Minimum Angle for 100-N Ladder Against Wall

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In summary, to determine the minimum angle at which a 100-N uniform ladder, 8.0m long, can rest against a smooth vertical without slipping, one must consider the conditions of the sum of all forces being zero and the sum of torques being zero. Using elementary trigonometry, the torque at the points where the ladder touches the wall and the floor can be calculated and set equal to zero, using the middle of the ladder as a reference point. These calculations will determine the minimum angle at which the ladder can rest without slipping.
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Homework Statement


A 100-N uniform ladder, 8.0m long, rests against a smooth vertical. The coefficient of static friction between ladder and floor is 0.40. What minimum angle can the ladder make with the floor before it slips?

The Attempt at a Solution



Not really sure where to start here. I do know since they told us the ladder is uniform, that i can somehow use the middle of the ladder as something. The sum of torques must be zero if the ladder isn't moving as well. But not quite sure what to do. Any help would be appreciated.
 
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the sum of all forces is also zero if the ladder isn't moving (friction + normal force+gravitional force(=weight))
so you have two basic conditions:
1)sum of all forces is zero
2)as you said , the sum of torques is also zero

you will calculate the torque(? moment of force) in the point where it touches the wall, and in the point where it touches the floor, and each of those equal zero ( here you will use the middle of ladder) actually it is probably necessary to calculate it around one of this points...

and at the end some elementary trigonometrics...

i am sorry, if I used some of the terms incorrectly, english is not my mother tongue, so...
and I apologize for any physics mistake in the above text, I am just a benevolent student
 

1. What is the minimum angle required for a 100-N ladder against a wall?

The minimum angle required for a 100-N ladder against a wall depends on the coefficient of friction between the ladder and the ground. If the coefficient of friction is 0.2, the minimum angle would be approximately 11 degrees.

2. How is the minimum angle for a 100-N ladder against a wall calculated?

The minimum angle is calculated using the formula tanθ = μ, where θ represents the angle and μ represents the coefficient of friction.

3. Why is the minimum angle important for ladder safety?

The minimum angle is important for ladder safety because it determines the stability of the ladder. If the angle is too small, the ladder may slip or topple over, causing potential injuries.

4. Can the minimum angle change for different ladder weights?

Yes, the minimum angle can change for different ladder weights because the weight affects the force of friction between the ladder and the ground. A heavier ladder may require a larger angle to maintain stability.

5. Is there a maximum angle for a ladder against a wall?

Technically, there is no maximum angle for a ladder against a wall. However, a larger angle may make it more difficult to climb and work on the ladder, so it is recommended to stay within a reasonable range for comfort and safety.

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