A small remote-controlled car with mass 1.60 kg moves at a constant speed of υ = 12.0 m/s in a track formed by a vertical circle inside a hollow metal cylinder that has a radius of 5.00 m (Fig. E5.45). What is the magnitude of the normal force exerted on the car by the walls of the cylinder at (a) point A (bottom of the track)

Video transcript

Welcome back everybody. We are making observations about a ferris wheel here and we have that a cart at the bottom here contains an individual. Now we are told that the mass of this individual is 70 kg. We are told that the radius of the ferris wheel is 40 m and we are told that it has a tangential speed of six m per second. Now we are tasked with finding what the normal force is of the seat exerted onto the passenger. Well in order to calculate that, let's write out a couple of other forces that are at play. Here we of course have the force due to gravity which is just equal to MG. And then always acting towards the center of rotation. We have the centripetal force which is always equal to M. V. Squared over R. Now the centripetal force in this case is going to be equal to our normal force minus our gravitational force because our gravitational forces acting in the negative direction. So if we add the force of gravity to both sides, we get that our normal force is equal to our centripetal force is Mv squared over R plus r gravitational force which is just MG. So now let's go ahead and plug in our values and find our normal force. We have that. Our normal force is equal to 70 times six squared Divided by plus 70 times 9.8. This gives us a final answer of 749 Newtons corresponding to our answer choice of the Thank you all so much for watching. Hope this video helped. We will see you all in the next one.