Is the Stick Lying Against the Wall at Rest?

[coconut62]

Homework Statement

A stick is lying at rest against the wall. Which of the following statements is true?

A) Friction must be present on both the wall and the floor surfaces.
B) The wall surface must be rough, but the floor may be smooth.
C) The floor surface must be rough, but the wall may be smooth.
D) The wall and the floor surfaces can both be smooth.

Homework Equations

None

The Attempt at a Solution

I chose D. The answer is C.

I know there's the weight of the stick acting downwards.
The reaction force of the wall on the stick.
The reaction force of the floor on the stick.

Because the reaction of the wall ----> must have a horizontal component (even if it's not horizontal), so there should be a <---- force provided by the floor.

But can't the floor just provide that by having a non-vertical reaction force?

 

[ehild]

Homework Statement

A stick is lying at rest against the wall. Which of the following statements is true?

A) Friction must be present on both the wall and the floor surfaces.
B) The wall surface must be rough, but the floor may be smooth.
C) The floor surface must be rough, but the wall may be smooth.
D) The wall and the floor surfaces can both be smooth.

Homework Equations

None

The Attempt at a Solution

I chose D. The answer is C.

I know there's the weight of the stick acting downwards.
The reaction force of the wall on the stick.
The reaction force of the floor on the stick.

Because the reaction of the wall ----> must have a horizontal component (even if it's not horizontal), so there should be a <---- force provided by the floor.

But can't the floor just provide that by having a non-vertical reaction force?

The reaction force from a surface is always normal to the surface. It is often called "normal force". Imagine that the reaction force from the floor has horizontal component. Then a box on the floor would accelerate by itself.


ehild

 

[coconut62]

Why the reaction force from a hinge can be slanted?

 

[ehild]

The cross section of the hinge is circular, the reaction force is radial, it can have any direction, normal to the surface of the hinge.

ehild

 

[haruspex]

The reaction force from a surface is always normal to the surface.

Not sure I go along with that. Why can't the friction be considered part of the reaction? It's a reaction against a tendency to slide, no? If I try to push a box along the floor, friction between the box and the floor applies a horizontal force to the floor, and I feel the floor's reaction to that.
I thought this in the OP was good enough:

Because the reaction of the wall ----> must have a horizontal component (even if it's not horizontal), so there should be a <---- force provided by the floor.

 

[ehild]

Usually we talk about normal force and friction separately in such problems, instead of "reaction force" as something, including both, and having arbitrary direction. Normal force is force of constraint. Friction is a force opposing relative motion, and related to the normal force. It does not exist without the normal force.

The original question was if the floor must be rough in order to keep the stick in rest. Coconut62's answer "C" was correct, the horizontal reaction force from the wall had to be balanced by a horizontal force from the floor. That force is provided by friction. He asked if the reaction force from the floor could have horizontal component, which meant he did not consider friction as reaction force.

ehild

 

[haruspex]

He asked if the reaction force from the floor could have horizontal component, which meant he did not consider friction as reaction force.

ehild

That's true, cocnut62 wrote:

But can't the floor just provide that by having a non-vertical reaction force?

But I don't think the right response is to say the reaction force is always normal to the surface. Rather, the reaction force consists of a normal component and a parallel component; the parallel component is what we call friction.

 

[ehild]

Well, the reaction force need not be normal to the ground even in case of no friction. The surface might be slightly deformed by the object and the deformed surface can exert a force parallel with the original surface. But the Introductory Physics courses consider a surface macroscopically smooth and not deformable, and call the force of constraint exerted by the support "normal force" as reaction force to weight or pressing force of the object.
What we call "reaction force" from a support, it depends on the definition, friction may or may not included. I could not know how it was taught to the OP, but it seemed to me, that they did not include friction. Anyway, he was right, the floor need not be rough, it can be sticky to prevent the stick from sliding.
ehild