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1. really need help with this question - i just cant get to the right answer

Find the least value of P that prevents the sledge (weight - 175kg) from sliding down the plane

The answer should be 580N but i cant get that
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2. I think it is wrong because i get P = 990N.
3. I've attached my version of the diagram. Because of the right angles marked in red, P is at an angle of 30 degrees to the slope. If it's not sliding, there will be no resultant force on the sledge. Parallel to the plane
Pcos30 = 175g*sin30
P = 175g*tan30 = 175*9.8/sqrt3 = 990.15...
Do you mean weight 175 N? Then it would be P = 175/sqrt3 = 101.03..
Neither is right answer so maybe it's wrong. Or I'm missing something - is there meant to be friction included too?
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4. (Original post by MiniBarSmarties)
really need help with this question - i just cant get to the right answer

Find the least value of P that prevents the sledge (weight - 175kg) from sliding down the plane

The answer should be 580N but i cant get that
If there is a "least" value, then there must be friction - otherwise there would only be one value for P that would keep the block in equilibrium. So your questions is impossible without giving us the coefficient of friction.
5. (Original post by mik1a)
If there is a "least" value, then there must be friction - otherwise there would only be one value for P that would keep the block in equilibrium. So your questions is impossible without giving us the coefficient of friction.
working backwards, µ comes out at exactly 0.2. So looks like maybe that's what's missing.
6. sorry yes there is a co-efficient to frcition
its 0.2
very sorry i missed that off!
ive just spent last hr tryin to work it out and still cant
7. ive worked it out now i was being incredibly dumb and had my angles wrong! i had 70 instead of 60 because im stupid
8. (Original post by MiniBarSmarties)
sorry yes there is a co-efficient to frcition
its 0.2
very sorry i missed that off!
ive just spent last hr tryin to work it out and still cant
Forces down plane
=============
F1 = 175*9.8*sin 30

Forces up plane
===========
F2 = Pcos30
F3 = F (friction)

Forces normal to the plane
==================
F4 = 175*9.8*cos30
F5 = Psin30

Therefore normal reaction is

N = F3 + F4
N = 1485.2 + P/2

Balancing forces up and down pl,ane,

F1 = F2 + F3
857.5 = P√3/2 +F
857.5 = P√3/2 +µN
857.5 = P√3/2 +0.2(1485.2 + P/2)
857.5 = P√3/2 + 297.04 + P/10
560.46 = P(√3/2 + 0.1)
560.46 = 0.966*P
P = 580.17
P = 580N
======

Edit: I had Psin30° at the wrong angle in the sketch - it's right now.
Attached Images

9. (Original post by MiniBarSmarties)
ive worked it out now i was being incredibly dumb and had my angles wrong! i had 70 instead of 60 because im stupid

My excuse,
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10. Not that it means much now, but i got the same answer as Fermat using the origional angle.

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