Uniform Circular Motion questions

[LostStudent]

1. A .25kg mass attached to a string of length 1m is spun in a horizontal circle. At what speed must it travel so that the angle the string makes with the horizontal is 30 degrees?

2. A block of mass m slides around a circular path in a conic surface with vertex angle 2theta. Determine the speed of rotation at a height h above the vertex.

Im lost at what to do for both problems. Any help would be appreciated. Thanks.

 

[Chi Meson]

1. think components. The mass makes no differnce here. all that matters is the tangential speed and the radius. Call the tension in the string "T" and ask yourself "what component of T provides centripetal force, and what component of T balances weight?"

 

[LostStudent]

"1. think components. The mass makes no differnce here. all that matters is the tangential speed and the radius. Call the tension in the string "T" and ask yourself "what component of T provides centripetal force, and what component of T balances weight?""

The centripetal force is provided by the horizontal component of T.
So: T*cos30 = m v^2/r

The vertical component of T balances the weight.
So: T*sin30 = mg
So T = (.25)(9.8) / sin30 = 4.9 N ?

Then use T to find V:
(4.9)(cos30) = (.25) v^2 / 1
4.24 / .25 = v^2
16.96 = v^2
v= 4.12 m/s

Right or wrong?

 

[Chi Meson]

doesn't it feel right? Notice how any value for mass would have worked?

 

[Chi Meson]

ask yourself the same questions for #2. Except it's the normal force, not tension. And find a value for radius in terms of h and theta.