Before 1960, people believed that the maximum attainable...

Before 1960, people believed that the maximum attainable coefficient of static friction for an automobile tire on a roadway was $\mu_{s}=1 .$ Around 1962 , three companies independently developed racing tires with coefficients of $1.6 .$ This problem shows that tires have improved further since then. The shortest time interval in which a piston-engine car initially at rest has covered a distance of one-quarter mile is about 4.43 s. (a) Assume the car's rear wheels lift the front wheels off the pavement as shown in Figure P5.42. What minimum value of $\mu$ , is necessary to achieve the record time? (b) Suppose the driver were able to increase his or her engine power, keeping other things equal. How would this change affect the elapsed time?

Key Concepts

Engine Power and Its Effect on Acceleration

Engine power is the rate at which work is done to increase a vehicle's kinetic energy. In automotive performance, higher engine power can result in greater acceleration. However, even if engine power increases, the maximum achievable acceleration is ultimately limited by the friction available between the tires and the road. This interplay determines how improvements in engine output affect overall elapsed time.

Weight Distribution and Traction

Weight distribution plays a crucial role in vehicle dynamics, especially during acceleration. When a car's rear wheels bear most or all of the load—as when the front wheels are lifted—the effective normal force on the driving wheels can change, influencing the available frictional force. Understanding how weight transfer affects traction is essential in determining the minimum friction requirements needed for rapid acceleration.

Static Friction

Static friction is the force that resists the initiation of motion between two surfaces in contact. In vehicle dynamics, the coefficient of static friction between the tire and the road determines the maximum force available for acceleration without slipping, which is a critical parameter in performance calculations and safety considerations.

Kinematics of Uniform Acceleration

The equations of kinematics relate displacement, time, and acceleration for objects in motion. In scenarios where a vehicle accelerates from rest, knowing the distance covered and the elapsed time allows one to compute the required acceleration. This analysis is fundamental when assessing how the available friction force translates into vehicle acceleration over a defined distance.

Transcript

00:01 All right, let's solve problem 42 in chapter 5.

00:04 This one is sort of a weird concept to understand.

00:07 We're usually used to thinking of friction as slowing us down.

00:12 But actually, if you think really carefully about it, friction is actually how we travel.

00:18 So we talk about a car in this problem, but i'm going to, to illustrate how friction helps us forward, imagine you're trying to, let's say, push a big rock, right? you're a person and you're trying to push a rock.

00:34 But the problem is, is, you know, maybe the ground you're on is like really slippery, right? and so what happens you can imagine is as you try and push on the rock, your feet are liable to slip backwards, right? but let's say you're not on slippery ground.

00:53 You're on just good firm ground.

00:55 Your feet don't move backward, right? what's helping you? well, there's actually friction pushing you forward.

01:04 Okay? and this is the same thing that happens when you walk.

01:08 The only way you can walk forward is, you know, one of your feet is planted.

01:15 And the other one is moving forward.

01:17 And so you require some friction to actually push your foot that's pushing you forward in order to accelerate for that speed.

01:25 Okay.

01:26 So the point of this is your forward acceleration is limited by the amount of friction that you have.

01:40 So basically forward acceleration is the same thing as sort of the acceleration of the friction pushing you forward.

01:46 That's really the big takeaway.

01:50 And so what that means is if you have a car, its acceleration is, limited by the amount of friction, which is just mu -g, right? because if friction is the only thing that's pushing us forward, we have f equals ma, so that's mu -m -g equals ma, and so the a equals mu -g.

02:23 Okay.

02:26 And so that friction is what is accelerating these piston cars forward...

Please give Ace some feedback