Confused as to what forces are acting on the ladder

In summary, Mr. X (mass 96.0 kg) was attempting to take down holiday lights when an ice storm hit. The coefficient of static friction between his ladder (mass 16.4 kg) and the ground was reduced to 0.090. To reach the lights, Mr. X must climb 4.20 m up the 5.00 m ladder, which makes an angle of 68° with the ground. To improve the frictional force, Mr. X has Mr. Y (mass unknown) stand on the first rung of the ladder, located 0.42 m from the ground. The forces acting on the ladder are the normal force from the wall, the normal force from the ground,
  • #1
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Homework Statement


Mr. X ( mass 96.0 kg ), he just finished a rather large breakfast) is finally getting around to taking down his holiday lights when a sudden ice storm hits. the coefficient of static friction between his ladder (mass 16.4 kg ) and the level ground has been reduced to 0.090. To reach the lights Mr. X must climb 4.20 m up the 5.00m ladder. To improve on his frictional force, Mr.X gets Mr.Y to stand on the first rung of the ladder which is located 0.42m from the ground, will Mr. X reach the lights safely? There is no friction between the ladder and the wall and the ladder makes an angle of 68° with the ground.


Homework Equations


Fun = ma
torque = R. F.
Ff= fn ( coefficient of friction)



The Attempt at a Solution



i really don't know where to start, what should i calculate first, i tried to calculate the amount of force that the co-efficient of friction can handle but i don't know how to do this, and I'm confused as to what forces are acting on the ladder.

i know that there will be a force off the wall, a normal force off of the ground and a gravity force from Mr.Y, but do i take account a gravitational force from Mr.X even though he's moving up the ladder ?
 
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  • #2


Scrambler said:
but do i take account a gravitational force from Mr.X even though he's moving up the ladder ?

You aren't really interested in him moving up the ladder though. In your problem, it asks whether he's going to fall when he reaches 4.20m up the ladder.

I would first draw a picture showing all the forces. Remember the weight of the ladder, too.
 
  • #3


draw a fbd of the problem
 
  • #4


okay so first i have to find the components that will make all the forces acting on the ladder perpendicular.

I will choose the very bottom of the ladder as my pivot point therefore eliminating the normal force from the ground and the frictional force on the ladder. because when R= 0, torque = 0.

so

Fw ( force of wall ) sin 68 ( 5 m ) = Force of gravity Mr. X ( 4.2m) + force gravity Mr. Y ( 0.42m) + force gravity ladder ( 2.1 m)

then find the force of the wall and use the sum of the forces in the x direction must = 0 to find the frictional force ! but

i don't get how i will find out if he falls or not ?
 
  • #5


Draw a picture first.

You should have three equilibrium equations, correct? You're going to need those.

What I would do is leave the friction force as a variable for now, that way you can find out just how much friction force is needed for the ladder to be in equilibrium. Then once you find that value, compare it with the maximum value (based on your coefficient of static).
 
  • #6


okay, I've uploaded a diagram so should the force off the wall equal the frictioanl force in equilubrium ?
 

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1. What are the forces that act on a ladder?

The main forces that act on a ladder are the weight of the ladder, the weight of the person on the ladder, and the reaction force from the ground.

2. How does the weight of the ladder affect its stability?

The weight of the ladder affects its stability by creating a downward force that can cause the ladder to tip over if it is not properly supported or if the weight distribution is not balanced.

3. Does the angle of the ladder affect the forces acting on it?

Yes, the angle of the ladder affects the forces acting on it. The steeper the angle, the greater the force pushing the ladder away from the wall or support, making it less stable.

4. Are there any other forces that may act on a ladder?

There may be other external forces such as wind or uneven ground that can affect the stability of a ladder. Additionally, the materials and construction of the ladder can also impact the forces acting on it.

5. How can one determine the forces acting on a ladder?

To determine the forces acting on a ladder, one can use the principles of equilibrium and Newton's laws of motion. By analyzing the forces acting on the ladder and ensuring that they are balanced, one can determine the stability of the ladder.

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