The only difference really is that this is a downward curved path where the center of this circular curve is under the slide instead of over it. (Again, the gray C-shape represents the rider’s path down the slide and the circular trajectory of his body, and the dot is the center of the circle.) This means that centripetal acceleration is also going down and towards the center of the circle .
Since the acceleration changes direction, the normal force must be (N). fewer as the radial component of the gravitational force pulling the person down towards the earth. What happens when the normal force decreases?
Remember that in order to get a rider to move in a circular path, there must be a net force pointing towards the center of the circle, which for a downward-curved chute is downward. Because the frictional force is always tangent to the slideway, this net radial force, which we call the centripetal force, is composed of the normal force (pushing away) and a component of the gravitational force (pulling toward the center).
If the driver’s speed is slow enough, you don’t need a very large centripetal force to make him move in circles. The gravitational force component alone might be enough to make this happen. The normal force from the slide might just be a small value pushing away.
If the rider’s speed gets too high, the force of gravity alone isn’t enough to create circular motion. For this you need the normal force Also drag to the center of the circle. But slides don’t do that: they just push away. This means that the sliding human would not actually be moving in a circle, but in a parabolic trajectory as they left the surface of the slide and become airborne – at least for a short time before falling back down the slide. That’s what happened to the slide riders from Detroit.
Let’s model the motion of a person on a downward-curving slide. I’ll start with a rider at the top of a corner. You can see that at some point the person flies off the track and becomes a free-falling projectile:
The speed of the person at the beginning of their journey is important. If a person starts the down turn with high enough speed, they will go off the track – but the exact value of the speed that will cause the person to go off the track depends on the starting and ending angles of the skid turn.
If you want to keep your riders on the slide, you need to increase the coefficient of friction between them and the slide. In the end, the Michigan Department of Natural Resources, which operates Belle Isle Park, posted a Facebook video explaining the updates they made: “We scrubbed the surface and started putting a little water on the slide between rides to spray to make it easier to control the speed,” they wrote. They also ask drivers to lean forward – which a park worker demonstrates in the video.
Why water? Water is actually a bit sticky, so adding a little bit of it could increase friction due to its cohesive nature. (Of course, adding enough to create a full-fledged waterslide could reduce friction and make the rider go even faster — but that would take a while a lot of more water.)
Leaning forward could help ensure each rider’s weight is on the cloth bag at their legs. The sacks are made of burlap, which is scratchy and creates friction – and since all riders are required to wear these sacks, this makes for a more uniform, familiar surface than the clothing the riders happen to be wearing. If you ask them to lean forward, make sure the burlap is in contact with the slide and not the material that makes up the person’s shirt—which would happen if they leaned backward.
If park operators wanted to get even more creative, another option would be to have riders slide while carrying something other than those canvas bags – maybe something with some rubber to increase the frictional interaction. It is also possible that painting increases the coefficient of friction.