Solving Wedge-like Problem with Physics

[EugeneZ]

Hey, guys! Not really my homework question, I am long past my days of studying physics (I stumbled upon this problem doing some engineering researches) but still i put it here cause it should be rather easy. Here is the picture I made:
http://img248.imageshack.us/img248/7700/riddlew.png

Basically, I've got a block of a known mass, I know friction factor and contacting area, thus I am able to calculate Friction force being exerted upon moving this block. Block is being moved by a cone. I need to know a formula for a Force needed to be applied to a cone to move the block. Thank you very much!

P.S. As for my own efforts of solving, it comes down to this: I realize I have to project and equate projection of cone force to friction force but here it got a bit tricky for me. I'm very rusty in mechanics and I'm not really sure if i should project forces in this system on the side of the cone or on the surface normal of the cone side.

 

[EugeneZ]

Maybe I posted in the wrong forum?

 

[EugeneZ]

C'mon guys

 

[EugeneZ]

Well, I am not going to let it go that easy.
F=Ffriction*tan(alpha) or F=friction factor*block's mass*tan(alpha). Am I correct?

P.S. Oh gosh i just realized i totally missed friction between cone and block. :( Guys, I really need your help! Thank you in advance.

 

[rwisz]

Hi there,

It's great to see that you are still interested in physics and using it in your engineering research. The problem you have presented is known as a wedge problem and it can be solved using basic principles of mechanics and friction.

First, let's define some variables to make the problem easier to understand. Let the mass of the block be m, the angle of the cone be θ, the coefficient of friction between the block and the surface be μ, and the force applied to the cone be F.

To solve this problem, we need to consider the forces acting on the block. There are two main forces at play here: the normal force (N) and the friction force (Ff). The normal force is perpendicular to the surface and is equal to the weight of the block (N = mg). The friction force is parallel to the surface and its magnitude is given by Ff = μN.

Now, let's consider the forces acting on the cone. The only force acting on the cone is the force applied (F). This force can be resolved into two components: one perpendicular to the surface (Fcosθ) and one parallel to the surface (Fsinθ).

To move the block, the force applied to the cone (F) must be greater than or equal to the friction force acting on the block (F ≥ Ff). This means that Fcosθ ≥ μmg.

Therefore, the minimum force needed to move the block is given by F = μmg/cosθ.

I hope this helps you solve the problem. Good luck with your research!