# Approach to solve a frictional problem?

I am having a bar and surface (made of aluminum). I need to attach some material to the end of the bar so that, if I apply any force (25 N-sideways) to bar it has to stick with the surface.

Force is applied normally to the flatter surface of the bar. I need to select a material at the end of bar so that the force applied on the bar is minimal.

What methodology should I choose to find an answer?

Aim is lowest necessary force to keep the rod intact (with a material added to rod end)

• For any answer, make the question clear : so a diagram & dimensions etc would help. – Solar Mike Oct 27 '18 at 18:40
• @SolarMike Hello i have added the image – Latheesh V M Villa Oct 27 '18 at 18:48
• @SamFarjamirad it's a robot arm...once the force is removed the the rod can move freely – Latheesh V M Villa Oct 27 '18 at 19:20
• @SamFarjamirad yeah..i aim to make it minimum and that applied force should be able to resist lateral force 25N – Latheesh V M Villa Oct 27 '18 at 19:51
• @SamFarjamirad sounds good . how lubrication can solve this problem. i feel lubrication increases the slip condition – Latheesh V M Villa Oct 27 '18 at 20:02

Here the applied forces are due to robotic arm and the weight of the rod: $$(F+mg)\mu_s=25\ [N]$$ or: $$F\mu_s=25\ [N] - mg\mu_s$$
As you can see we have an equation with two unknowns, $$F$$ the vertical force of robots arm and the material dependent parameter $$\mu_s$$.
you observe if you increase the $$\mu_s$$, the applied force will decrease, but it makes it difficult for the rod to move freely, if you increase the force the coefficient of friction will decrease but you want to keep the applied force minimum so this is not an option. So we need to define a range for the force $$F$$ to solve the problem with bounded extrema, or simply choose a heavier rod, but make sure the force $$25\ [N]$$ can pull it back.