Max Force on a Ladder When "Walking" it to Vertical Position

[Richard D.]

Homework Statement

Imagine raising a long ladder by "walking" it from a horizontal position to a vertical one as illustrated n the Figure. The first few steps are not difficult, but the job becomes increasingly difficult. However, beyond a certain point the job becomes easier again and when the ladder is vertical all you have to do is keep the ladder balanced.

Consider a uniform ladder of mass m and length l, lying on the ground with its base anchored against a brick. The ladder is slowly raised to a vertical position by applying a force at a constant height h above the ground. Consider the case where the ladder is raised using minimal effort.

a)Find the angle the ladder makes with the ground when lifting force is a maximum.

b)Find the magnitude Fmax of this maximum force.

Homework Equations

torque = rF sin(theta)

The Attempt at a Solution

I used L for r and Fmax was when it had the max force. So i tried using mg for the force of the ladder, but I'm unsure how to apply height in finding the Force, since using mg the force is the same no matter what. Some tips to help me in the right direction would be appreciated.

 

[Orodruin]

You did not attach the image and it is difficult to imagine how the situation looks without it. Could you perhaps provide it?

 

[haruspex]

I note that the direction of the force is not given. You maybe should not assume it is horizontal.
What forces apply? What equations are available? You quoted a torque equation. What point would you take torques about?

 

[Bystander]

from a horizontal position to a vertical one

applying a force at a constant height h

You've got two different starting points here. Is there something you've omitted from the problem statement?

 

[haruspex]

You've got two different starting points here. Is there something you've omitted from the problem statement?

Good point. Further, it probably should specify L is at least a specified multiple of h.

 

[Richard D.]

the problem consists of a ladder on the ground with a person picking it up, then he walks in slowly pulling the ladder up as he walks toward the center of the pole.

i was thinking maybe if i set the ladder as "rotating" around the center point as the person walks inward it may work somewhat like torque, i am really confused and some tips to hint me in the right direction would be appreciated.

Thank you everyone for replying

 

[haruspex]

the problem consists of a ladder on the ground with a person picking it up

Right, but that means the force is not always at height h. I guess we can read it as thye person lifts one end up to height h, then walks in always holding the ladder at the point that's at that height currently.

then he walks in slowly pulling the ladder up as he walks toward the center of the pole.

Sure, but do you suppose the force is always horizontal, or should it be at that angle which minimises the required force? (I suggest it's the latter.)

set the ladder as "rotating" around the center point

It will be much simpler if you take the point which it is actually rotating about - which is?

 

[Richard D.]

the center where the ladder is being pulled up to?

 

[haruspex]

the center where the ladder is being pulled up to?

What point on the ladder does not move?

 

[Richard D.]

it is pined to the ground on one point

 

[haruspex]

it is pined to the ground on one point

Then that must be the point it rotates about.

 

[ehild]

Is this the set-up?
At stage A the man lifts the end of the ladder up to the height of his shoulder (B). Then he keeps his arms horizontal and pushes the ladder while walking forward (C). ladder rotates around the fixed point on the ground. Find the force that keeps the ladder in equilibrium at different angles with the horizontal.

 

[haruspex]

Is this the set-up?
At stage A the man lifts the end of the ladder up to the height of his shoulder (B). Then he keeps his arms horizontal and pushes the ladder while walking forward (C). ladder rotates around the fixed point on the ground. Find the force that keeps the ladder in equilibrium at different angles with the horizontal.

View attachment 79972

The direction of the force the man applies to the ladder is not given. I suggest it should be taken to be the direction which minimises the force.

 

[jbriggs444]

The verbiage "keeps his arms horizontal" suggests that the intent is to use a horizontal force instead.

Edit: That wording is present in ehild's rephrasing but was not present in the original. In addition, the original mentions that the task "becomes increasingly difficult". This rules out the horizontal interpretation. I believe that Haruspex has the correct interpretation.

 

[ehild]

The verbiage "keeps his arms horizontal" suggests that the intent is to use a horizontal force instead.
.

Horizontal arm does not necessarily mean to apply force horizontally. It can be directed normal to the ladder. You grab the ladder with your hands, and can exert a normal force. With horizontal arms, I meant the application point of the force at constant height, so you have to shift your hands along the length of the ladder.