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## Homework Statement

http://www.sumoware.com/images/temp/xzfrbardcbliotkt.png [Broken]

[/B]

A box travels in a circular track like the picture above.

How much velocity it must have in point A to get out of the track when reaching point B ?

## Homework Equations

F

_{centripetal}= m V^2/R

E = E'

## The Attempt at a Solution

First, I draw the free body diagram of the forces in point B

http://www.sumoware.com/images/temp/xzstkkpbgobpmjmi.png [Broken]

Actually, I want to draw the normal force, but I don't know where the normal force direction is.

I know that the centripetal force is the force that's accelerating to the center.

So, I think that Wb sin Θ is the same as the centripetal force.

I use

Wb sin Θ= F centripetal

mg sin Θ= m v^2/r

g sin Θ= v^2/r

v = √(g r sin Θ)

Then, I use the mechanical energy conservation formula. (I assume that the point A is zero in y axis)

E = E'

1/2 mv

_{a}^2 = mgh + 1/2 m v

_{b}^2

1/2 v

_{a}^2 = gh + 1/2 v

_{b}^2

v

_{a}^2 = 2gh + v

_{b}^2

v

_{a}^2 = 2g(R+R sin Θ) + v

_{b}^2

v

_{a}^2 = 2g(R+R sin Θ) + (√(g r sin Θ))^2

v

_{a}^2 = 2g(R+R sin Θ) + g r sin Θ

v

_{a}^2 = 2gR+2gRsinΘ+gr sin Θ

v

_{a}^2 = 2gR+3gRsinΘ

v

_{a}^2 = gR (2+3sinΘ)

v

_{a}= √(gR (2+3sinΘ))

But, I'm not sure my answer is right.

What I doubt is when I think the W sinΘ equals centripetal force and when I don't know where the normal force direction is pointing. Actually, I want to use ∑F = ma , but I just know the weight force to draw.

Please help me.

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