Particle constrained to move on a sphere

[dray]

Homework Statement

A particle of mass m is constrained to move on a sphere of radius R by an applied force F(theta,phi). Write the equation of motion.

Homework Equations

x=vtRcos(phi)sin(theta)
y=vtsin(phi)sin(theta)

The Attempt at a Solution

F=m(del)²(x+y)

 

[kuruman]

Hi dray. Welcome to PF.

Forces are vectors. How would you write the given force as a vector? What does the problem say? Is this a force in the radial direction only or does it have angular components?

What does your attempt at a solution represent? It cannot be an expression of Newton's Second law because the "del" operator has to do with spatial derivatives and the Second Law involves a second time derivative.

Your relevant equations should be

x = R sinθ cosφ
y = R sinθ sinφ
z = R cosθ

There is no explicit time dependence in these expressions, but theta and phi themselves are functions of time.