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A little block with mass m lies still on the top of a frictionless sphere with radius R. Somebody gently hits the block, causing it to slide down the sphere. The mass loses contact with the sphere when the angle between the positionvector and the vertical equals 0c. The drawing below shows the position of the block on two moments in the movement. The velocity caused by the hit in the beginning is negligible.

http://img453.imageshack.us/img453/6496/sphericalsurface0qu.gif [Broken]

The question is:

Find the angle 0c where the block begins losing contact with the surface.

Unfortunately I may not use energy laws, because my teacher wants me to do it another way, but I just don't know how! Please give me a little start here...

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Questions I've already answered are:

a) Express the distance s in R and 0.

b) Which forces work on the block if it's sliding down the sphere? Draw them.

c) Split the forces in tangential components and perpendicular components on the spherical surface.

d) Express the centripetal acceleration Ac and the tangential acceleration At in the forces found by b.

http://img453.imageshack.us/img453/6496/sphericalsurface0qu.gif [Broken]

The question is:

Find the angle 0c where the block begins losing contact with the surface.

Unfortunately I may not use energy laws, because my teacher wants me to do it another way, but I just don't know how! Please give me a little start here...

-----------------------------------------------------------------------

Questions I've already answered are:

a) Express the distance s in R and 0.

*s= R * 0 That is when 0= in rad. If 0 is in degree it should be s= R (2pi *0 / 360)*b) Which forces work on the block if it's sliding down the sphere? Draw them.

*The gravitationforce and the normal force, drawn below:*

http://img173.imageshack.us/img173/4374/sphericalsurface25zz.gif [Broken]

http://img173.imageshack.us/img173/4374/sphericalsurface25zz.gif [Broken]

c) Split the forces in tangential components and perpendicular components on the spherical surface.

*http://img467.imageshack.us/img467/2815/sphericalsurface35tt.gif [Broken]*

d) Express the centripetal acceleration Ac and the tangential acceleration At in the forces found by b.

*If 0 is chosen well in the x-direction (the direction of the tangential acceleration) Fres= Fz,//= Fz sin 0 = m * At. Therefore At= (Fz sin (0))/m*

In the y-direction (the direction of the centripetal acceleration) Fres= Fz,|- Fn= Fz cos 0 - Fn= m* Ac. Therefore Ac= (Fz cos(0) -Fn)/m.In the y-direction (the direction of the centripetal acceleration) Fres= Fz,|- Fn= Fz cos 0 - Fn= m* Ac. Therefore Ac= (Fz cos(0) -Fn)/m.

**e) At the point where the mass begins losing contact with the surface there are two conditions:**

Condition 1: |Ac|= g cos(0)

Condition 2: |Ac|= v^2/R where v= the speed of the block.Condition 1: |Ac|= g cos(0)

Condition 2: |Ac|= v^2/R where v= the speed of the block.

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