The Cosmo Clock 21 Ferris wheel in Yokohama, Japan, has a diameter of 100 m. Its name comes from its 60 arms, each of which can function as a second hand (so that it makes one revolution every 60.0 s). (d) What then would be the passenger's apparent weight at the lowest point?

Video transcript

Welcome back everybody. We have a stone that is being rotated in a circular fashion here, this stone right here. Now it is attached to some string and we are told a couple different things about this system. We are told that the mass of the stone is one kg and that the radius of rotation is two m. Now there are a couple different forces acting on this stone at all times. We have the tension of the, of the rope, right, which will always be acting in words. Then we always have the force due to gravity acting on the stone always acting downwards. Now we are told another bit of key information. We are told that at the top here the tension at the top is equal to zero. But how is that possible? Well, there's one more force at play here, and that is the centrifugal force. It's like the centripetal force accepted acts in the opposite direction. It always acts outward as opposed to inward. Right? So at the bottom point of the circle, both the force due to gravity and the centrifugal force will be acting in the same direction at the top here, the force due to gravity will be acting downward and the centrifugal force will be acting upward. So now we can make sense of this claim right here, if you sum up the forces in the y direction we have that our centripetal, sorry centrifugal force minus our force due to gravity is equal to zero. The rocks not going up and it's not going down. Therefore our force due to gravity is equal to our radial acceleration. Now that all this has been said, we are tasked with finding what the tension at the bottom is, knowing that the tension at the top is zero. Well let's go ahead and sum up these forces one more time. But this time we'll do it at the bottom as you'll see these are acting in the same direction here and these are opposite and equal to the tension. But if you remember, our M. G. Is equal to m Times our Centrifugal acceleration. So we really just have that. The tension at the bottom is equal to two times our mass times the acceleration due to gravity. So if we plug in some numbers here, we have two times are massive, one times the acceleration due to gravity, which is 9.8 giving us a final answer of 19. newtons corresponding to our answer choice of C. Thank you all so much for watching. Hope this video helped. We will see you all in the next one