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 )

 

[asteriatic]

I would approach this problem by first understanding the mechanics of the wall of death. The wall of death is a circular structure where a vehicle, such as a car, drives on the vertical wall at a high speed without falling off. This is possible due to the centripetal force provided by the wall pushing against the tires of the vehicle.

To calculate the speed at which the vehicle must travel to avoid slipping down the wall, we need to consider the forces acting on the vehicle. These forces include the weight of the vehicle, the friction between the tires and the wall, and the centripetal force provided by the wall.

The friction between the tires and the wall must exceed the weight of the vehicle in order to prevent it from slipping down the wall. This can be calculated using the equation F(friction) = μN, where μ is the coefficient of friction and N is the normal force, which is equal to the weight of the vehicle in this case.

The centripetal force provided by the wall can be calculated using the equation F(centripetal) = mv^2/r, where m is the mass of the vehicle, v is the velocity and r is the radius of the wall.

In order to avoid slipping down the wall, the friction force must be greater than the centripetal force. Therefore, we can set the two equations equal to each other and solve for the velocity, as follows:

μN = mv^2/r

v = √(μgr)

Where g is the gravitational acceleration, which is approximately 9.8 m/s^2.

Therefore, the velocity at which the vehicle must travel to avoid slipping down the wall can be calculated using the above equation. However, it is important to note that this equation assumes ideal conditions and does not take into account any external factors such as wind or imperfections in the surface of the wall.

In order to accurately calculate the velocity, a free body diagram of the wall of death would be helpful. This diagram would show all the forces acting on the vehicle and their directions, allowing for a more precise calculation of the required velocity.

In conclusion, the mechanics of the wall of death involve balancing the forces acting on the vehicle to prevent it from slipping down the wall. To calculate the required velocity, we need to consider the friction between the tires and the wall, the centripetal force provided by the wall, and the weight of the vehicle. A free body diagram would be

 

[asteriatic]

I can provide some insight into the mechanics of the wall of death. The wall of death is a motorcycle stunt where the rider performs tricks and maneuvers while riding inside a cylindrical wooden structure. In order to stay on the wall and not slip down, the friction between the tires and the wall must exceed the weight of the motorcycle and rider combined. This can be calculated using the coefficient of friction between the tires and the wall, which is typically around 0.6.

To calculate the minimum speed required to prevent slipping, we can use the centripetal force equation: F = mv^2/r, where m is the mass of the motorcycle and rider, v is the velocity, and r is the radius of the wall. The centripetal force provided by the wall pushing against the tires must be equal to or greater than the weight of the motorcycle and rider in order to prevent slipping.

To determine the minimum speed, we can set the friction force equal to the centripetal force and solve for v:

F(friction) = F(centripetal)
0.6F(centripetal) = mg
0.6mv^2/r = mg
v^2 = gr/0.6

Therefore, the minimum speed required to prevent slipping is v = √(gr/0.6).

In order to create a free body diagram for this scenario, we can consider the forces acting on the motorcycle and rider as they ride on the wall. These forces include the weight of the motorcycle and rider (mg), the normal force from the wall (N), and the friction force between the tires and the wall (F). The centripetal force (F(centripetal)) is also acting on the motorcycle and rider, but it is not a separate force as it is a result of the normal force and friction force working together.

In conclusion, the wall of death requires a careful balance of forces to prevent slipping and maintain the rider's safety. By understanding the mechanics involved, we can calculate the minimum speed required and create a free body diagram to visualize the forces at play.