Tension in circular motion with connected masses

[Greenlime770]

1. The problem statement, all variables, and given/known data
A block of mass m₁ = 2.00kg is attached to a rope of length L₁ = 0.50m, which is fixed at one end to a table. The mass moves in a horizontal circle supported by a frictionless table. A second block of mass m₂ = 1.25kg is attached to the first mass by rope of length L₂ = 0.75m. The mass also moves in a circle, as shown in the image. If the period of the motion is T = 15s, find the tension in each rope. (Assume all ropes are massless).

Image of Figure here: https://imgur.com/a/c9RXR

Homework Equations

F_c = F_T
F_c = 4π²mr/T²

The Attempt at a Solution

I assume that there are more forces acting on m₁ than m₂. Although unsure if tension can act on both sides of an object in the same direction.

 

[TSny]

I assume that there are more forces acting on m₁ than m₂.

Yes.

Although unsure if tension can act on both sides of an object in the same direction.

No. If an object has strings attached to opposite sides of the body, the tensions cannot act in the same direction. Tension forces always "pull" on an object, so the direction of the tension force on a body is always along the string in the direction away from the body.

Make sure you carefully draw a free body diagram for each mass.

 

[QuantumQuest]

1. The problem statement, all variables, and given/known data
A block of mass m1 = 2.00kg is attached to a rope of length L1 = 0.50m, which is fixed at one end to a table. The mass moves in a horizontal circle supported by a frictionless table. A second block of mass m2 = 1.25kg is attached to the first mass by rope of length L2 = 0.75m. The mass also moves in a circle, as shown in the image. If the period of the motion is T = 15s, find the tension in each rope. (Assume all ropes are massless).

Image of Figure here: https://imgur.com/a/c9RXR

Homework Equations

Fc = FT
Fc = 4π2mr/T2

The Attempt at a Solution

I assume that there are more forces acting on m1 than m2. Although unsure if tension can act on both sides of an object in the same direction.

Additionally to what TSny suggests I would recommend to find the force(s) and period for each body separately.

EDIT: I mistakenly said period. I meant to write the resulting tension.

 

[Greenlime770]

Additionally to what TSny suggests I would recommend to find the force(s) and period for each body separately.

If I were to solve for m₂ and the tension of L₂ do I have to take into account the mass of m₁ as I would have to with L₁?

 

[QuantumQuest]

If I were to solve for m₂ and the tension of L₂ do I have to take into account the mass of m₁ as I would have to with L₁?

Note that you have two rotating bodies connected with rope and this system connected to a fixed point by another piece of rope. How do the two bodies interact?