(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A small body is set on the surface of a smooth sphere at an angle of 45 degrees from the center. At this point the sphere is given a constant acceleration in the horizontal direction of 9.8 m/s/s. There is more in the question, but the goal is to find when the body will leave the circle.

2. Relevant equations

I'm wondering if from the s' frame I can treat the accelerations from psuedoforce due to the sphere's acceleration and the force from gravity as one acceleration toward the center of the sphere for the first quadrant. Since both equal 9.8 m/s/s, I want to simplify dealing with the normal force with a centripetal acceleration of 9.8 m/s/s.

3. The attempt at a solution

I figure since where ever the body lies on that quadrant, the force from gravity will be the sin and the psuedoforce from the acceleration will be the cos of the same angle. Thus, the net force from the two would be

=sqrt( {9.8sinx}^2 + {9.8cosx)^2 )

=sqrt( 9.8^2 {sin^2x + cos^2c} ) and the cos and sin squares would equal 1

=sqrt ( 9.8^2 ) which just equals 9.8

Does this make sense or am I missing something?

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# Homework Help: Small Body on a Sphere loss of contact

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