physics-KE question

Question

A girl on a playground swing starts from rest at an angle θ=34.2 from the vertical. The chains have length L=6.8 meters. Find her speed as she passes through the bottom of the swing. Assume no pushing, pumping, air resistance, etc.

 

Any help would be great, thank you!

Answer 1

You can solve this using energy conservation.

At the top, starting from rest, potential energy is

U = mgy = mg(L - L cosθ) = mgL(1 - cosθ)

Kinetic energy K = 0 at the top. At the bottom,

U = 0
K = mv²/2

U at top = K at bottom

mv²/2 = mgL(1 - cosθ)

v = [2gL(1 - cosθ)]^1/2

Just substitute given values and simplify. Can you finish from here? Feel free to post a comment if you need more help.  (Also, note this is correct only for θ defined from the vertical.)