Super hard M1 question Watch
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.
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:
1) T - 0.2R = 2ma
2) R = 2mg
therefore for particle A; T - 0.4mg = 2ma
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!
wow thx LOADS ^^
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.
Don't worry bout it, that'd be the longest question on the paper by far.. just think logically and work through it..!
Lol I'm not worrying - gonna love this test, full marks in the mock.