Find angle of ladder equation

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The key equations here are the equations for torque about the base of the ladder and for the equilibrium of forces in the horizontal and vertical directions. In summary, a man weighing 75 kg stands on a 25 kg ladder that is 8 meters long and 6 meters above the bottom, with a coefficient of friction of 0.3. The angle of the ladder can be found by solving the equations for torque and equilibrium of forces.
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physicsstudent101
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New user has been reminded that showing an attempt at the solution is mandatory in homework threads at the PF.

Homework Statement


A 75 kg man stands on a 8meter 25kg ladder at 6 meters above the bottom when it just starts to slip. Mu(s) is.3. What is the angle of the ladder?

ladder mass=25kg
ladder length=8m
man mass= 75kg
radius of man slipping = 6m
Mu=.3
angle= ?

Homework Equations


F= Mu x Normal force
Torque=rFsintheta
X: P=F(s)=Mu(s) x Normal Force = Mu(s) (Weight of ladder + Weight of man) = Mu(s) (Ladder mass x g + mass man x g)
Y: Normal force = weight of ladder + weight of man
(radius of p)(P)(sin angle)= (radius of ladder)(weight of ladder)(cos theta)+(height of man slipping)(weight of man)(cos theta)

The Attempt at a Solution


not sure where to start... [/B]
 
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physicsstudent101 said:
not sure where to start...
As with ALL such problems, you start with a force vector diagram. That generally clarifies how all the forces interact and gives you a starting point for writing equations.
 
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Likes jim mcnamara

1. What is the "Find angle of ladder equation"?

The "Find angle of ladder equation" is a mathematical formula used to determine the angle at which a ladder is leaning against a wall. It takes into account the length of the ladder, the height of the wall, and the distance between the base of the ladder and the wall.

2. Why is it important to find the angle of a ladder?

Knowing the angle of a ladder is important for safety purposes. If the angle is too steep, the ladder may slip or topple over. It is also important for optimizing the ladder's stability and ensuring that it is properly positioned against the wall.

3. How do I use the "Find angle of ladder equation"?

To use the equation, you need to measure the length of the ladder, the height of the wall, and the distance between the base of the ladder and the wall. Once you have these measurements, plug them into the equation: angle = arctan(height/wall distance). The resulting angle is the angle at which the ladder is leaning against the wall.

4. Can the "Find angle of ladder equation" be used for all types of ladders?

Yes, the equation can be used for any type of ladder as long as the ladder is leaning against a flat wall or surface. It is important to note that the equation assumes the ladder is placed on a level surface and is not being used on stairs or uneven ground.

5. Are there any safety precautions I should take when using the "Find angle of ladder equation"?

Yes, it is important to always use caution when using ladders. Make sure the ladder is placed on a stable surface and is securely positioned against the wall. It is also important to follow the weight limit for the ladder and to never stand on the top rung. If you are unsure about the angle or stability of the ladder, it is best to seek assistance from a professional.

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