Particle P in Sphere: Find Force & Speed

[AK2]

this the problem
A particle P of mass M moves on the smooth inner surface of a fixed hollow
spherical bowl,centre O and inner radius r,describing a horizontal circle at constant speed.The centre C of this circle is at a depth r/3 vertically below O.Determine
(a)The magnitude of the force exerted by the surface of the sphere on P
(b)the speed of P
i know conservation of energy is involved but don't know how to go about it.

 

[quasar987]

The particle is describing a uniform circular motion! Therefor there must be a central force acting on it. Draw the force diagram (gravity and normal), take the vectorial sum of the force ans you will see that it is so. (Finding the normal force will require that you use what you know about the geometry of a sphere and the information you are given about where the circle C is)

Use F=ma to find what the centripetal acceleration produced by this force is. I'm sure you know the relation btw the velocity of a particle in a uniform circular orbit and the centripetal acceleration is. Use that formula to find the speed.

 

[AK2]

thanks i will go on it rigth away.

 

[quasar987]

uuuuuuummmmmmmmmm... I don't understand this problem anymore. You might as well disregard everything I said.

Help!

 

[StatusX]

The bowl can only exert a force on the particle in a direction normal to its surface. The vertical component of this force must exactly balance gravity if the particle is not to accelerate vertically, and so since you know the direction of the force, this also determines its radial component. Then there is a certain speed the particle must travel for this radial force to balance the centrifugal force mv^2/r, so that the particle maintains circular motion.

 

[quasar987]

AAAAaahh... I was certain the normal force was only allowed to "offer a reaction" to the component of the force perpendicular to the surface. But how the normal force really behaves is much less shyly. Instead, it pushes on the mass perpendicularly to the surface with a magnitude such that the other force is "anihilated".

The steeper the slope, the greater the normal force and the greater the centripetal acceleration and thus the greater the velocity needed to maintain circular motion. It makes sense.

 

[AK2]

thanks a lot . i followed ur analysis and i got rigth answers to the question.