Question

Is a ladder leaning against the wall in static equilibrium when there is sufficient friction between the ladder and both the ground and wall? Or does there only need to be friction between the ladder and at least one of the surfaces mentioned?

Answer 1

What do you think?

Answer 2

I think we need both.

Answer 3

Why?

Answer 4

Well if there was only friction at one end where the ladder makes contact with a surface, the other end of the ladder would slip, right?

Answer 5

But I have done problems where we could ignore the friction between the wall and ladder, and still have static equilibrium. So it got me wondering if that was realistic or not...

Answer 6

No. The ladder can't "slip" into the wall on which it is resting because the building is pushing back.

Answer 7

I don't mean slip into the wall. I mean slip down the wall

Answer 8

It will only slip down the wall if there is insufficient friction on the ground to keep it from slipping.

Answer 9

I do not understand why that is so.

Answer 10

The bottom of the ladder pushes down at an angle. There are two components, one down, and the other one away from the wall. The normal force counteracts the vertical component, and friction is necessary to offset the horizontal component. The wall itself can be completely frictionless and the ladder will not move as long as the forces at the bottom of the ladder completely cancel out. Try drawing a vector diagram.

Answer 11

I hope this helps ...

Answer 12

But the ladder makes contact with the wall too right? In order for that end of the ladder to stay still, we would need friction to counteract the direction of sliding, no?

Answer 13

Since gravity pulls down on that end.

Answer 14

The top of the ladder would also push the wall at an angle as well, so why does what you said not apply to the top?

Answer 15

When the ladder is motionless there is a force pushing horizontally into the wall. The building opposes that force. The horizontal component is transferred to the bottom of the ladder, so long as the ladder is motionless. Once the ladder starts slipping, there will be a vertical frictional force on the top of the ladder as well. It only begins to take effect once the ladder starts moving.

Answer 16

But in order for the ladder to not move in the first place, there would need to be static friction, right?

Answer 17

Hence wouldn't that mean there must be sufficient friction that the ladder must not be able to overcome between both the wall and ground?

Answer 18

Alright so the best way to start this like any equilibrium problem or question is identify the forces present and draw a free body diagram

Answer 19

So the ladder experiences forces due to gravity, friction, and normal forces since those must be present for equilibrium to exist based on our knowledge of physics

Answer 20

and even though we take gravity and take at the center of gravity of the object it really acts along all points of the ladder

Answer 21

now let us just look at the part of the ladder pressing against the wall

Answer 22

we see that the only force acting solely on that part is gravity if we ignore the rest of the ladder

Answer 23

since gravity is directed down, it is parallel to the wall

Answer 24

but no static friction?

Answer 25

to counteract the gravity?

Answer 26

Otherwise, what would hold that part of the ladder up? There must be a force to counteract gravity in that section to keep it up, no?

Answer 27

that's where the other end of the ladder matters because in that instance gravity is down and right beneath it is the ground so a normal force would be present

Answer 28

so are you saying that the normal force at the bottom of the ladder accounts for gravity at the base and tip of the ladder?

Answer 29

Yes

Answer 30

okay, but the tip of the ladder interacts with the wall at an angle, hence it pushes on the wall with a horizontal and vertical component... the horizontal component is balanced by the normal force of the wall. What is the vertical component balanced by?

Answer 31

In problems I've seen in physics books, they mention static friction going in upwards direction. Isn't that the force to counteract the vertical component that the tip of the ladder exerts?

Answer 32

The vertical component is counteracted by the normal force of the ladder pushing against the ground at the base of the ladder remember that even though the ladder is not a point mass in physics problems we can treat as a point mass that exists at the center of mass of the ladder.

Answer 33

If you want to look at it from each end we can view it as a torque problem with the center of mass being the point of rotation

Answer 34

wait from what i see in that diagram, both g's would not cause the ladder to rotate since they move in opposite directions.

Answer 35

Hence they would cancel out.

Answer 36

now if we take all points left of the point of rotation to be negative and to the right to be positive we have that the point against the wall with a torque that is negative meaning it is clockwise and the point at the base would be positive meaning counter clockwise