Why Does Torque Equilibrium Not Solve for Fcy in Static Equilibrium Problems?

In summary: When the person is leaning against the wall with their back to the ladder, the spikes will be pushing against the wall and the rubber pads will be pushing against the person. This creates a larger normal force on the wall than if the person is standing on the ladder.
  • #1
Sunwoo Bae
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4
Homework Statement
A 5m long ladder leans against a smooth wall at a point 4m above a cement floor as shown in the figure (image below). The ladder is uniform and has mass m = 12kg. Assuming the wall is frictionless (but the floor is not), determine the forces exerted on the ladder by the floor and by the wall.
Relevant Equations
total torque = 0
problem.jpg

I have two questions regarding this problem

1. The following is my attempt to solve Fcy using the fact that the addition of torque = 0. I considered force mg and Fcy and their lever arms to set up the equilibrium. But this method seems not to work? Why?

attempt.jpg

2.At the bottom of the question, it reads, "Why is it reasonable to ignore friction along the wall, but not reasonable to ignore it along the floor?" What would be an answer to this problem?
 
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  • #2
I presume you are taking torques about the point of contact with the wall in your equation. But you haven't included the torque of ##\vec{F}_{C,x}## in your equation (N.B. you also missed an "##=0##" :wink:).

Sunwoo Bae said:
2.At the bottom of the question, it reads, "Why is it reasonable to ignore friction along the wall, but not reasonable to ignore it along the floor?" What would be an answer to this problem?

Is it possible for the ladder to be in static equilibrium if there is zero friction from the floor?
 
  • #3
etotheipi said:
I presume you are taking torques about the point of contact with the wall in your equation. But you haven't included the torque of ##\vec{F}_{C,x}## in your equation (N.B. you also missed an "##=0##" :wink:).
Alternatively, @Sunwoo Bae is taking moments about the base of the wall, in which case it is FW that is missing.
 
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  • #4
Sunwoo Bae said:
2.At the bottom of the question, it reads, "Why is it reasonable to ignore friction along the wall, but not reasonable to ignore it along the floor?" What would be an answer to this problem?
Since force of friction depends on the normal force, where will you see the biggest normal (to ground or wal) force, especially when a person is climbing that ladder and the angle of lean is moderated?
Hint: Most extension ladders have rubber pads and spikes at bottom end and nothing at top end.

parts-of-extension-ladder-1.png
 
  • #5
Sunwoo Bae said:
Homework Statement: A 5m long ladder leans against a smooth wall at a point 4m above a cement floor as shown in the figure (image below). The ladder is uniform and has mass m = 12kg. Assuming the wall is frictionless (but the floor is not), determine the forces exerted on the ladder by the floor and by the wall.
Relevant Equations: total torque = 0

View attachment 267227
I have two questions regarding this problem

1. The following is my attempt to solve Fcy using the fact that the addition of torque = 0. I considered force mg and Fcy and their lever arms to set up the equilibrium. But this method seems not to work? Why?

View attachment 267228
2.At the bottom of the question, it reads, "Why is it reasonable to ignore friction along the wall, but not reasonable to ignore it along the floor?" What would be an answer to this problem?
Good day. Can I know the name of the textbook you took the image from?. Thank you
 
  • #6
JoeDGreat said:
Good day. Can I know the name of the textbook you took the image from?. Thank you
Hi. Welcome to PF. It may be worth noting that the post to which you are replying is over 3 years old. You may not get a response from the OP!
 
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  • #7
Steve4Physics said:
Hi. Welcome to PF. It may be worth noting that the post to which you are replying is over 3 years old. You may not get a response from the OP!
Alright, thanks. I just love the explanation by the textbook.
 
  • #9
JoeDGreat said:
Alright, thanks. I just love the explanation by the textbook.
That is out of "Physics for Scientists & Engineers", Giancoli. Fourth Edition has the problem ( I have the text book ), I would imagine theirs is a later version, but maybe not.
 
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Related to Why Does Torque Equilibrium Not Solve for Fcy in Static Equilibrium Problems?

1. What is static equilibrium?

Static equilibrium refers to a state in which an object is at rest and all the forces acting on it are balanced, resulting in no net force or acceleration.

2. How do you determine if an object is in static equilibrium?

An object is in static equilibrium if the sum of all the forces acting on it is equal to zero and the sum of all the torques acting on it is also equal to zero. This means that the object is not moving and is not rotating.

3. What is the difference between static equilibrium and dynamic equilibrium?

Static equilibrium refers to a state of balance in which an object is at rest, while dynamic equilibrium refers to a state of balance in which an object is moving at a constant velocity. In static equilibrium, the forces are balanced, while in dynamic equilibrium, the forces are unbalanced but the object is moving at a constant speed.

4. What is the importance of static equilibrium in science?

Static equilibrium is important in science because it helps us understand how objects behave when they are at rest. It is also used in engineering to design structures that can withstand various forces and remain in static equilibrium.

5. How do you solve a static equilibrium problem?

To solve a static equilibrium problem, you need to first identify all the forces acting on the object and their directions. Then, set up equations for the sum of forces and sum of torques in both the x and y directions. Finally, solve the equations to find the unknown variables, such as the magnitude and direction of the forces.

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