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At an amusement park there is a ride in which cylindrically shaped chambers spin around a central axis. People sit in seats facing the axis, their backs against the outer wall. At one instant the outer wall moves at a speed of 3.2 m/s, and an 83-kg person feels a 560-N force pressing against his back. What is the radius of the chamber?

1.5$m$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

Rutgers, The State University of New Jersey

University of Washington

University of Sheffield

Lectures

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and this problem, we're given the velocity, the mess and some force pushing up against a person on a river ride. And we have defined the radius of that ride. So fearing out what this force that were given a 560 Newtons actually is becomes easier when we draw free body diagram like I've done on the left here. So because of the force, if the red dot is the person, then we know that the force of gravity is always pointing down right. But the normal force in this crazy opposing the force of gravity, right? Because normal forest always points for particular to whatever surface something is resting on, so it's pointing towards the center of the circle. As you can see here, I was also a frictional force, which is counteracting gravity and that is caused by whatever surface we're on. But that's actually not important to this problem. So the force that is described to us and the problem is pushing up against the person's back. So, considering the way that the rebel forces pointing that must be our 560 Newtons and so that force hope wrong, him must also be equal to centripetal force since that is, the force is always pointing towards the in the center of shirt promotion. And we know the equation for the centripetal force is and B squared overnight. Now if we want to help me, remember too right that it's five minutes to see mutinies. Now, if you want a sulfur, are all we have to do is rearrange. We get our because then we squared over 160 n Now when we played that are quantities for every earlier or n is equal any three kilograms and RV is 3.2 meters per second and that's over 500 and 60 n. Now we're gonna find that are equal to 1.518 And when we check out our units, we remember that a newton is equal to kilograms times meters per seconds squared shrill Is that up here? I forgot to square my velocity right here to forget to do that but we just wear it. The 1.5 is a result. But that squared is also important for units because remember, a newton is equal to telegrams times meters per second squared. So our units cancel out to give us a result just meters, which of course makes sense for calculating or radius, and that is going to be our final answer.

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