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An 830-kg race car can drive around an unbanked turn at a maximum speed of 58 m/s without slipping. The turn has a radius of curvature of 160 m. Air flowing over the car’s wing exerts a downward-pointing force (called the downforce) of 11 000 N on the car. (a) What is the coefficient of static friction between the track and the car’s tires? (b) What would be the maximum speed if no downforce acted on the car?

0.9138$m / s$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

University of Michigan - Ann Arbor

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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.

04:21

An $830-\mathrm{kg}$ race …

04:29

An 830-kg race car can dri…

13:00

A racetrack curve has radi…

11:59

05:33

Determine the speed $v$ at…

01:28

A race car is making a U-t…

02:09

01:23

A car racing on a flat tra…

02:10

A curve in a stretch of hi…

A car rounds a flat circul…

05:15

A road with a radius of $7…

01:30

Friction provides the forc…

05:49

Air rushing over the wings…

01:36

A 615 -kg racing car compl…

here we have defined first the coefficient of static friction and then the maximum velocity for a car traveling run unbanked curve in two different scenarios. So let's start by drawing the free body diagram for a first scenario, the red dot here is our car moving along the curve. Then gravity, as always, will be pointing straight down and the normal force we pointing straight up from the curve to oppose it. But what's different about this problem is that we have another fourth pointing straight down our taking into account the air pressing on the car, which gives us another downward force of downforce, is called the problem, which we're just gonna label Ft. Our final force is the force of friction, which, as always, in these problems gonna be pointing inward toward the center of the circle, composing inertia. All right, So since F friction is, the one is the force pointing inward, that must be what's responsible for our centripetal force and without the force of friction is always equal to the normal force times the coefficient of static friction, which what we're looking for in this problem, the centripetal force is equal to M v squared over our our radius. So in order to solve this problem and so for the 2nd 15 static friction we have to solve for FN now, F N has to oppose the two downward pointing forces in order for the car to not either float up or sinks to the ground. So we know that the normal force has to be equal to the downward force plus the gravitational force. And since we know all these quantities, we can plug in and solve numerically, the downward force has given to us as being equal to 11,000 Newtons and f g is just mg which we are given G is 9.8 meters per second. Actually, what's with this? Well, the next page running on a space here, read it somewhere else here. But you get the picture. It's 11,000 plus 830 kilograms times 9.8 meters per second squared. And when we solve that, we're gonna find that our noble force is equal to 19,134 Newtons. Now we can plug into our equation for the criminal forth and we consult so that normal force that we just found multiplied by our coefficient that we're looking for is equal to M v squared over r We know em. It's 830 kilograms and we know our velocity 58 meters per second square that and we're dividing by our radius which is 160 meters. When we solve for the coefficient of static friction calculator, we find that is equal to 0.91 and disco efficient. It doesn't have units and that is our answer to part a Now in part B. We're not considering downward force anymore. We're just saying that if you go back to our free body diagram that we're erasing this force right here and they want us to find the maximum velocity in this scenario. So once again, we're gonna do something similar to what we did in this part of the problem. Right where he said that OK, we have We're gonna find FN using what we know about the forces that it has stick balance and from there we're gonna find the centripetal force. So once again, we're going to say that fn times the coefficient of friction. You just the friction force is equal to M V squared over r r centripetal force nothing you hear. But what changes is that we now we know that f n is equal to F. G. C is no longer opposing the downward force. So this just ends up being equal to mg and the coefficient of friction be evil to n v squared over r We can't let her EMS we get that. The the maxillary that we're trying to find is equal to G 100 coefficient. Times are now in this case, we can plug in our coefficient from earlier because remember that the coefficient of friction is just a property of the material of the road is made of in the material of the tires. It doesn't change when we change things like the forces acting on the road because it is a constant of the materials that were working with. So when we plug in our numbers, we get that V is equal to 9.8 meters per second squared times 0.91 times 160 Mears, and we find that the maximum velocity isn't equal to 38 on our units work out to be meters per second, which makes sense. That's a good sign. Better answer makes sense as well. And that is gonna be your final result for B.

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