Question

A particle of mass m slides down a fixed, friction less sphere of radius R. starting from rest at the top. a. In terms of m, g, R. and θ, determine each of the following for the particle while it is sliding on the sphere.

 

i. The kinetic energy of the particle 

ii. The centripetal acceleration of the mass

Answer 1

h = R – R cosθ = R (1 – cosθ)

(i) K₂ = U_top

k₂ = mg(R(1 - cosθ))

(ii) From, K = 1/2mv² = mgR(1 - cosθ) ..... v² = 2gR(1 – cos θ)

Then ac = v²/R = 2g(1 – cos θ)