How Fast Must a Car Drive to Avoid Slipping on the Wall of Death?

[ehabmozart]

Homework Statement

I guess wall of death mechanic is not easy. Moving to the question. We have a mass of 1000 kg driving on the wall of death with radius 20 m. TO avoid slipping down the wall, the friction between the tyres.. Asuming that the mass is something like a car for example. Anyway, the friction between the tyres and the wall must exceed the weight. The centrepital force provided by the wall pushing against the tyres will affect the friction according to the equation. F(friction) = 0.6 F(Centripetal) ... Work put how fast he must drive in order to avoid slipping down the wall!? My attempt was weak cs i really have no idea how to calculate the friction. Infact, the full process is confusing so anyone who could thankfully dominate a free body diagram of wall of death and attempt this question. It's urgent. I really need ur help folks.. Thanks in advance :)

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

hi ehabmozart!

there are three forces on the car, the normal force (which is horizontal), and the friction and gravitational forces (which are vertical)

the vertical acceleration of the car is zero, and the horizontal acceleration is the centripetal acceleration, which you can find from the speed

so find how much the friction force must be to balance the gravitational force,

from that find what the normal force must be,

from that find what the speed must be …​

what do you get?

 

[ehabmozart]

Hi.. Thanks for dominating... I understand that there are 3 forces.. That's good. Normal force is horizontal.. I get it 100%... G.F is vertically downwards.. yes? isn't it?? .. My doubt is how does the friction force act upwards... I mean how is it vertical.. I should be opposing the motion which is eventually horizontal... I need more clarification... Where exactly does the G.F and Friction forces act?... Thanks!

 

[tiny-tim]

hi ehabmozart!

Hi.. Thanks for dominating...

"dominate" means command, control, rule …

i think you mean "replying" or "helping" or "explaining"! ​

G.F is vertically downwards.. yes? isn't it??

yes, gravity is always downwards, even if the body is moving

My doubt is how does the friction force act upwards... I mean how is it vertical.. I should be opposing the motion which is eventually horizontal... I need more clarification... Where exactly does the G.F and Friction forces act?... Thanks!

there's no forward-or-backward acceleration (if the speed is constant), so there's no forward-or-backward friction

so the direction of friction must be up or down the wall!

the gravitational force (the weight) acts through the centre of mass

the friction acts through the wheels

the normal force also acts through the wheels, though it will mostly act through the lower wheels, to counteract the torque (if this was a bike, the bike would need to be at an angle)

(if you're still worried about the direction of friction, then say that there are only two forces, the gravitational force and the reaction force … use a vector triangle to find the direction of the reaction force, then the upward component of that will be the friction )