Finding Tension and Angle for a Child's Indoor Swing

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To solve for the tension T in the rope and the angle θ for a child's indoor swing, the problem involves applying centripetal acceleration principles. The approach requires using the equations of motion (F = ma) separately for horizontal and vertical forces. By setting up two equations, one for the horizontal circular motion and one for the vertical forces, both T and θ can be determined. The tension in the rope is responsible for both supporting the child and providing the centripetal force necessary for swinging. Solving these equations simultaneously will yield the desired results.
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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

 
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welcome to pf!

hi bcd201115! welcome to pf! :smile:
bcd201115 said:
… It's centripetal acceleration problem right?

yup!

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

what do you get? :smile:​
 
but how does that help me get the tension in the rope?
 
The tension keep the child from falling to the ground AND keep her swing in a circle.
 
tiny-tim said:
do F = ma twice, once for horizontal and once for vertical …
what do you get? :smile:​
bcd201115 said:
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 :smile:​
 
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