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stanny
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#1
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Particles A and B of mass 2m and m respectively are attached to the ends of a light inextensible string. The string passes over a smooth pulley fixed at the edge of a rough horizontal table. Particle A is held on the table, while B rests on a smooth plane inclined at 30 degrees to the horizontal. The string is in the same vertical plane as a line of greatest slope of the inclined plane. The coefficient of friction between A and the table is miu. The particle A is released from rest and begins to move.

When each particle has moved a distance h, the string breaks. The particle A comes to rest before reaching the pulley. Given that miu = 0.2.

Find, in terms of h, the total distance moved by A.

Help plz... this is super hard.
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Sahir
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Okay i got total distance of A moved = 7h/6 metres;

First of all, obviously draw a diagram, indicating acceleration of both particles and resolve parallel and perpendicular to the surface for both particles A and B:

PARTICLE A:
1) T - 0.2R = 2ma
2) R = 2mg

therefore for particle A; T - 0.4mg = 2ma

PARTICLE B:
1) mg.sin30 - T = ma
2) R = mg.cos30

note that you don't need to use equation 2 because R is irrelevant - the surface on which B rests is SMOOTH

therefore for particle B; mg - 2T = 2ma

Eliminate the 2ma and find T

mg - 2T = T - 0.4mg
1.4mg = 3T

T = 1.4mg/3 = (7mg/15) Newtons

Find initial acceleration (which will be the same for both particles:

T - 0.4mg = 2ma
7mg/15 - 0.4mg = 2ma

a = 49/150 m.s^-2

Find what the velocity of A is when the string breaks and displacement = h

a = 49/150
u = 0
s = h
v = ?

v^2 = u^2 + 2as
v^2 = 49h/75

Draw another diagram, just for particle A once the string has broke and there is no tension / driving force and resolve:

-0.2(2mg) = 2ma
a = -0.2g

use v^2 = u^2 + 2as again..

from before.. u^2 = 49h/75
v = 0
a = -0.2g
s = ?

v^2 = 0 = 49h/75 + 2(-0.2g)s

s = (49h/75) / 0.4g = h/6 metres AFTER THE STRING HAS BROKEN

Total displacement = h + h/6 = 7h/6 metres!

Btw.. that took fking ages!
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stanny
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wow thx LOADS ^^
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Sahir
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(Original post by stanny)
wow thx LOADS ^^
You're v welcome mate
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stanny
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no wonder... this was from the paper that my bro did and he got the highest in class, which was only 85... the q's were esp hard... somehow
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stanny
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ppl here are too smart i guess
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john !!
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That's not harder than the average question, it's just a lot longer. With a diagram and some time anyone studying M1 could do that... you usually get a question like that at the last question anyway, where it asks about how far a particle has travelled after a force is removed.
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Sahir
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(Original post by mik1a)
That's not harder than the average question, it's just a lot longer. With a diagram and some time anyone studying M1 could do that... you usually get a question like that at the last question anyway, where it asks about how far a particle has travelled after a force is removed.
Also helps that i'm resitting M1 this year after having finished M2 aswell, and i feel a lot more comfortable with mechanics this year.. just used to it i guess!

Don't worry bout it, that'd be the longest question on the paper by far.. just think logically and work through it..!
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john !!
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Lol I'm not worrying - gonna love this test, full marks in the mock.
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Sahir
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(Original post by mik1a)
Lol I'm not worrying - gonna love this test, full marks in the mock.
lol sorry, no i meant stanny hehe i just pressed quote instead of reply i guess *shrug*
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john !!
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lol np :eek:
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