Recent content by algebra topology

$$ v\frac{\mathrm{d} v}{\mathrm{d} \theta } + gRcos \theta + \mu gRcos \theta = \mu v^2 $$

##v\frac{\mathrm{d} v}{\mathrm{d} \theta } + gRcos \theta + \mu gRcos \theta = \mu v^2 ##On the right, I get a complex differential equation.

Yes.

China.

The terminal velocity is the instantaneous velocity to the end of another circular orbit

In our semi-finals Physics Olympiad here, differential equation are a common occurrence.

I mean just consider gravity, elasticity and friction.

This is a problem in space.But it is confined to a plane.The wire stands for a rough transversal semicircle.Because the speed is not big, so do not consider the speed is too big and out of orbit.The support force divided by the friction force is considered constant μ.

Thanks.I am sure that there is sliding friction.So the difficulty of the problem is to solve the sliding friction.

TL;DR Summary: Almost as difficult as the Physics Olympics semi-finals or finals The coefficient of friction of the two arcs is the same.The radius of the ball is not taken into account.The roll of the ball is ignored.Can it be calculated or estimated quantitatively?The difficulty is estimated...