Really, the only difference is that this is a downward curve path, with the center of this circular curve below the slide and not above. (Again, the gray C-shape represents the rider’s path down the slide and the circular trajectory of their body, and the point is the center of the circle.) This means that the centripetal acceleration is also downward and toward the center of the circle.
Since the acceleration has changed directions, the normal force (N) must be Less than the radial component of the gravitational force, which pulls the person down towards the Earth. What happens when the normal force becomes smaller?
Remember that to make a rider move in a circular path, there must be a net force directed towards the center of the circle, which is downward for a downward curved slide. Since the friction force is always tangent to the sliding path, this net radial force, which we call the centripetal force, is composed of the normal force (the push) and a component of the gravitational force (the pull toward the center).
If the speed of the rider is low enough, you don’t need a very large centripetal force to move it in a circle. Only the gravitational force component could be enough to reach it. The normal force from sliding might just be a small amount that goes away.
If the speed of the rider becomes too high, then the force of gravity alone would not be sufficient to produce circular motion. You need normal strength to also drag to the center of the circle. But slides don’t do that: they just push. This means that the man sliding would not actually be moving in a circle, but instead along a parabolic path as they leave the surface of the slide and become airborne – at least for a short time, until when they crash back into the chute. That’s what happened to the slides in Detroit.
Let’s model the motion of a person on a downward curved slide. I’ll start with a rider at the top of a curve. You can see that at some point the person flies off the track and becomes a free-falling projectile:
The speed of the person when they start their journey is important. If a person starts the downslope at a high enough speed, then they will fly off the runway, but the exact amount of speed that will cause the person to go off the runway depends on the start and end angle of the glide curve.
If you want to keep your riders on the slide, you need to increase the coefficient of friction between them and the slide. Finally, the Michigan Department of Natural Resources, which runs Belle Isle Park, posted a video on Facebook explaining the updates they made: “We cleaned up the surface and started spraying some water on the slide between rides to help control. speed,” they wrote. They also urge riders to lean forward, which a park employee demonstrates in the video.
Why water? Water is actually kind of sticky, so just adding a bit of it could increase friction due to its cohesive nature. (Of course, adding enough to create a full water slide could reduce friction and make the rider even faster, but that would require a lot more water.)
Leaning forward could help ensure that each rider’s weight is on the duffel bag on their feet. The bags are made of canvas, which scratches and provides some friction – and because all riders have to wear these bags, it makes for a more consistent and recognizable surface than any clothing they happen to be wearing. Asking them to lean forward ensures that the burlap is in contact with the chute, not the material that makes up the person’s shirt – which would happen if they were to bend over backwards.
If park operators want to get even more creative, another option would be to have the riders slide while wearing something other than those canvas bags – maybe something with a bit of rubber to increase frictional interaction. It is also possible that a coat of paint will increase the coefficient of friction.