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Two banked curves have the same radius. Curve A is banked at an angle of $13^{\circ},$ and curve $B$ is banked at an angle of $19^{\circ} .$ A car can travel around curve $A$ without relying on friction at a speed of 18 $\mathrm{m} / \mathrm{s}$ . At what speed can this car travel around curve $\mathrm{B}$ without relying on friction?

22$m / s$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

Cornell University

University of Michigan - Ann Arbor

University of Sheffield

McMaster University

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.

02:20

Two banked curves have the…

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05:53

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01:15

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03:18

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02:07

01:30

A car is driving in a circ…

02:15

A car rounds an unbanked c…

09:31

A car rounds a banked curv…

02:58

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03:47

in this problem, you have to find the velocity that a car can go around a bank crew without any friction. Given that we know that same velocity for a different banked curve with a different angle. So ever with Oliver banked curve problems, we start out by taking our normal force on our bank curve and decomposing it. And so if we draw our lines, we have the normal force here. The gravitational force here. And we'll split up our components like that. So we have our white component here and our X component right here. All right, so from here, we can see that FX must be right. That earlobe specify that scenario. A FX must be responsible for our centripetal force. And if X must be equal to FN times the sign of data Now, what is f an equal do by the same logic that we just used to find our f n um, sign of quit side of later equals X equation. We can see that, um, f y must be equal to if in coast data, which must be equal to M G. Since you're the vertical force to cancel out our force of gravity, so f n equals mg divided by Costa. And that means that f of X is equal to mg tennis data. So that means that since F of X is the centripetal force that, um V is equal to the square root of g r tan theta and that just comes from rearranging um, f of X and empty tent Better. All right, so we know the in this scenario, and we know angle 13 and what we want. What we don't know for both of these problems is our radius are so we're gonna isolate this little gr portion of our equation. Maybe that is that Republican right that 18 equals gr times 10 of 13. And that means that the squared of gr must be equal to 18. Divided by companion of 13 G is just a constant right. It's the it's the coefficient of gravity. Ah, you could take that over to the other side and divide by it as well, or leave it in there. It is really up to you. Your answer will be the same. I'm gonna leave it in there. And when I saw that division, I find that that you are is equal. You No square root sign, actually, 37 0.462 All right, how does this help us? Well, this is our scenario for a right, but now we can set up with the same equation for B. So be we know that the same equation for V must be true. Since our general set up f C equals FX, everything that followed is exactly the same. So that means that the it be also equals the square root of gr times, a squared of our theater there which in this case is 19 that's given to us in the problem set up. You can see you all right. So let's do like, let's take v, be divided by the square root of canyon of 19. And we know what g times are is equal to. That's 37.462 So we can solve for that means that we can solve for VP. That's equal, then to 21 0.982 And so, by comparing our to velocities, you solved the problem

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