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A curve in a speed track has a radius of $1000 \mathrm{ft}$ and a rated speed of $120 \mathrm{mi} / \mathrm{h}$. (See Sample Prob. 12.6 for the definition of rated speed.) Knowing that a racing car starts skidding on the curve when traveling at a speed of $180 \mathrm{mi} / \mathrm{h}$, determine $(a)$ the banking angle $u,(b)$ the coefficient of static friction between the tires and the track under the prevailing conditions, $(c)$ the minimum speed at which the same car could negotiate the curve.

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Physics 101 Mechanics

Chapter 12

Kinetics of Particles: Newton’s Second Law

Newton's Laws of Motion

Rutgers, The State University of New Jersey

Simon Fraser University

University of Winnipeg

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.

09:37

Isaac Newton (4 January 1643 – 31 March 1727) was an English mathematician, physicist, astronomer, theologian, and author (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy"), first published in 1687, laid the foundations of classical mechanics. Newton also made seminal contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.

10:57

A curve in a speed track h…

11:59

A racetrack curve has radi…

03:52

If a car takes a banked c…

20:35

A car rounds a banked curv…

03:09

04:15

If a car takes a banked cu…

04:09

A circular curve of highwa…

13:00

Hello, everyone. Here it is given up occurred in high speed track having the radius 1000 fit and rated speed That is also called optimum speed. 1 20 my whatever. All right. 1 76. 50 per second If racing car starts skidding on the car when traveling spirits 1 80 mile per hour. So maximum speed is 1 80 mile. But of it, that is to 64 50 per second to negotiate the car without escape, Calculate angle of fainting, coefficient of friction and minimum speed to negotiate the car. Let us start solving normal acceleration of the car Will be we square by room, not going free. Body diagram off the car. Just symbolic. I'm going here. I hope the card here it will be normal reaction date off the car. Just a moment, bitch. Friction? Uh huh. And Mars into normal acceleration. Taking this is Toby XX is Yeah, and this be will consider by access submission off forces along X axis If we take the four Friction Force plus component off. Wait in the direction off X. We will get this angelic already. We know. Hitter The blue sign off theater His call to I'm a cause of Tito. So from here friction force we will get acceleration is we square By also M b squared by rule cause off theater minus Wait, wait is mg sign up theater se equation But taking submission off force along via taxes So it will be and minus component off weight in the direction off by axis Sign off sitter That will be am a sign off sitter So you may write And Toby equal toe and B squared by rule signed off Fotopoulos MD Cost of theater This is the question of murder too. First case toe find Angela Banking speed is rated speed which is given 1 76 fit per second and and we'll build with zero r friction force will be zero. So dividing equation one in tow or you may right from equation but f is to be taken. Jiro I am rated B Square by Ruben cause off theater minus mg Sign off theater So 10 off theater We will get we rated square upon ruin to G. That is 1 70 60 square releases 1000 and toe G is 32.2. So 10 off theater We will get 0.96199 That is angle of fainting, Toby. 43.9 degrees. This is the answer off part a now part we in part we we have to find a coefficient of friction. Muche. So this is the case off silting outward that is f should be It's called, um You went so musical toe half upon and dividing Equation one and two We will get we square cause off Peter minus ruin to G Sign off theater upon we square Sign off Giotopoulos Rudy cause off theater here Well, he is given at with helping will start that is to 64 50 per second Substituting here Yeah, to 64 square angle off thinking we have obtained 43.9 minus radius off the card party 1000 ft G is 32.2 angle a flanking again 43.9 divided by square off velocity at which silting may start Sign up 43 point night plus row is 1000 into G 32.2 cause off 43.9 So it will be a point 390 That is coefficient of friction no see part We have to find minimum speed, the minimum be required. So for minimum speed, absolutely minus me went minus musical toe We square cause off theater minus Rajhi Sign off Theater upon the square Sign off Peter Plus Luigi Casa Peter Car. So by using this equation, speed can be written is solving every question for its speed that is minimum his feet. It would be roll into ji sign off theater minus new cause off theater divided by course of data. Less new sign off theater. Subjecting the value Radio 6000 g is 32.0 sign off 43.8 night minus milk 0.390 cause off 43.8 night divided by cars off 43.89 mu is quite 390 Sign off 43.89 So you we will get minimum speed by which vehicle can negotiate doctor path and that minimum speed is 78.8. Here you will get 105.6 to 50 per second on In terms off miles, it will be 78.8 miles, but but that's all for it. Thanks for watching it

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