Understanding the Mechanics of Walking on an Inclined Plane

[Vibhor]

Hello ,

This is a question related to an everyday activity .

My thinking - The base of the inclined plane is along the x-axis and it makes an angle θ with positive x-axis .We are looking from the +z axis .

There will be three forces acting on the person . Weight , normal(perpendicular to the plane) and friction(upwards along the plane) .

If a man does not lean forward and remains along a perpendicular to the plane then there would be an anticlockwise torque from friction about the COM .This unbalanced torque would cause instability .

But if the person is leaning forward , the line of action of normal force will not pass through the COM .A clockwise torque from normal about the COM will get balanced by an anticlockwise torque from friction resulting in stability .

Is my understanding correct . If not , please give a correct explanation and help me understand this .

Thanks

 

[CWatters]

The expression "lean forwards" is a bit ambiguous. It could mean ...

1) lean forward relative to the vertical/gravity
or
2) lean forward relative to a normal to the plane.

It appears you mean 2). In which case your description is correct.

There will be three forces acting on the person . Weight , normal(perpendicular to the plane) and friction(upwards along the plane) .

If the man is standing still (eg not accelerating) then these three forces sum to zero in all directions. So the normal force and friction must sum to provide a force that is vertical to counter gravity. So yes the man can't stand perpendicular to the surface but he doesn't need to do anything more than stand vertically upright. Does standing vertically really count as "leaning forward"?

Walking actually involves "falling" and that also requires us to "lean forward" or at least it requires us to put our COM in front of our point of contact with the ground (the rear foot). So actually we lean forward slightly when walking on level ground.

 

[Vibhor]

Thank you for replying .

It could mean ...

1) lean forward relative to the vertical/gravity

Is it possible to remain stable in this ?

My question is something similar to
https://www.quora.com/Why-do-we-lean-forward-while-climbing-up-a-hill

I don't quite understand the explanation of keeping feet in line with the center of gravity to achieve stability .

Is it that in the link above the axis of rotation is taken to be the feet whereas I considered axis about the Center of Mass/Center of gravity ?

Is it correct that for stability , while walking up an inclined plane a person's body remains close to being vertical so that the force due to gravity doesn't create an unbalanced torque about the feet ?

 

[CWatters]

I don't quite understand the explanation of keeping feet in line with the center of gravity to achieve stability .

I don't think the reply at that link is very clear. I think what they mean is you need to keep your centre of mass between your feet as below...

 

[Vibhor]

Thanks for the nice picture :)

I don't think the reply at that link is very clear. I think what they mean is you need to keep your centre of mass between your feet as below...

How does that help in achieving stability ?

Is it that for stability , while walking up an inclined plane a person's body remains close to being vertical so that the force due to gravity doesn't create an unbalanced torque about the feet ?

 

[CWatters]

You explained it in #1. If the COM is outside of your feet as per the right-hand drawing then a clockwise torque is created that pulls you over.

 

[Vibhor]

OK.

In simple words , while walking up an inclined plane a person's body remains as vertically aligned as possible .

Is this correct ?

 

[CWatters]

It's not super critical. Read up on the process of walking, it involves falling forwards.