A 65- kg child sits in a swing suspended with 3.1- m-long ropes. The swing is he

Question

A 65- kg child sits in a swing suspended with 3.1- m-long ropes. The swing is held aside so that the ropes make an angle of 56 o with the vertical. Use conservation of energy to determine the speed the child will have at the bottom of the arc when she is let go.


I've solved most of this I just can't get past this one part,
this is what I have:

Loss in Potential Energy = Gain in Kinetic Energy
mgh(1-cos) = 0.5*m*v2

h = 3.1 - 3.1cos(56 deg)

   = 1.3665 meters

so v = 2gh(1-cos)

But when I plug the numbers in I don't get the correct answer

Explanation / Answer

What might have happened was with all the different h's and 1-cosines, you got a little confused and messed up

Instead, let's go with Givens:

mass, m=65kg

length of ropes, L=3.1m

angle ropes make with vertical, =56o

We have
h = L - Lcos = L(1-cos) = 3.1(1-cos56) = 1.36650m

Using conservation of energy, we have

0.5 mv2 = mgh

0.5 v2 = gh

v = [2gh] = [2*9.8*1.36650] = 5.17527 m/s

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