My trip through Physics: Will I survive?!?!? - The "Sphere of Fear" through Physics

Essentially, when examining the “Sphere of Death,” one can ask the basic question: “Why does the rider and motorcycle combination stay in the air and not fall down when riding in all of the crazy circles: vertical, horizontal, and everything in between?” Well, this can easily be answered through some knowledge of physics concerning the field of dynamics, and more specifically, circular motion.

The FBD would look something like this:

In this case, the net force (centripetal force Fc that is keeping the rider and the motorcycle in the circle) acting on the rider and motorcycle happens to be just the normal force Fn. So why doesn’t the rider slip down the wall? To answer that question, let’s look at what is going on.

As the rider builds up speed in the circle, he eventually gains enough speed where he can ride horizontally. But how would you show this?

The equation Fc = (m*v^2)/r , where m is the mass, v is the velocity, and r is the radius, shows that as the rider’s velocity increases (the mass and radius are constant for this rider), so does the centripetal force/normal force (Fc or Fn) that is keeping him/her in the circle. Next, the equation Ff = μ"mu"*Fn shows that as Fn increases, so does the friction that is countering the rider’s weight. When the rider reaches a certain speed, the force of friction pushing up on him (opposing the desired motion of the rider/motorcycle downward due to Fg) equals the rider and motorcycle’s weight, and he/she does not slip down the wall of the sphere. As the rider goes faster, Fn is large enough to make more static friction than is needed. Therefore, the static friction still cancels out the weight and the rider survives.

Ff = "mu"*Fn

Fc = (m*v^2)/r

The motion of the rider in the vertical circle is a little more interesting (and complicated)! Same as in the horizontal loop, the forces that are acting on the motorcycle/rider combo are Fn, Ffs, and Fg. For the vertical circle, the centripetal force Fc that is keeping the cycle in the circle is the vector sum of the three forces (Fn, Ffs, and Fg) that are acting on the motorcycle/rider. So as we asked when we looked at the horizontal loop, “Why doesn’t the rider and motorcycle fall when they are going upside down?” Whether or not the rider and motorcycle fall depends upon how fast they are going.

If the cycle is going too slow:

As can be shown with the same equation that was used during the horizontal explanation (Fc = (m*v^2)/r), if the speed is slower, the centripetal force reduces too. With this reduction, the weight Fg ends up changing Fc enough to bring the rider and motorcycle out of the desired circle. The new Fc pulls the motorcycle into a smaller arc, causing it to fall.

If the speed is perfect:

If the speed of the cycle is perfect, then at the top of the circle, the weight of the cycle/rider is equal to the centripetal force that is keeping the cycle in the circle. This speed is known as the critical speed, the speed that is needed to keep an object from falling. Hypothetically, the sphere wouldn’t even need to be there at the very top to keep the motorcycle in the circle (besides providing a means to maintain the constant speed). However, driving with this perfect speed is very risky because if he/she travels just a tinny bit slower, he/she will fall.

If the speed is too fast:

If the speed of the cycle is too fast, then Fc is greater than before. Thus, the weight alone cannot equal the new Fc to keep the cycle in the arc. Thus, there must be another force that can be added to the weight to achieve the correct Fc. The sides of the metal cage make up the difference by providing a normal force for the motorcycle to press against. Thus, the combination of the weight, Ffs, and Fn combine to make the centripetal force. The only consideration when going faster than needed (even though it is safer) is that the sphere might not be physically able to apply the amount of normal force needed and might break apart. However, since the sphere is made out of steel or a metal rather than paper, this would usually not happen.

With the knowledge of the possibility of vertical loops and horizontal loops, it is logical that a rider should also be able to perform any loop that is a combination of the two. Now that you are a master with “The Sphere of Death,” next time you go to Six Flags, a circus or a stunt show and see this act, you can say, “Oh…That is easy. I understand that.” But don’t underestimate the hazard: 1 small sphere + 5 people + 5 motorcycles + nowhere to go = danger! Even with knowledge of physics, it takes over three moths of practice to perform the vertical loops in relative safety. Performing these intricate, intersecting loops comes down to precise timing and a lot of practice.

The "Sphere of Death" from a physical mind!

For your own enjoyment, here is one more little quirk about the motion in the vertical circle:

As can be seen from the FBDs at right, when the rider is at the top of the circle, Fc = Fn + Fg and when the rider is at the bottom of the circle, Fc = Fn – Fg. Therefore, the normal force at the top is generally less than the normal force at the bottom.

Note: This Diagram is not an FBD. Fc is not a force separate from the weight, but the net force that is acting on the cycle to keep it in the circle. The creator of this diagram is merely showing how only the weight is affecting the motorcycle and thus the weight is Fc.

Now, let’s look at what happens when the rider is performing a vertical circle:

First, let’s examine the horizontal loop:

In this example, the motion would be just like if you were swinging a pale of water around your head or a rock before you were about to throw it. The three forces that are acting on the rider/motorcycle combo are Fn (the normal force applied by the sphere), Fg (the weight of the rider and motorcycle pulling it downward due to the mass of the Earth), and Ffs (the force of static friction pushing against the desired motion of the tires due to their physical contact with the sphere).

In this case, the motion is similar to riding in a loop on a rollercoaster or when swinging one’s arms to throw a softball.

This Diagram shows how the normal force and the weight (Fg) add up to create a net centripetal force (Fc) pointing downwards.

Ff

Fn

.

a

This diagram shows how the weight would change the net force (Fnet or Fc) on the bike and thus pull it off of the course that it would take if the net force (Fnet or Fc) was as shown.

Fg

So what would happen if the rider went to slow?

Fn would not be large enough to create enough Ffs to overcome the weight of the rider and motorcycle. The motorcycle and rider would slip down the side of the sphere and crash at the bottom.

Yikes!

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This work by Christopher Ponners is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA.