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

[Sunwoo Bae]

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

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?

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?

 

[etotheipi]

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 "$=0$" ).

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?

 

[haruspex]

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 "$=0$" ).

Alternatively, @Sunwoo Bae is taking moments about the base of the wall, in which case it is F_W that is missing.

 

[Lnewqban]

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.

 

[JoeDGreat]

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

 

[Steve4Physics]

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!

 

[JoeDGreat]

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.

 

[haruspex]

Alright, thanks. I just love the explanation by the textbook.

I see the identical problem at http://www.sfu.ca/~mxchen/phys1010901/LectureCh12.pdf, https://katierevision.files.wordpress.com/2017/09/chapter-12.pdf, https://www.scribd.com/document/636002266/Untitled…
Whether any of these have the explanatory text you seek I do not know.

 

[erobz]

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.

 

[JoeDGreat]

I see the identical problem at http://www.sfu.ca/~mxchen/phys1010901/LectureCh12.pdf, https://katierevision.files.wordpress.com/2017/09/chapter-12.pdf, https://www.scribd.com/document/636002266/Untitled…
Whether any of these have the explanatory text you seek I do not know.

Thanks very much. I've been able to access the textbook.