Conservation of Energy/Motion Question

1. Feb 21, 2012

Victorzaroni

1. The problem statement, all variables and given/known data

A small mass m slides down from rest at the top of a frictionless spherical surface of radius R=.5 meters. What is the speed of the particle at position x where it loses contact with the surface, and velocity makes an angle of θ=48.2 with the vertical?

(A) 1.28 m/s
(B) 1.82 m/s
(C) 1.93 m/s
(D) 2.36 m/s
(E) 2.58 m/s

2. Relevant equations

Conservation of Energy?

3. The attempt at a solution

I thought maybe start with PE1=PE2+KE, where h=2r, and then find the cosine component of the height when velocity is at that angle, to do: mg(2r)=(1/2)mv2+mg((cos48.2)+R), but that didn't work. I got .57, which is not even close to any of the choices.

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2. Feb 21, 2012

kushan

Hi Victorzaroni
try equating component of weight with centripetal force

3. Feb 21, 2012

Victorzaroni

Component of weight as in the cosine component or sine?

4. Feb 21, 2012

kushan

see at the point when it leaves the contact
mgcos(θ) will be equal to centripetal force

5. Feb 21, 2012

Victorzaroni

thanks. I get it now! It's 1.82, choice B