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 >.<

 

[Nickie]

I can understand your confusion with the acceleration equation in this exercise. However, the relationship between the two particles' accelerations is not simply a matter of one being twice the other. It is important to consider the forces acting on each particle and how those forces affect their accelerations.

In this situation, both particles are experiencing friction and a tension force from the wheel. The tension force is equal for both particles, but the friction force will differ due to the different masses of the particles. This means that the acceleration of each particle will also differ.

Using your equations, we can see that the acceleration of particle 1 is dependent on the friction force, while the acceleration of particle 2 is dependent on both the friction force and the tension force. Therefore, the acceleration of particle 2 will be affected by both forces, resulting in a different value than that of particle 1.

To fully understand the relationship between the accelerations of the two particles, we would need to solve the equations for each particle and then compare their values. It is not as simple as one being twice the other, as there are multiple factors at play. I suggest revisiting the equations and considering all the forces acting on each particle in order to fully understand the relationship between their accelerations.