- #1

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a) From what height should circular hoop of radius R be released in order to equal the sphere's speed at the bottom?

First i started with the sphere

mgh=.5mv

^{2}+.5Iw

^{2}

I=.5mR

^{2}

w=v/r

so

mgh=.5mv

^{2}+.25mv

^{2}

gh=.75v

^{2}

h=30

v

^{2}=40g

next the hoop

the only difference is we dont know h and I is different

I=mR

^{2}

so gh=v

^{2}

therefore setting them equal, h=40.

However the answer is 43. I did neglect to include R in the height because both objects have this height R. However when i included R in to h. I found 40+(1/3)R=h which leave me know where.

Any ideas? There is no mention of friction...