Maximum Angle for Rod Moving Up Ramp 1

[ddowns46]

This should be a pretty simple problem I just can't remember from my college physics days how to solve this.

Basically a steel rod with a ball end is inserted into a vertical bore that is fixed. This vertical bore is rigidly mounted and moves in the positive X direction so that the ball end on the steel rod slides across the surface of a steel ramp. As it slides, it will retract the rod up into the bore in the positive Y direction. The force acting downward on the steel rod is just the force of gravity. See simple sketch here (

https://imgur.com/a/KUW2jXr).

My question is, what is the maximum ramp angle that the steel rod can travel up before the system binds instead of retracting the piston into the bore?

Any help would be greatly appreciated!

 

[handleman]

Draw an FBD of the rod.

 

[btrueblood]

You also need to know with some degree of precision the coefficient of friction of the rod in the sleeve, and the tip of the rod on the ramp.

 

[SwinnyGG]

It's not too tough, really.

You need to know coefficients of friction for both interfaces, as others have stated.

You're creating a force balance between normal contact force in the cylinder bore and the force driving the cylinder up- find the point where they are the same, and you've found the point where the rod will no longer travel vertically without help.

 

[rb1957]

and the clearance between the rod and the tube.

and the real stiffness of the tube (I know you say "rigid", but what is truly "rigid" ?).

a clue may be in looking at ball point pens (ie having a free spherical ball at the tip of the rod, instead of a fixed spherical machined end) ... they should be able to work at much higher ramp angles ?

another day in paradise, or is paradise one day closer ?

 

[hydtools]

The tangent of the ramp angle from horizontal must be equal to or less than the coefficient of friction between the ball and ramp. Or the ball end will bind not slide on the ramp.

Ted

 

[desertfox]

Hi

When the angle of the ramp creates a vertical component of force which is less than the mass of the rod then you are in trouble, add to that losses for friction on both the sliding on the ramp and in the receptacle you're in trouble, so the absolute maximum angle of slope ignoring friction is that at which the mass of the rod exceeds the vertical component force created on the ramp, like others have said do an FBD and work it out, you don't give any sizes, mass etc in the problem statement.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein