Stuck on mechanics ladder question

[Jasonsdonervan]

Hi Guys, I'm really stuck on this question attached below. I understand that I may need to take moments about A to find the distance of x? But I'm really a bit confused. It reads:

• A non-uniform ladder AB of mass 20 kg and length 5 m rests with its end A on smooth horizontal ground and its end B against a rough vertical wall. The coefficient of friction between the ladder and the wall is 0.4. The centre of mass of the ladder, C, is x m from A. The ladder lies in a vertical plane to the wall and the ground and the angle α between the ladder and the ground is given by tan α = . The minimum horizontal force that must be applied at A to prevent the ladder from sliding down the wall is 40 N.
• By modelling the ladder as a non-uniform rod, find x .

Thanks for any answer or walkthrough you provide,

Jason

 

[Deleted member 4993]

Hi Guys, I'm really stuck on this question attached below. I understand that I may need to take moments about A to find the distance of x? But I'm really a bit confused. It reads:

• A non-uniform ladder AB of mass 20 kg and length 5 m rests with its end A on smooth horizontal ground and its end B against a rough vertical wall. The coefficient of friction between the ladder and the wall is 0.4. The centre of mass of the ladder, C, is x m from A. The ladder lies in a vertical plane to the wall and the ground and the angle α between the ladder and the ground is given by tan α = . The minimum horizontal force that must be applied at A to prevent the ladder from sliding down the wall is 40 N.
• By modelling the ladder as a non-uniform rod, find x .

Thanks for any answer or walkthrough you provide,

Jason

If I were to do this problem - I would have drawn a free-body-diagram (FBD) showing dimensions and external forces. Then apply the equations of static equilibrium.

Please show us what you have tried and exactly where you are stuck.

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