How Can I Calculate the Speed at Which a Motorcycle Falls Off the Wall of Death?

[jwhitley]

Motorcycle Wall of Death

Some pointers would be greatly appreciated please.

A motorcycle is slowing down, but maintaining its height on a 'wall of death' (a vertical cylinder where the motorcycle 'drives' around the inner circumference as a stunt).

A spectator takes timings in milliseconds as the motorcycle passes a set point. Armed with only these timings, the wall dimensions and the time at which the motorcycle dropped, how might I determine the actual speed at which the motorcycle finally falls off the wall, and the position around the wall relative to the timing point (or total distance covered since anyone of the timings) when this happens.

I'm not sure that the basic equations of constant acceleration will work out here as I assume friction will be a factor which decreases as the cycle speed decreases. It's been 20 years since I sat in a maths / physics lesson and any help would make me look like the intelligent father I often pretend to be!

Thanks to all.

 

[Doc Al]

I'm not sure that the basic equations of constant acceleration will work out here as I assume friction will be a factor which decreases as the cycle speed decreases.

Start by identifying the forces that act on the motorcycle. (There are three forces.)

Apply Newton's 2nd law to both the vertical and horizontal directions. In the horizontal direction, the acceleration is given by the usual centripetal acceleration formula. In the vertical direction, there is equilibrium.

 

[jwhitley]

Start by identifying the forces that act on the motorcycle. (There are three forces.)
Apply Newton's 2nd law to both the vertical and horizontal directions. In the horizontal direction, the acceleration is given by the usual centripetal acceleration formula. In the vertical direction, there is equilibrium.

Thanks for the pointers. So, I'm thinking the forces acting on the motorcycle are:

1.) Gravity (but I don't know the mass of the motorcycle)
2.) The centripetal force from the wall acting towards the centre (again, I don't know the mass) - a portion of which (but I'm not sure what portion) is counteracting gravity and keeping the height constant.
3.) Friction of the tyres against the wall, the wheels bearings and the motion through air.

I was kind of hoping that it would be possible to calculate the overall friction coefficient from the timings I would have (as these are at a set distance which is the circumference of the wall, which I also have), and this would allow me to extrapolate the deceleration. As I know the time that the cycle falls I would then be able to work out the speed, and with some other magic formula, which I also don't posses, work out the area under the 'velocity - time' line and calculate distance travelled.

Sorry that I've not yet seen the light, but any chance of another pointer or two.

Thanks again.

 

[Doc Al]

So, I'm thinking the forces acting on the motorcycle are:
1.) Gravity (but I don't know the mass of the motorcycle)
2.) The centripetal force from the wall acting towards the centre (again, I don't know the mass) - a portion of which (but I'm not sure what portion) is counteracting gravity and keeping the height constant.
3.) Friction of the tyres against the wall, the wheels bearings and the motion through air.

When the motorcycle is circling at a constant speed, the forces on it are:

(1) Gravity (equals mg), acting down.
(2) The normal force, N, that the wall exerts on the cycle, acting towards the center.
(3) Static friction, f, which has a maximum value of $\mu N$, acting up.​

As long as the motorcyle is not slipping down the wall, then we know that vertical forces must be in equilibrium. Thus: f = mg.

We also know that the normal force must produce the centripetal acceleration. Thus: $N = m v^2/r$. If the speed is too low, the normal force will not be able to provide enough friction to support the weight of the motorcycle.

I hope this helps a bit. I'm not exactly sure what problem you are solving, and what data you have. Is the motorcyle speed decreasing at a constant rate? If you know the speed at which it begins to slip, then you can use that to find the coefficient of friction.