Finding Tension and Angle for a Child's Indoor Swing

[bcd201115]

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 the child and seat is m. They swing in a horizontal circle with constant speed v. As they swing around, the rope makes a constant angle θ 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

Sorry i know this is a long worded problem but can anyone give me a hand getting started with this one? It's centripetal acceleration problem right?

The Attempt at a Solution

 

[tiny-tim]

welcome to pf!

hi bcd201115! welcome to pf!

… It's centripetal acceleration problem right?

yup!

do F = ma twice, once for horizontal and once for vertical …

what do you get? ​

 

[bcd201115]

but how does that help me get the tension in the rope?

 

[azizlwl]

The tension keep the child from falling to the ground AND keep her swing in a circle.

 

[tiny-tim]

do F = ma twice, once for horizontal and once for vertical …

what do you get? ​

but how does that help me get the tension in the rope?

the tension T and the angle θ are both in both equations,

so you have two equations with two unknowns … which you can solve!

show us what you get ​