Vertical Circular Motion of a giant wheel

In summary, the conversation discusses a giant wheel with a 40-meter diameter and a cage that rotates at a specific speed. When the cage is at the top, the force exerted by a man standing on the platform is equal to his weight. Using Newton's law, it is determined that the normal force applied by the platform is equal to the weight of the man, and by summing the forces in the normal direction, the problem can be solved.
  • #1
c.melissas
5
0
1. A giant wheel, 40 meters in diameter, is fitted with a cage and platform on which a man can stand. The wheel rotates at such a speed that when the cage is at the top of the wheel, then the force exerted by the man on the platform is equal to his weight. The speed of the man is:

2. T + mg = mv^2 / r and in this specific problem, v = m.

3. T + m(9.81) = mv^2 / 40
40(T + m(9.81)) = mv^2
Square root of [ (40(T + m(9.81))) / m ]

I think I am on the right track, but I am not really sure what do from this point.
 
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  • #2
Can you draw a free body diagram?

40m is the diameter.
 
  • #3
First there is not a tension force really, it is more of a normal force since it is applied from the platform. That being said the key idea involves using Newtons law that forces are equal and opposite. If the platform feels a force of W by the man then what force is applied on the man by the platform? This is your normal force N. Then sum the forces in the normal direction to get N+W=mv^2/r. As mentioned above determine your normal force and the problem is solved.
 

Related to Vertical Circular Motion of a giant wheel

1. What is vertical circular motion?

Vertical circular motion refers to the movement of an object in a circular path that is perpendicular to the ground. In the case of a giant wheel, this means the wheel is rotating around a central axis while also moving up and down.

2. How is the motion of a giant wheel different from that of a regular wheel?

The motion of a giant wheel is different from that of a regular wheel because it involves both circular motion and vertical motion. The speed and acceleration of the giant wheel also vary as it moves around the vertical axis, creating a unique and dynamic ride experience.

3. What factors affect the vertical circular motion of a giant wheel?

The main factors that affect the vertical circular motion of a giant wheel are its radius, rotational speed, and the weight and distribution of the riders. These factors determine the amount of centrifugal force and gravitational force acting on the wheel, which in turn determine the ride experience.

4. Why does a rider feel weightless at the top of a giant wheel?

At the top of a giant wheel, the rider is experiencing a brief moment of freefall due to the balance between the downward force of gravity and the upward centrifugal force. This creates a feeling of weightlessness as the rider's body is not being pulled down by gravity.

5. How is the safety of a giant wheel ensured in terms of vertical circular motion?

The safety of a giant wheel is ensured through careful design and regular maintenance. Engineers use mathematical calculations and computer simulations to test the structural integrity and stability of the wheel. Additionally, safety features such as seat belts and restraints are in place to keep riders securely in their seats during the ride.

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