The Force Again Acts in a Vertical Plane Through a Line of Greatest Slope of the Plane

A particle of mass 0.3 kg lies on a smooth plane inclined at an angle α to the horizontal, where tanα=3
iv
. The particle is held in equilibrium by a horizontal force of magnitude Q newtons. The line of action of this force is in the same vertical plane as a line of greatest slope of the inclined plane. Calculate the value of Q, to 1 decimal place.

Now I don't empathize why Q is horizontal, instead of perpendicular to R (Parallel to gradient)

Tin can somebody explicate the writing in assuming...

I presume that when information technology says vertical aeroplane information technology's just trying to say that you can model it every bit a 2nd situation.
I think it would exist parallel to the gradient if it was the same Horizontal plane.

(Original post by Woodsy92)
The line of action of this strength is in the aforementioned vertical plane equally a line of greatest slope of the inclined plane.

If y'all imagine a stick lying on the inclined airplane. Fix 1 terminate, and rotate the stick round (still lying on the plane) until information technology points upward the plane and its bending with the horizontal is as large equally possible. This is the line of greatest slope.

Now prototype a vertical plane/sheet going through that line and there's your required airplane.

(Original postal service past ghostwalker)
If y'all imagine a stick lying on the inclined airplane. Fix 1 stop, and rotate the stick round (nonetheless lying on the plane) until it points up the plane and its angle with the horizontal is as large every bit possible. This is the line of greatest slope.

Now image a vertical airplane/sheet going through that line and there'due south your required plane.

That is really helpful but I still can't quite visualise it.

Perhaps a few pictures to assist me understand.

Number 1 - Stick lying on inclined plane..

Number 2 - Largest bending with horizontal?

Equally y'all volition see, I may exist getting dislocated?

(Original post by Woodsy92)
That is really helpful but I still tin't quite visualise information technology.

Maybe a few pictures to help me understand.

Number 1 - Stick lying on inclined plane..

Number 2 - Largest angle with horizontal?

As yous will come across, I may be getting confused?

I think yous missed the bit that the stick is always lying apartment on the plane as it is rotated - it does not leave the plane, and then never stands vertically upright.

(Original post by ghostwalker)
I think you missed the scrap that the stick is always lying flat on the plane as it is rotated - information technology does non leave the plane, so never stands vertically upright.

Argh I merely don't get it!

It is incommunicable to rotate the stick whilst keeping it on the plane, unles you rotate the whole plane?

(Original post past Woodsy92)
Argh I only don't get it!

It is impossible to rotate the stick whilst keeping it on the aeroplane, unles you rotate the whole aeroplane?

Ok. Lets start with a level airplane, apartment basis. You'd agree you can rotate the stick on the ground, and information technology can stay on the basis?

(Original post by ghostwalker)
Ok. Lets start with a level plane, flat ground. You lot'd agree you can rotate the stick on the basis, and it can stay on the ground?

NO, not really?

One edge can stay on the ground,whilst the stick rotates 180 degrees, if that is what you meant?

(Original post by Woodsy92)
NO, not really?

Ane edge can stay on the ground,whilst the stick rotates 180 degrees, if that is what you meant?

I mean like, put a pencil on the floor and spin it around.

(Original post by ghostwalker)
I mean like, put a pencil on the floor and spin it effectually.

Is that what you mean nearly all sticks being on the slope, simply rotated?

Argh, this is really irritating every bit I can't answer any of the tougher questions on Statics.

A rough slope is inclined at an angle α to the horizontal, where α<45°. A small parcel of mass Yard is at residual on the slope, and the coefficient of friction betwixt the parcel and the slope is μ. A force of magnitude kMg, where thousand is a constant, is practical to the parcel in a management making an angle α with a line of greatest gradient, equally shown in the diagram.

The line of action of the force is in the same vertical plane every bit the line of greatest slope.

How come this one has the line of action parallel to the slope, whereas the other one was parallel to the horizontal?

(Original mail by Woodsy92)
Is that what y'all mean almost all sticks being on the slope, simply rotated?

Lamentable. I can't recollect of any other way to explain it, other than what I've posted and PM'ed y'all. You really need an animated drawing, and that's beyond my capabilities.

Perhaps someone else be able to explain it differently or may know of a website or youtube video that might by useful.

(Original mail service by ghostwalker)
Sorry. I can't think of any other mode to explain it, other than what I've posted and PM'ed yous. You actually demand an animated drawing, and that's across my capabilities.

Possibly someone else be able to explain it differently or may know of a website or youtube video that might past useful.

Ok fair enough

Practise you lot sympathise though, the divergence betwixt the ii questions?

Both said the line of action of the forcefulness is in the same vertical airplane equally the line of greatest slope.

Yet for one, the force was parallel to the horizontal airplane, and the other parallel to the inclined plane...

(Original post by Woodsy92)
Ok fair enough

Do you understand though, the departure between the two questions?

Aye, but since I can't explicate to you the vertical airplane through the line of greatest gradient in a way that makes sense to you, at that place is no point in me fifty-fifty trying to explain this departure, every bit information technology depends on the former.

(Original post past ghostwalker)
Ok. Lets start with a level plane, flat basis. You'd hold you lot can rotate the stick on the basis, and information technology can stay on the ground?

tin you delight behave on explaining from here?

http://imgur.com/a/40YDu

and so there is a picture of a mountain, the bottom of the mountain is labelled A and the pinnacle is labelled B.

Practise you concord that it doesnt matter if y'all walked on the cerise, greenish or yellow path y'all would somewhen reach the top of the mountain, albeit at dissimilar points? (dissimilar points meaning that if you walked on the dark-green line, and even more than so if you walked on the yellow line, you lot would finish much further correct than if you walked up the scarlet line)

Can you also encounter how on the second diagram these "unlike points" cannot be captured, every bit far as 2D goes the top is the top, it doesnt thing how far to the left or right of your starting point you are.

Therefore when we've just got a 2D diagram we need a phrase to let others know we are talking about the 'cherry-red line', the phrase we employ is "line of greatest slope".

Thats all there is to information technology

schneiderolve1987.blogspot.com

Source: https://www.thestudentroom.co.uk/showthread.php?t=1076843

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