Force Vectors and Circular Motion

[Ronnin]

This is a case where I know the results but am fighting the math. At the top of a ferris wheel your acceleration in Y is 0. Ol' Newton says all all forces then must cancel, got that. I know my weight at this point will feel less at this point. Here is where I am troubled, vector for gravity points down so does the vector for the circle's accleration but my Normal points up and must have the same magnitude as Fg and Fc. The answer given subtracts Fc from Fg to get Fn (which feels right, but contradicts my vectors). Any conceptual help is appreciated.

 

[Chi Meson]

Your acceleration at the top of a ferris wheel is NOT zero. Assuming you are undergoing perfect circular motion, you will have a centripetal force at the top. Gravity will supply the centripetal force, but all of the weight will be too much centripetal force, so therefore the normal force will balance some of the weight.

In perfect circular motion, the only unbalancd force will be centripetal and equal (mv^2)/r . At the top of the ferris wheel the unbalanced force is equal to mg-N.

 

[kyle8921]

First of all, it is completely normal to struggle with the math behind force vectors and circular motion. These concepts can be complex and require a solid understanding of physics principles. However, with practice and a deep understanding of the underlying concepts, you will be able to confidently solve these types of problems.

Now, let's address the specific issue you are having. At the top of the ferris wheel, your acceleration in the y-direction is indeed 0. This means that the net force in the y-direction must also be 0, as stated by Newton's second law (ΣF=ma). This does not necessarily mean that all forces must cancel out, but rather that the sum of all forces in the y-direction must equal 0.

In this case, the forces acting on you are your weight (Fg), the normal force (Fn), and the centrifugal force (Fc). The normal force is the force exerted by the seat of the ferris wheel on your body, perpendicular to the surface of the seat. This force is what allows you to feel the seat supporting you and prevents you from falling out of the ride.

Now, let's consider the vectors for these forces. Fg and Fc both point downwards, while Fn points upwards. This may seem like a contradiction, but remember that vectors represent both magnitude and direction. The magnitude of Fg and Fc are equal, but their directions are opposite. The magnitude of Fn must also be equal to Fg and Fc, but its direction is opposite to both of them.

When you subtract Fc from Fg, you are essentially taking into account the opposite directions of these forces. This results in a net force of 0, as required by Newton's second law. So, while it may seem counterintuitive that the normal force is equal to the difference between Fg and Fc, it is a result of taking into account the direction of these forces.

I hope this explanation helps clarify your understanding of force vectors and circular motion. Remember to always consider the direction and magnitude of forces when solving these types of problems. With practice and a solid understanding of the underlying principles, you will be able to confidently solve any physics problem.