How to calculate the ratio of weight?

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To calculate the ratio of weights for two bodies connected by linear actuators, the forces acting on each body must be analyzed using Newton's second law (F=ma). The bodies move apart under the influence of a force F, with friction considered, and their movements are defined by their respective equations of motion. The key is to establish the relationship between the masses (m1 and m2) based on the total distance L they travel, which is the sum of their individual distances. The discussion emphasizes the need to derive the mass ratio from the equations of motion while considering the forces acting on each body. Understanding this relationship is crucial for determining the mass ratio when the total distance traveled is fixed.
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Homework Statement


Two body move apart by force. Frictional forces are considering. How to calculate the ratio of weight?
m1<m2
Ft1=k*g*m1
Ft2=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.
 

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welcome to pf!

hi asteorit! welcome to pf! :smile:

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

what is the connection between these two bodies?
 


tiny-tim said:
hi asteorit! welcome to pf! :smile:

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

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?
 
hi asteorit! :wink:

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

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

what do you get? :smile:​
 
tiny-tim said:
hi asteorit! :wink:

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

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

what do you get? :smile:​

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.
 

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