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). (b) A passenger weighs 882 N at the weight-guessing booth on the ground. What is his apparent weight at the highest and at the lowest point on the Ferris wheel?

Video transcript

Welcome back everybody. We are riding a roller coaster and this roller coaster has this loop de loop right here and we are told a couple different things about this loop. We are told that the diameter is 16 years. We are told that our track or ride vehicle that we are riding in as a mass of 50 mg and a top speed of 20 five years second. And we are asked to find what the weight of our cart is at the bottom of the loop de loop and what the weight of our cart is at the top. So let's go ahead and start with the weight at the bottom here. So our cart is going to be right here on the now, before we get started, I do want to clarify one thing just to make it easier since we're dealing with weight, I'm actually gonna say that the downwards, why direction is going to be our positive y direction. That just makes the numbers a little bit more work in just a second. So our cart is at the bottom here. So there are a couple of different forces acting on at first and foremost. We are always going to have uh the force due to gravity which doing mass times the acceleration due to gravity. We are also going to have the cart pushing back on the loop de at this point. Formula for that is going to be m times its velocity squared over the radius of the looping loop. Now, this v right here is going to be our top speed here at the bottom of the loop. So let's go ahead and uh plug in some values to here. And then we can actually just some these values together to get our total weight At the bottom of the loop. So this is going to be our mass times gravity. So 50 times our acceleration due to gravity of 9. plus a mass of 50 times our top speed five squared all over the radius, which is just one half of our diameter. So 30. And when you plug this into the calculator that this is 1532. Great. So now let's go ahead and find the weight of our cart at the top here. Now, just a quick note, we are told that the velocity at the top is then decreased to 20 m per second. So this is the velocity we're gonna have to use. But let's go ahead and draw out all the forces acting on here, just like before we have our force due to gravity. So that gravity and the cart is still pushing on the loop de loop, but this time it's at the top. So it's pushing on the loop in the negative y direction. Because you remember we said that downward was the positive Y direction. Still going to have the same formula though. So let's go ahead and plug in some values and then we will sum these two together to get the weight of our cart at the top. so the weight at the top is equal to while we have our mass. That age times our acceleration gravity 9.8 plus hour mass times our new speed of 20 where Over 30, which when you plug into your calculator -177. Now we have found the weight of our cart at the bottom and the weight of our cart at the top or responding to answer choice. Thank you guys so much for watching. Hope this video helped. We will see you all in the next one.