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A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to twice her weight as she goes through the dip. If r 20.0 m, how fast is the roller coaster traveling at the bottom of the dip?

14.0 $\mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

University of Michigan - Ann Arbor

University of Washington

Hope College

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

01:42

A roller coaster at an amu…

01:59

A roller coaster car is go…

02:00

Roller coaster ride A roll…

02:23

10:34

A roller coaster is design…

02:25

The passengers in a roller…

02:20

A roller coaster is moving…

01:44

05:04

A roller coaster has a ver…

03:39

The weight of passengers o…

03:13

A frictionless roller coa…

02:21

A roller coaster car cross…

03:37

A particular Ferris wheel …

here we have to find the velocity of a person going through a semicircle through a dip at the bottom of the water slide. Now, the first piece of information that we're given is that the normal force is equal to two mg. So if you draw free body diagram and label that I'm drawing or, um or close up here on the side, we have N g pointing downwards and a force of two mg equal to our normal floors pointing upwards. Now, in order to find the speed, we're going to have to find the centripetal force. And we can see from this report diagram that since we're a force of two, um MG, pointing inward and a force of MG pointing outward are total centripetal force is going to be two mg minus mg, which of course is just equal to M. G again. All right, so you said that that's equal toward centripetal force. So that means that this equation here has to be true. Now we can find an equation for V by simply solving, so he is going to be equal to the square root of G of gr. If you might have seen earlier when we were doing, um problems about roller coasters and loop de loops. It comes up a lot, all right. So now, since we nog and were given are always able to do is plug in, that turns out to be 9.8 meters per second times our radius, which we were told earlier to be 20 meters. And when we plug that into our calculator, we're going to get that V is equal to the square root of 196 meters per second. I mean, it was squared second, and that is going to be equal to 14 meters per second, and that's gonna be our final answer.

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