Calculating Static Equilibrium for Ladder Climb

In summary, the conversation involved a question about a window cleaner's ladder, with the ladder's mass and angle against a wall given, along with information about the surface's friction coefficient. The conversation then discussed using moments and torque to determine the maximum length the window cleaner can climb before the ladder slips.
  • #1
PhysicsDud
24
0
I'm not sure how to go about doing this question. Any help would be great.

A window cleaner of mass 95 kg places a 22-kg ladder against a frictionless
wall, at an angle 65° with the horizontal. The ladder is 10 m long and rests on a
wet floor with a coefficient of static friction equal to 0.40. What is the maximum
length that the window cleaner can climb before the ladder slips?

Thanks!
 
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  • #2
Try taking moments about a point.
 
  • #3
Draw a free body diagram and then find what force is enough for the ladder to slip. Here torqueplays the role. You take a general point on the ladderabove its centre. Find normal reaction, friction, torque, etc. And then equate them with the distance from centreas variable.
 
  • #4
Sorry here centre of axis is not the centre of ladder, it is the poit at which it touches the surface..
 
  • #5
Thanks

Thanks so much for the help!
 

1. How do you calculate the static equilibrium for a ladder climb?

To calculate the static equilibrium for a ladder climb, you need to consider the forces acting on the ladder and the climber. These forces include the weight of the ladder, the weight of the climber, and the reaction forces at the points where the ladder rests against the wall and the ground. You can then use the equations of static equilibrium to determine if the ladder is stable or if it will tip over.

2. What is the equation for static equilibrium?

The equation for static equilibrium is ΣF = 0, where ΣF represents the sum of all the forces acting on an object. This equation states that for an object to be in static equilibrium, the net force acting on it must be zero. This means that all the forces acting on the object must be balanced and cancel each other out.

3. How do you determine the direction of the reaction forces at the points where the ladder rests?

The direction of the reaction forces at the points where the ladder rests can be determined by considering the forces acting on the ladder and the climber. If the ladder is stable, the reaction forces at these points will be equal and opposite to the weight of the ladder and the climber. This means that the reaction forces will be pointing upwards at the points where the ladder rests against the wall and the ground.

4. Can the center of mass of the ladder and the climber affect the static equilibrium?

Yes, the center of mass of the ladder and the climber can affect the static equilibrium. The center of mass is the point where the weight of an object is concentrated. If the center of mass of the ladder and the climber is not directly above the points where the ladder rests, it can cause the ladder to become unstable and potentially tip over. Therefore, it is important to consider the position of the center of mass when calculating static equilibrium for a ladder climb.

5. How can you make sure the ladder is in static equilibrium before climbing?

To ensure that the ladder is in static equilibrium before climbing, you can perform a simple test. Gently push or pull on the ladder from different points and observe its response. If the ladder remains stable and does not tip over, it is in static equilibrium. If the ladder starts to tip, it is not in static equilibrium and needs to be adjusted or stabilized before climbing. It is important to always check for static equilibrium before using a ladder to prevent accidents or injuries.

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