# Line of greatest slope - M1

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Thread starter 11 years ago
#1
A particle of mass 0.3 kg lies on a smooth plane inclined at an angle α to the horizontal, where tanα=3
4
. 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 one decimal place.

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

Can somebody explain the writing in bold...
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11 years ago
#2
I presume that when it says vertical plane it's just trying to say that you can model it as a 2D situation.
I think it would be parallel to the slope if it was the same Horizontal plane.
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11 years ago
#3
(Original post by Woodsy92)
The line of action of this force is in the same vertical plane as a line of greatest slope of the inclined plane.
If you imagine a stick lying on the inclined plane. Fix one end, and rotate the stick round (still lying on the plane) until it points up the plane and its angle with the horizontal is as large as possible. This is the line of greatest slope.

Now image a vertical plane/sheet going through that line and there's your required plane.
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Thread starter 11 years ago
#4
(Original post by ghostwalker)
If you imagine a stick lying on the inclined plane. Fix one end, and rotate the stick round (still lying on the plane) until it points up the plane and its angle with the horizontal is as large as possible. This is the line of greatest slope.

Now image a vertical plane/sheet going through that line and there's your required plane.
That is really helpful but I still can't quite visualise it.

Maybe a few pictures to help me understand.

Number 1 - Stick lying on inclined plane..

Number 2 - Largest angle with horizontal?

As you will see, I may be getting confused?
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11 years ago
#5
(Original post by Woodsy92)
That is really helpful but I still can't quite visualise it.

Maybe a few pictures to help me understand.

Number 1 - Stick lying on inclined plane..

Number 2 - Largest angle with horizontal?

As you will see, I may be getting confused?

I think you missed the bit that the stick is always lying flat on the plane as it is rotated - it does not leave the plane, and so never stands vertically upright.
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Thread starter 11 years ago
#6
(Original post by ghostwalker)
I think you missed the bit that the stick is always lying flat on the plane as it is rotated - it does not leave the plane, and so never stands vertically upright.
Argh I just don't get it!

It is impossible to rotate the stick whilst keeping it on the plane, unles you rotate the whole plane?
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11 years ago
#7
(Original post by Woodsy92)
Argh I just don't get it!

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

Ok. Lets start with a level plane, flat ground. You'd agree you can rotate the stick on the ground, and it can stay on the ground?
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Thread starter 11 years ago
#8
(Original post by ghostwalker)
Ok. Lets start with a level plane, flat ground. You'd agree you can rotate the stick on the ground, 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?
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11 years ago
#9
(Original post by Woodsy92)
NO, not really?

One 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.
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Thread starter 11 years ago
#10
(Original post by ghostwalker)
I mean like, put a pencil on the floor and spin it around.
Is that what you mean about all sticks being on the slope, but rotated?

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Thread starter 11 years ago
#11
Argh, this is really irritating as 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 M is at rest on the slope, and the coefficient of friction between the parcel and the slope is μ. A force of magnitude kMg, where k is a constant, is applied to the parcel in a direction making an angle α with a line of greatest slope, as shown in the diagram.

The line of action of the force is in the same vertical plane as 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?
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11 years ago
#12
(Original post by Woodsy92)
Is that what you mean about all sticks being on the slope, but rotated?

Sorry. I can't think of any other way to explain it, other than what I've posted and PM'ed you. 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.
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Thread starter 11 years ago
#13
(Original post by ghostwalker)
Sorry. I can't think of any other way to explain it, other than what I've posted and PM'ed you. 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.
Ok fair enough

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

Both said the line of action of the force is in the same vertical plane as the line of greatest slope.

Yet for one, the force was parallel to the horizontal plane, and the other parallel to the inclined plane...
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11 years ago
#14
(Original post by Woodsy92)
Ok fair enough

Do you understand though, the difference between the two questions?
Yes, but since I can't explain to you the vertical plane through the line of greatest slope in a way that makes sense to you, there is no point in me even trying to explain this difference, as it depends on the former.
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4 years ago
#15
(Original post by ghostwalker)
Ok. Lets start with a level plane, flat ground. You'd agree you can rotate the stick on the ground, and it can stay on the ground?
can you please carry on explaining from here?
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4 years ago
#16
(Original post by Woodsy92)
x.
(Original post by aaa2000)
x
http://imgur.com/a/40YDu

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

Do you agree that it doesnt matter if you walked on the red, green or yellow path you would eventually reach the top of the mountain, albeit at different points? (different points meaning that if you walked on the green line, and even more so if you walked on the yellow line, you would finish much further right than if you walked up the red line)

Can you also see how on the 2D diagram these "different points" cannot be captured, as far as 2D goes the top is the top, it doesnt matter how far to the left or right of your starting point you are.

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

Thats all there is to it
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4 years ago
#17
(Original post by DylanJ42)
http://imgur.com/a/40YDu

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

Do you agree that it doesnt matter if you walked on the red, green or yellow path you would eventually reach the top of the mountain, albeit at different points? (different points meaning that if you walked on the green line, and even more so if you walked on the yellow line, you would finish much further right than if you walked up the red line)

Can you also see how on the 2D diagram these "different points" cannot be captured, as far as 2D goes the top is the top, it doesnt matter how far to the left or right of your starting point you are.

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

Thats all there is to it
Thank you soooo much
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