Conservation of Energy/Motion Question

[Victorzaroni]

Homework Statement

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?

The answer choices are:

(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

Homework Equations

Conservation of Energy?

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.

 

[kushan]

Hi Victorzaroni
try equating component of weight with centripetal force

 

[Victorzaroni]

Component of weight as in the cosine component or sine?

 

[kushan]

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

 

[Victorzaroni]

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