- #1

joker_900

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## Homework Statement

OK this involves vectors but I can't use the normal notation on the internet so I'm using u^ to mean the unit vector along the vector u - i hope you can help me!

A particle of mass m is constrained to slide on the inside of a vertical smooth semi-circular ring of radius r. The position of the particle is described by a polar coordinate system whose origin is at the centre of the circle with axes along the orthogonal unit vectors r^ and b^ where

**b**is the angle between the radius vector

**r**and the vertical line that passes through the origin.

Assuming the particla is released from rest at the top of the semi-circle, use conservation of energy and Newton's Second Law in the r^ direction to calculate the reaction force exerted by the surface at b=60 degrees.

## Homework Equations

The first part of this equation led to finding the formula for acceleration:

[/b]a[/b] = r*b''b^ - (v*v/r)r^ where b'' is the second derivative of the angle

## The Attempt at a Solution

For conservation of energy I had

2grcosb = v*v, at b=60 => gr = v*v

And for Newton in the r^ direction I had

ma = mgcosb - R , at b=60 => ma = 0.5mg - R where R is the reaction force

From the equation for acceleration in the section above, I took the acceleration in the r^ direction to be

v*v/r and I substituted this into the equation above, and then substituted the energy conservation equation to get

R=1.5mg

However the given answer is 0.5mg - where have I gone wrong?!?