Can You Calculate Tension and Angle in a Child's Indoor Swing?

[fisselt]

Homework Statement

A child’s indoor swing consists of a rope of length L anchored to the ceiling, with a seat at the lower end. The total mass of child and seat is m. They swing in a horizontal circle with constant speed v, as shown in Fig. 6-2; as they swing around, the rope makes a constant angle 0 with the vertical. Assuming the time τ for one revolution (i.e., the period) is known, find the tension T in the rope and the angle θ.

Homework Equations

ƩF=ma_c=m(v²/r)
ƩF=mg

The Attempt at a Solution

I decided the force from the child on the swing would be F_total=( ƩF=mg and ƩF=ma_c=m(v²/r)).
And the tension of the line is T_y= F_total cosθ and T_x= F_total sinθ

Therefore T=F_total(cosθ+sinθ)
where F_total=m(v²/r+g)
Rewritten: T=(m(v²/r+g))(cosθ+sinθ)

And, rearranging this equation would give me θ if I so desired.

Am I doing this right??

Thanks for help

 

[Quinzio]

Draw a simple FBD.
In any istant, the (rope tension) x (cos θ) must equal the gravity force.
Do you agree ?
Then you easily have the rope tension.

 

[fisselt]

Since, T_ycosθ=mg then T_y=mg/cosθ. Then T_x =m(v²/r)sinθ

Is this correct?