The Physics of a Motorcycle Ride in a Sphere

In summary, a physics major is performing in a traveling carnival to pay for college tuition. He rides a motorcycle inside a transparent plastic sphere with a radius of 13.0 m. To prevent the tires from losing contact with the sphere, he must have a minimum speed at the top of the circle. At the bottom of the circle, his speed is twice the value calculated at the top. A free-body diagram is needed to determine the magnitude of the normal force exerted on the motorcycle by the sphere at this point.
  • #1
midnightassassinx
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1) A physics major is working to pay his college tuition by performing in a traveling carnival. He rides a motorcycle inside a hollow transparent plastic sphere. After gaining sufficient speed, he travels in a vertical circle with a radius of 13.0 m. The physics major has a mass of 70.0 kg and the motorcycle has a mass of 40.0 kg. What minimum speed must he have at the top of the circle if the tires of the motorcycle are not to lose contact with the sphere? At the bottom of the circle, his speed is twice the alue calculated at the top. What is the magnitude of the normal force exerted on the motercycle by the sphere at this point?
 
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  • #2
As always, begin with a free-body diagram. Show us what you have done, please.
 
  • #3


The physics of a motorcycle ride in a sphere is a fascinating topic that involves several principles of physics. In this scenario, the physics major is performing a stunt where he is riding a motorcycle inside a hollow transparent plastic sphere. To ensure a safe and successful ride, the physics major needs to understand the forces acting on the motorcycle and himself.

Firstly, we need to consider the centripetal force that is keeping the motorcycle in a circular motion. This force is provided by the normal force exerted by the sphere on the motorcycle. At the top of the circle, the normal force must be equal to the weight of the motorcycle and the rider, which is given by the formula Fc = mv^2/r, where m is the combined mass of the motorcycle and the rider, v is the minimum speed required, and r is the radius of the circle. Substituting the given values, we get Fc = (70.0 kg + 40.0 kg)(v^2)/(13.0 m) = 110.0 kg(v^2)/(13.0 m).

To ensure that the tires of the motorcycle do not lose contact with the sphere, the normal force must be equal to or greater than the weight. This means that the minimum speed required at the top of the circle is given by v = √(g*r), where g is the acceleration due to gravity (9.8 m/s^2) and r is the radius of the circle (13.0 m). Substituting the values, we get v = √(9.8 m/s^2 * 13.0 m) = 11.4 m/s.

At the bottom of the circle, the speed of the motorcycle is twice the value calculated at the top, which means that the normal force must also be twice the value. Therefore, the magnitude of the normal force at the bottom of the circle is given by Fc = 2*110.0 kg(v^2)/(13.0 m) = 220.0 kg(v^2)/(13.0 m).

In conclusion, to ensure a safe and successful motorcycle ride inside a sphere, the physics major must have a minimum speed of 11.4 m/s at the top of the circle and the magnitude of the normal force at the bottom of the circle must be 220.0 kg(v^2)/(13.0 m). This demonstrates the application of centripetal force and
 

What is the physics behind riding a motorcycle in a sphere?

The physics behind riding a motorcycle in a sphere is mainly based on the principles of circular motion and centripetal force. As the motorcycle and rider move along the curved surface of the sphere, the centripetal force acts towards the center of the circle, keeping the motorcycle in motion and preventing it from flying off the sphere. The speed and angle of the motorcycle also play a crucial role in maintaining balance and stability.

How does the shape and size of the sphere affect the ride?

The shape and size of the sphere can greatly affect the ride on a motorcycle. A larger sphere will require the rider to travel at a higher speed in order to maintain balance, while a smaller sphere will have a tighter curve and require slower speeds. The shape of the sphere can also impact the turning radius and stability of the ride.

What role does gravity play in riding a motorcycle in a sphere?

Gravity plays a significant role in riding a motorcycle in a sphere. The gravitational force acts downwards towards the center of the sphere, providing the necessary centripetal force to keep the motorcycle and rider in motion. Without gravity, the motorcycle would not be able to maintain its circular motion and would fly off the surface of the sphere.

How do forces such as friction and air resistance affect the ride?

Forces such as friction and air resistance can greatly impact the ride on a motorcycle in a sphere. Friction between the tires and the surface of the sphere can slow down the motorcycle and make it more difficult to maintain balance. Air resistance can also affect the speed and stability of the ride, especially at higher speeds.

What are some safety precautions for riding a motorcycle in a sphere?

Riding a motorcycle in a sphere can be a risky activity, so it is important to take certain safety precautions. These include wearing proper safety gear, such as a helmet and protective clothing, and making sure the sphere is properly inflated and free from any sharp objects. It is also important to maintain a safe and consistent speed, and to be aware of any potential hazards on the surface of the sphere.

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