Particle in Sphere Problem: Force Exerted & Speed Calculation

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A particle of mass M moves along the smooth inner surface of a hollow spherical bowl, maintaining a horizontal circular path with its center C located 1/3r below the sphere's center O. The problem requires calculating the magnitude of the force exerted by the sphere on the particle and determining the particle's speed. The scenario assumes a constant speed and smooth surface, which simplifies the analysis of forces acting on the particle. Key considerations include gravitational force and centripetal acceleration in the context of circular motion. The discussion highlights the importance of understanding the dynamics of motion within a constrained environment.
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I got a quite interesting problem. ere it goes.
A particle P of mass M,moves on the smooth inner surface of a sphere 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 1/3r vertically below O. Determine
the magintude of force exerted by sphere and speed of p
 
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um i made a mistake.i am actually new to this site.
 
Thread 'Have I solved this structural engineering equation correctly?'

Thread 'Have I solved this structural engineering equation correctly?'

Hi all, I have a structural engineering book from 1979. I am trying to follow it as best as I can. I have come to a formula that calculates the rotations in radians at the rigid joint that requires an iterative procedure. This equation comes in the form of: $$ x_i = \frac {Q_ih_i + Q_{i+1}h_{i+1}}{4K} + \frac {C}{K}x_{i-1} + \frac {C}{K}x_{i+1} $$ Where: ## Q ## is the horizontal storey shear ## h ## is the storey height ## K = (6G_i + C_i + C_{i+1}) ## ## G = \frac {I_g}{h} ## ## C...
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