physics question involving kinetics (3) please help :)

Question

A girl on a playground swing starts from rest at an angle θ=25.3 from the vertical. The chains have length L=4.6 meters. Find her speed as she passes through the bottom of the swing. Assume no pushing, pumping, air resistance, etc.
In your answer:
give precision to 0.01!!

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.