I don't get the acceleration relation in this ex

[Lenjaku]

Homework Statement

find the relationship between the 2 particles' accelerations.

Homework Equations

m1=20kg
m2=40kg
wheel doesn't weigh but can move.

both particles move with friction.

μs=μk=0.2

F(t)=98e^0.1t

The Attempt at a Solution

I came up with 3 equations:
F(t)-fk₁-T₁=m₁a₁
T₁=2T₂
T₂-fk₂=m₂a₂

Why is the acceleration equation
a₂=2a₁?

 

[CWatters]

Why is the acceleration equation
a₂=2a₁?

Due to the pulley.

If M1 moves 1 meter to the right how far does M2 move?

If M1 moves at a velocity of 1m/s to the right how fast does M2 move?

If M1 accelerates at 1m/s^2 to the right how fast does M2 accelerate?

 

[superdave]

The pulley is attached to m1. So they have to have the same acceleration when the rope between them is under tension. If the pulley moves 1 meter, then 1 meter of the m1 rope has moved on both sides of the pulley, so 2 meter of rope has gone past the pulley, so m2 moves twice as much as m1.

 

[Lenjaku]

There is no mathematic explanation then? :( .Since the rope near the wall 'lengthens' the same value it 'shortens' near m2 while m1 keeps on going does it mean that m1 moves twice the distance m2 moves?If so it makes sense for me :S

edit:
I just noticed I mean m1 moves less than m2, m2 moves twice the distance >.<