How to calculate the ratio of weight?

[asteorit]

Homework Statement

Two body move apart by force. Frictional forces are considering. How to calculate the ratio of weight?
m₁<m₂
F_t1=k*g*m₁
F_t2=k*g*m₂

Homework Equations

v₁(t₁)=$\frac{F_{t1}-F}{m_{1}}$*t$_{1}$
x₁(t₁)=$\frac{F_{t1}-F}{m_{1}}$*$\frac{t^{2}_{1}}{2}$

v₂(t₁)=$\frac{F-F_{t2}}{m_{2}}$*t$_{1}$
x₂(t₁)=$\frac{F-F_{t2}}{m_{2}}$*$\frac{t^{2}_{1}}{2}$

What is the procedure of calculation.
Thank you for your help.

 

[tiny-tim]

welcome to pf!

hi asteorit! welcome to pf!

sorry, but i don't understand the set-up

what is the connection between these two bodies?

 

[asteorit]

hi asteorit! welcome to pf!

sorry, but i don't understand the set-up

what is the connection between these two bodies?

Hi tiny-tim,

These two bodies are connected by linear actuators. Force F of the linear actuator, will act on both the bodies. We know that the bodies should move along the path L, L=x₁(t₁)+x₂(t₁). We know that m1<m2.
If I assume correctly, and the trajectory of bodies depends on the mass ratio. Or is also dependent on the time t1?
What is the ratio of the mass of bodies$\frac{m_{2}}{m_{1}}$=?, if the sum of their orbits must be equal to L?

 

[tiny-tim]

hi asteorit!

i see … so it's equal-and-opposite-reaction-forces, but without contact

ok, then start by writing out F_total = ma for each body …

what do you get? ​

 

[asteorit]

hi asteorit!

i see … so it's equal-and-opposite-reaction-forces, but without contact

ok, then start by writing out F_total = ma for each body …

what do you get? ​

I do not understand it, to me you ask? Some will not understand it?
Because I need to know what is the ratio of the masses.