Task with ball, cyllinder and inclined plane - problem -help

[Pawell]

Hello everybody! ;)

I've got problem with task below, I've got few days to solve it and I've got some troubles:

On inclined plane with variable angle of inclination we set cylinder and ball on the same height above the ground. The friction factor for both objects comes to 0,1 - it's the same and constant for both of them. Compare the times, after which both of these objects reach the base of inclined plane (the ground) - count the ratio of these times. Consider two situations:

a) for small angles of plane's inclination, when movement of bodies is held without slip.
b) for big angles of plane's inclination, when movement of bodies is held with slip.

Calculate, for what range of angles situations a) and b) are considered.


I've no problem with situation in point a). But I can't manage the situation b) because I think these "times" depend on angel too - not only on friction factor and inertial moment of bodies. How to solve this? Have no idea.. I've thought about this very long time and still nothin' ;) If you know, please help me. I'll be very grateful even for little help :)

 

[LowlyPion]

Welcome to PF.

If I am understanding your question right, maybe look at the relationship between the normal force that defines the force with which tangential acceleration will be imparted to rotational kinetic energy. As the angle steepens won't the force normal to the incline lessen and hence its ability to rotationally accelerate the objects will diminish at the same time as the force parallel to the plane increases, accelerating the object faster than the surface can spin the objects to keep up?

In the extreme case of 90° it will skip rather dramatically one would think.

 

[thomate1]

Hi there,

It seems like you have a very interesting problem to solve! In order to solve this problem, we need to consider the forces acting on both the cylinder and the ball.

In situation a), where there is no slip, the only force acting on the objects is gravity. This means that the acceleration of both objects down the incline will be the same, regardless of their shape or mass. Therefore, the ratio of their times will simply be the ratio of their distances traveled.

In situation b), where there is slip, we need to consider the additional force of friction acting on the objects. This force will depend on the angle of inclination, as well as the mass and shape of the objects. Therefore, the acceleration of the objects will not be the same and the ratio of their times will also depend on the angle of inclination.

To solve this problem, you will need to use the equations of motion and consider the forces acting on the objects in both situations. You will also need to use the given friction factor and inertial moment of the objects. I suggest breaking the problem down into smaller parts and solving each part individually, then putting them together to find the overall solution.

I hope this helps and good luck with your problem!