Not sure of the dynamics of the following situation. Suppose there is a mass that can slide on a straight track with one degree of freedom. Assume no friction in this scenario. On top of this mass is a track that forms a quarter circle. On this track is a sphere that can slide(again assume no friction) on this track.(adsbygoogle = window.adsbygoogle || []).push({});

The sliding mass moves along the y-axis. At some point in time the sphere is given an initial velocity, and then enters one end of the quarter-circle curved track. As the sphere moves in a counter-clockwise direction along this track, it eventually reaches the end of this quarter-circle, moving in the negative x-direction, where it makes an inelastic collision at the end of the track.

During the time the sphere rounds the curve, the centrifugal reactive force acting on the sliding mass causes the sliding mass to accelerate at a non-constant rate in the positive y-direction. After the sphere collides at the end of the track, the whole system continues to move in the positive y-direction by Newton’s law of inertia.

Suppose there is an observer on the accelerating mass as the sphere rounds the curve. He will observe a strange gravitational effect that increases as the sphere rounds the curve. He can verify this easily by noting the reading on an accelerometer.

The answer to this question that is not clear to me is will the sphere maintain a constant speed as it rounds the curve, or will it slow down? According to the principle of equivalence the observer in the frame of the moving mass will experience a gravitational effect, even though it is not constant, and would expect the speed of the sphere to slow down due to this gravitational field the observer experiences in his frame. Or would it retain a constant speed?

I ask this question because an observer in an inertial laboratory frame would not experience this gravitational effect, so wouldn’t he correctly expect the sphere to maintain a constant speed as it rounds the curve? The only Newtonian force he would accept as real would be the centripetal force acting on the sphere, which would always be perpendicular to the instantaneous tangential velocity of the sphere.

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# I An exception to the principle of equivalence?

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