The Physics of a Motorcycle Ride in a Sphere

[midnightassassinx]

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?

 

[Sirus]

As always, begin with a free-body diagram. Show us what you have done, please.

 

[wais]

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