Ferris Wheel Centripetal Force: Solving a Vertical Circular Motion Problem

[gaborfk]

I have a ferris wheel problem with four parts. I have completed the first three. Acceleration, Centripetal force on top and on bottom. However, I am having a hard time to come up with a FBD for a cart which is halfway up. I got a normal force towards the top, and gravity towards the bottom. So how do they add up to be a centripetal force to the side (center of ferris wheel)?

I supposed to find the magnitude and direction of the Centripetal force.

Any suggestions or may be a website with a FBD?

Thanks in advance

 

[Doc Al]

I have a ferris wheel problem with four parts. I have completed the first three. Acceleration, Centripetal force on top and on bottom. However, I am having a hard time to come up with a FBD for a cart which is halfway up. I got a normal force towards the top, and gravity towards the bottom. So how do they add up to be a centripetal force to the side (center of ferris wheel)?

Since the cart is attached to the wheel, not just sitting on it, I would not call the force the wheel exerts on the cart a "normal" force. The free body diagram should be easy: there are just two forces on the cart (1) gravity, acting down, and (2) the force of the wheel on the cart. That last force acts at some angle, not just up or just sideways.

I supposed to find the magnitude and direction of the Centripetal force.

Do you know the mass and the acceleration? Use Newton's 2nd law.

 

[wais]

Great job on completing the first three parts of the problem! It sounds like you have a good understanding of the concepts of acceleration and centripetal force. As for the fourth part of the problem, finding the magnitude and direction of the centripetal force for a cart halfway up the ferris wheel, there are a few things you can keep in mind.

First, remember that the centripetal force is always directed towards the center of the circular motion. In this case, the center of the ferris wheel. This means that the centripetal force will be acting horizontally towards the center, not towards the top or bottom.

Next, think about the forces acting on the cart at this point. As you mentioned, there is a normal force acting towards the top and gravity acting towards the bottom. Since the cart is halfway up, these two forces are not equal in magnitude. The normal force is greater than the force of gravity, as the cart is accelerating upwards. However, the centripetal force must be equal to the net force acting on the cart in the horizontal direction. So, you can use the magnitude of the normal force and the component of gravity that is acting horizontally to find the magnitude of the centripetal force.

As for the direction, you can use the right-hand rule to determine the direction of the force. Point your fingers in the direction of the velocity of the cart, and then curl your fingers towards the center of the circular motion. Your thumb will then point in the direction of the centripetal force.

If you are still having trouble visualizing the forces and their directions, there are many websites and videos available that can provide helpful visuals and explanations. One website that may be helpful is Khan Academy, which has a section on centripetal force and circular motion. You can also try searching for videos or animations specifically related to a ferris wheel problem.

I hope this helps and good luck with the rest of your problem!