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A special electronic sensor is embedded in the seat of a car that takes riders around a circular loop-the-loop ride at an amusement park. The sensor measures the magnitude of the normal force that the seat exerts on a rider. The loop-the-loop ride is in the vertical plane and its radius is 21 m. Sitting on the seat before the ride starts, a rider is level and stationary, and the electronic sensor reads 770 N. At the top of the loop, the rider is upside down and moving, and the sensor reads 350 N. what is the speed of the rider at the top of the loop?

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17 $\mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

Simon Fraser University

Hope College

University of Winnipeg

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.

02:07

A special electronic senso…

02:27

0:00

02:54

'44. special electron…

12:22

Riding a Loop-the-Loop. A …

01:27

Example 5.7: A roller-coa…

08:57

CP Riding a Loop-the-Loop.…

04:11

A roller coaster travels i…

07:12

05:38

A child of mass 40.0 kg …

04:20

A roller-coaster car shown…

02:41

A popular carnival ride co…

03:02

You take a homemade "…

03:41

At amusement parks, there …

and this problem. We want to find the velocity at the top of a critical loop, given that we know the normal force of the object going around the loop at two different points. So let's start out by trying to find the quantities that we aren't given. We know the radius in this problem. It's 21 meters. But in order to solve for the centripetal force later on, we will need to know the quantity. And since VI's heir unknown, both of our other variables need to be known in order for us to be able to solve. So in order to solve for M let's look at our free body diagram. We can see that at 0.1 f end must be equal to F. G. Seeing as this is the only force to balance it out at this point, after is always equal to M G. And luckily for us, we know the quantity friend one. So that means that we can solve for rent for em by dividing 770 by g. R. Gravitational constant. The man is gonna give us the result of 78.57 kilograms. So now we know our mass, and that means that we can plug into our equation for the centripetal force. So let's go back to that equation that ever done earlier. F c equals M. V squared over r who want to sell for V and that V Square is equal to R F C. Over. So what is F C equal to? Well, we consult our free body diagram again. We can see that the point that we're looking at 0.0.2 at the top of the circle, there are two forces pointing inward toward the center of our circular motion F g and F N. That means the FC must be equal to F G plus f n. So you plug that into our equation to get our times that quantity over the M that we just calculated. Now everything is in terms of qualities that we know. All that we have left to do is plug in, are are is 21 years should be multiplied by 350 end. That's the normal force appoint one that were given plus 78.57 kilograms times 9.8 meters per second squared. That's our gravitational force at that point and all that is going to be all that is going to be divided by our mess. 78.57 kill. And when we do this math out, we get that D. So remember to square, with all this, this equation appears equal to the square. So it's at that. We get that V is equal to 17.3 meters per second and to get to a whole number, we can run that to 17 meters per second, which is our final answer.

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