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 (b) point B (top of the track)? (image)

Accepted Answer

Welcome back everybody. We are given a ferris wheel and we are told that a kid is in the ferris wheel and then he is in the top cart while the ferris wheel is in motion. And we are told a couple of things here, we're told the mass of the child Is kg. Were told that the radius of the ferris wheel is m that it is rotating with a period of seconds. And we are tasked with finding what the normal force is of the ferris wheel seat acting on the child. Well, our normal force here is going to be equal to the summation of forces that are acting on the child here. Now, here's the thing. Just for for convention sake, I'm actually going to have the downward direction. The the positive Y direction makes working with our numbers a little bit easier. So what are our forces acting on the child? Well, we have the force due to gravity which is just mass times our gravitational acceleration. And then since the Earth wheel is spinning there's going to be a so called centripetal force. And the formula for this is going to be mass times the velocity squared over R. But it is going to be negative since it is going against our positive Y direction, this is equal to M G minus M V squared over R. Now we have our mass. We know what are gravitational acceleration is and we know what the radius, but what is our V. Here? Well, since we are dealing with centripetal motion, our V. At that point is just simply going to be equal to two times I times the radius of our ferris wheel all over the period. So let's go ahead and plug in those values. We have to high times 15/20 seconds, which when you plug into your calculator gives us a speed of 4.7 m per second. Now we have all of our variables for this equation. So let's go ahead and plug our values in here. We have that the normal force of the ferris wheel acting on the child is going to be his mass times the acceleration due to gravity minus his mass times our speed that we just found Squared all over the radius of 15. When you plug this into your calculator, you get that the normal force has a magnitude of newtons corresponding to answer choice b. Thank you guys so much for watching. Hope this video helped. We will see you all in the next one.

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