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# M2 help:( watch

1. A small smooth phere of mass 3kg moving on a smooth horizontal plane with speed 8ms^(-1) collides directly with a sphere of mass 12kg which is at rest. Given that the spheres move in opposite directions after the collision, obtain the inequality satisfied by e
2. By conservation of momentum
24 = 12V2 - 3V1
8 = 4V2 - V1
V2 = (8+V1)/4

also, coefficient of restitution
e = (V2+V1)/8
so V1 = 8e - V2
sub in V2

V1= 8e - (8+V1)/4
4V1 = 32e - 8 + V1
3V1 = 32e - 8

But V1 < 0 as spheres r moving in opposite direction as shown in diagram where towards right is the positive direction
so 32e - 8 < 0
e<1/4

and 0<e<1

0 < e < 1/4
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3. Hajira, if you are treating V1 as a vector quantity and assigning it a sign (-ve quantity), then you would have had to write ...

24 = 12V2 + 3V1
and
e = (V2 - V1)/8

rewriting what you did,

By conservation of momentum
24 = 12V2 + 3V1
8 = 4V2 + V1
V2 = (8-V1)/4

also, coefficient of restitution
e = (V2 - V1)/8
so V1 = V2 - 8e
sub in V2

V1= (8-V1)/4 - 8e
4V1 = 8 - V1 - 32e
5V1 = 8 - 32e

Min value of V1 is V1 = 0, giving
0 = 8 - 32e
e = 8/32 = 1/4

but particle is actually moving, so e ≠ 1/4, and e < 1/4 gives a +ve value for V1 (wrong direction!) so e > 1/4

and 0<e<1

so

1/4 < e < 1
4. (Original post by Fermat)
Hajira, if you are treating V1 as a vector quantity and assigning it a sign (-ve quantity), then you would have had to write ...

24 = 12V2 + 3V1
and
e = (V2 - V1)/8
e=speed of separation/speed of approach

as its the speed of separation...u add them because of the fact that they r in opposite directions
think about two particles moving in opposite directions at speeds 1m/s and 3m/s
the speed by which they r separating is actually 3 + 1, n not 3 - 1...even tho being in opposite directions would make one of em negative as a vector!

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