Magnetic force to hold machine and required Torque to drive

[Chilu1234]

Homework Statement

The robot crawler has a magnet attached to it. The idea is to get the crawler up the wall.

What is the magnetic force required to hold a object (in this case) a robot crawler with an attached Magnet?
Is more magnetic force required to hold the crawler while it goes up the wall?

What is the Torque required to drive the robot crawler up the vertical steel wall while overcoming gravity and magnetic force.

Homework Equations

Sum of forces with x and y-axis is 0
and Torque based on Radius of wheel and friction force

3. The Attempt at a Solution
I have made a PDF file of the problem setup and variables and my solution.All formula I used is also there. I hope someone take a look at it and tell me if OK

 

[mfb]

If friction and gravity both act downwards, how can the robot stay in place or even accelerate upwards as those are the only external forces?
The robot is not sliding, you have static friction.

 

[Chilu1234]

@mfb .

Are you saying the friction acts in the same direction of wheel motion? I did not fully understand your comment. Please clarify. sorry for the trouble.
I am 100% that gravity acts downwards. But don't understand friction direction?
Also, there is a magnet attached to the robot that is suppose to pull the machine to the vertical steel wall.

 

[mfb]

There are two vertical forces acting on the robot: gravity and friction. If the robot is not accelerating, their sum has to be zero. Gravity is pointing downwards, so friction has to point upwards.
If the robot is accelerating upwards, the net force has to point upwards, so you need even more friction pointing upwards.

Also, there is a magnet attached to the robot that is suppose to pull the machine to the vertical steel wall.

That is a horizontal force only. It is necessary to get friction, of course.