewhere really stupid! ), and it'll still work

(though it make the maths easier if you always take the axis through one of the forces, in this case one of the two people or the centre of mass )

 

[rwisz]

From the first equation, we can solve for F2 as F2 = 450 - F1. Substituting this into the second equation, we get:

4.6(450-F1) - 2.8*450 = 0

Solving for F1, we get F1 = 196.3 N. Therefore, the first person is exerting a force of 196.3 N on the beam, while the second person is exerting a force of 253.7 N (450-196.3) on the beam.

In order for the beam to be in equilibrium, the sum of all forces and torques acting on it must be equal to zero. This means that the beam is not moving or rotating. By setting up equations for the sum of forces and torques, we can solve for the unknown forces and determine the equilibrium of the system.

In this case, we have two unknown forces, F1 and F2, and two equations from the sum of forces and torques. This allows us to solve for both forces and determine that the first person is exerting a smaller force than the second person. This makes sense as the first person is holding the beam closer to its center of gravity, while the second person is holding it further away. This distribution of forces allows for the beam to remain in equilibrium.

As a scientist, it is important to analyze and understand the forces and torques acting on a system in order to determine its equilibrium state. This can be applied to various real-world scenarios, such as engineering structures or balancing objects, and helps us make informed decisions based on the laws of physics.