A particle of mass m kg lies on the top of a smooth sphere of radius 2 m.
The sphere is fixed on a horizontal table at P.
The particle is slightly displaced and slides down the sphere.
The particle leaves the sphere at B and strikes the table at Q.
(i) the speed of the particle at B
(ii) the speed of the particle on striking the table at Q.
F = mv^2/r
The Attempt at a Solution
I had no way to go about this question (however part ii can be easily gotten from conversion from potential energy to kinetic), but it is from a section on circular motion, and in the marking scheme for this question, they write force equations for the mass as if it were undergoing circular motion ie they use the equation for centripetal force F = mv^2/r . The solution is at http://www.examinations.ie/archive/markingschemes/2010/LC020ALP000EV.pdf [Broken] for anyone interested, it's question 6 part a. I'm just questioning their use of the formula for circular motion - surely, the formula only holds if v is a constant, however, the mass is clearly accelerating so this is not the case, so how can they justify using this equation in their solution? Thanks.
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