A small remote-controlled car with mass 1.60 kg moves at a consta...

Question

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) (image)

Accepted Answer

Welcome back everybody. We are told that we have a ferris wheel and we have a person who is sitting in a cart at the bottom of the ferris wheel, why the ferris wheel is moving. And we're told a couple of things, we're told that the mass of the person is 70 kg. Were told that the radius of the ferris wheel is 40 m and we are told that the tangential speed is six m per second and we are asked to find what the normal force is exerted on the passenger, by the seat at the bottom. The normal force is going to be acting upwards on the passenger. Right? So we are looking for this F. N. Right here, but what is F. N. Well, fn is just going to be equal to the summation of the forces acting in the vertical direction on the passenger. But what are those forces? Well, we are going to have the force due to gravity and this is just equal to mass times the acceleration due to gravity. But since we are dealing with centripetal motion, we're also going to have this force acting inward of the cart pushing on the person. And this is going to be equal to mass times our velocity squared over the radius of our ferris wheel. Now our force due to gravity is going to be negative since it's in the negative Y direction. But if we sum up these two values, we will get the force that we are looking for. So our normal force that we are looking for is mv squared over r minus MG And we have all these values. So let's just go ahead and plug them in. So we have that the normal force that we're looking for is equal to a mass of 70 times are tangential speed square All over our radius of 40 The mass times the acceleration due to gravity. Which when you plug all of this into your calculator, you get 749 Newtons. Giving us our final answer of E. Thank you guys so much for watching. Hope this video helped. We will see you all in the next one.

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