Kinematics - Statics - Free Body Diagram

[nahanksh]

Homework Statement

https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/spring09/homework/11/two-beams/fig3a.gif
Two identical uniform beams, each of mass "M" and length "L", are symmetrically set up against each other on a floor with which they have a coefficient of static friction "u". The acceleration due to gravity is "g".

Find the minimum angle θmin that the beams can make with the floor without falling.

Homework Equations

The Attempt at a Solution

When drawing a Free Body Diagram, i figured out at the center of mass in each rod and the surface between rod and the ground..

But i am confused with the surface between rods.

Is there going to be only horizontal force(pushing each other) or since they are inclined, there should be both horizontal and vertical forces?

Really confusing...

Could someone help me out here?

 

[tiny-tim]

Hi nahanksh!

From symmetry, the vertical components of force between the beams must be equal.

But good ol' Newton's third law says that the forces of each beam on the other must be equal and opposite.

So the vertical components must be zero.

 

[nahanksh]

Thanks for your reply.

Then there is no horizontal forces between the beams ?

 

[tiny-tim]

From symmetry, the horizontal components of force between the beams must be equal and opposite.

Newton's third law agrees … the forces of each beam on the other must be equal and opposite.

So the horizontal components don't have to be zero!