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A Level Maths - Mechanics Q. Please could you kindly help me out with this Q?

A rough plane is inclined to the horizontal at an angle A, where tanA=3/4.
A brick P of mass m is placed on the plane.
The coefficient of friction between P and the plane is Y.
Brick P is in equilibrium and on the point of sliding down the plane.
Brick P is modelled as a particle.
Using the model,
a) find, in terms of m and g, the magnitude of the normal reaction of the plane on brick P
b) Show that Y=3/4
Reply 1
Original post by samasama
A rough plane is inclined to the horizontal at an angle A, where tanA=3/4.
A brick P of mass m is placed on the plane.
The coefficient of friction between P and the plane is Y.
Brick P is in equilibrium and on the point of sliding down the plane.
Brick P is modelled as a particle.
Using the model,
a) find, in terms of m and g, the magnitude of the normal reaction of the plane on brick P
b) Show that Y=3/4

Have you sketched the problem, formed the force equilibrium equations, ...?
Reply 2
Original post by mqb2766
Have you sketched the problem, formed the force equilibrium equations, ...?

Yes this is the answer, but I'm unsure of how to get to that answer
(In the question I used 'Y' instead of 'µ')
(a) Resolve perpendicular to the plane
R =mgcosA = 4/5mg
(b) Resolve parallel to the plane or horizontally or vertically
F mg = sinA or RsinA= FcosA
Use F = µR and solve for µ
µ = 3/4
Reply 3
Original post by samasama
Yes this is the answer, but I'm unsure of how to get to that answer
(In the question I used 'Y' instead of 'µ')
(a) Resolve perpendicular to the plane
R =mgcosA = 4/5mg
(b) Resolve parallel to the plane or horizontally or vertically
F mg = sinA or RsinA= FcosA
Use F = µR and solve for µ
µ = 3/4

Did you draw the diagram / what are you unsure about?
Rather than posting someone elses solution, why not post your own working?
(edited 2 years ago)
Reply 4
Original post by mqb2766
Did you draw the diagram / what are you unsure about?
Rather than posting someone elses solution, why not post your own working?

That was the markscheme answer. I don't know how to get 3/4 for µ, I get as far as mgsinA/(4/5)mg
Reply 5
Original post by samasama
That was the markscheme answer. I don't know how to get 3/4 for µ, I get as far as mgsinA/(4/5)mg

What is sin(A)? Im presuming you;ve found cos(A) = 4/5 so its similar.
You know tan(A)=3/4, so ...
Reply 6
Original post by mqb2766
What is sin(A)? Im presuming you;ve found cos(A) = 4/5 so its similar.
You know tan(A)=3/4, so ...

Sorry I'm not too sure what you mean
Reply 7
Original post by samasama
Sorry I'm not too sure what you mean

You have a right angled triangle and
tan(A) = 3/4
What is the opposite and adjacent lengths and hence work out the hypotenuse? So then work out cos(A) and sin(A).
Reply 8
Original post by mqb2766
You have a right angled triangle and
tan(A) = 3/4
What is the opposite and adjacent lengths and hence work out the hypotenuse? So then work out cos(A) and sin(A).

I see, but I think you have to use an alternative method for A-Level maths because going via that method doesn't follow through what the markscheme looks for to award marks
Reply 9
Original post by samasama
I see, but I think you have to use an alternative method for A-Level maths because going via that method doesn't follow through what the markscheme looks for to award marks


Original post by mqb2766
You have a right angled triangle and
tan(A) = 3/4
What is the opposite and adjacent lengths and hence work out the hypotenuse? So then work out cos(A) and sin(A).

So I got cosA=4/5 and sinA=3/5, how do you proceed from here to work out µ?
Original post by samasama
So I got cosA=4/5 and sinA=3/5, how do you proceed from here to work out µ?

mu = mgsin(A)/mgcos(A) = (mg3/5)/(mg4/5) = ...
You should be able to get the answer direclty using either of the two expressions, simpify either the trig or the numerical fractions. Either would get you full marks in an exam, though the former is more direct/less error prone.

If you're having troubles with this, even with the mark scheme, I'd maybe go back in your textbook and build up your skills a bit with some simpler questions.
(edited 2 years ago)

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