Ladder against wall. (If you help me, you are a legend).

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In summary, the Homework Statement is saying that a uniform ladder, of weight 3wp and length 2.5m, rests against a vertical wall with its foot on horizontal ground. The ladder is kept in position by a light rope that joins the wall to a point on the ladder, such that the angle between the wall and the point on the ladder is equal to theta. The tension in the rope is given by 3wp/(8cos(theta)-6sin(theta)).
  • #1
xduckksx
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Homework Statement



A uniform ladder AB, of weight W and length 2.5m rests against a smooth vertical wall OA with its foot on smooth horizontal ground OB. The ladder is in a vertical plane perpendicular to the wall. It is kept in position with OA=2m and OB=1.5m by a light rope OC joining O to a point C on the ladder such that angle COB=theta. Show that the tension T in the rope is given by

T=(3W)/(8cos(theta)-6sin(theta))

Homework Equations



This is just a moments question.

The Attempt at a Solution



I've tried taking moments about B, but don't seem to get why there are two terms in theta in that equation.
 
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  • #2
Show what you have tried, and where you are stuck, so we can help you.
 
  • #3
I'm really not sure how to proceed. If I take moments about B, there seem to be two forces I need to include: the tension in the rope, and the weight force. Am I correct?
 
  • #4
Use the moment about A.
 
  • #5
When I try moment about A,
Clockwise moment is due to the tension, with value moment=2Tcostheta. as well as weight.
Anticlockwise moment is due to the normal force at B (which is twice the weight force), hence moment here is 0.75W.
Then solving I get T=3W/(8costheta). So where does the -6sintheta come from?
 
  • #6
Does the problem state anything about the location of point C? (I doubt that it does.)
 
  • #7
Nope, C can vary.
 
  • #8
xduckksx said:
When I try moment about A,
Clockwise moment is due to the tension, with value moment=2Tcostheta. as well as weight.
Anticlockwise moment is due to the normal force at B (which is twice the weight force), hence moment here is 0.75W.
Then solving I get T=3W/(8costheta). So where does the -6sintheta come from?
Why do you say that the normal force is twice the weight force?
 
  • #9
I'm not sure. Should it be the same?

And can you explain where that -6sin theta comes from?
 
  • #10
A component of T is vertical. The normal force at B must cancel both the force of gravity and the vertical component of T.
 
  • #11
Isn't this accounted for in calculating the clockwise moment of the overall tension?

Oh, I see. The normal force at B also takes into account this vertical component. FML.
 

Related to Ladder against wall. (If you help me, you are a legend).

1. What is the purpose of a ladder against a wall?

A ladder against a wall is typically used to provide access to higher levels or to perform tasks at a height that cannot be reached by standing on the ground. It is commonly used in construction, maintenance, and other types of work that require working at elevated levels.

2. How do I safely set up a ladder against a wall?

To safely set up a ladder against a wall, make sure the ground is level and free of any obstacles. Place the base of the ladder against the wall at a 75 degree angle, with the feet of the ladder firmly on the ground. Use a ladder stabilizer or have a helper hold the base of the ladder for added stability. Climb the ladder with caution and always maintain three points of contact.

3. What is the proper way to climb a ladder against a wall?

The proper way to climb a ladder against a wall is to face the ladder while ascending or descending, and to always maintain three points of contact (two hands and one foot, or two feet and one hand) at all times. Do not lean too far to either side and do not overreach. If you need to move the ladder, climb down and reposition it.

4. Can a ladder against a wall be used for any type of work?

No, not all types of work can be safely performed on a ladder against a wall. Ladders should only be used for tasks that can be completed within a short period of time and do not require too much movement or weight. For tasks that require longer periods of work or involve heavy materials, it is recommended to use scaffolding or other types of elevated platforms.

5. Is there a weight limit for using a ladder against a wall?

Yes, there is a weight limit for using a ladder against a wall. The maximum weight capacity should be indicated by the manufacturer and should be strictly followed. It is also important to consider the weight of any tools or materials being used while on the ladder. Overloading a ladder can lead to accidents and injuries.

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