Simple Nature - Light and Matter

Maximum acceleration of a car example 25⊲ Rubber on asphalt gives µ k ≈ 0.4 and µ s ≈ 0.6. What is theupper limit on a car’s acceleration on a flat road, assuming thatthe engine has plenty of power and that air friction is negligible?⊲ This isn’t a flying car, so we don’t expect it to accelerate vertically.The vertical forces acting on the car should cancel out. Theearth makes a downward gravitational force on the car whoseabsolute value is mg, so the road apparently makes an upwardnormal force of the same magnitude, F n = mg.Now what about the horizontal motion? As is always true, the coefficientof static friction is greater than the coefficient of kineticfriction, so the maximum acceleration is obtained with static friction,i.e., the driver should try not to burn rubber. The maximumforce of static friction is F s,max = µ s F n = µ s mg. The maximumacceleration is a = F s /m = µ s g ≈ 6 m/s 2 . This is true regardlessof how big the tires are, since the experimentally determinedrelationship F s,max = µ s F n is independent of surface area.self-check EFind the direction of each of the forces in figure k. ⊲ Answer, p. 922k / 1. The cliff’s normal force onthe climber’s feet. 2. The track’sstatic frictional force on the wheelof the accelerating dragster. 3.The ball’s normal force on thebat.Locomotives example 26Looking at a picture of a locomotive, l, we notice two obviousthings that are different from an automobile. Where a car typicallyhas two drive wheels, a locomotive normally has many —ten in this example. (Some also have smaller, unpowered wheelsin front of and behind the drive wheels, but this example doesn’t.)Also, cars these days are generally built to be as light as possiblefor their size, whereas locomotives are very massive, and noeffort seems to be made to keep their weight low. (The steamlocomotive in the photo is from about 1900, but this is true evenfor modern diesel and electric trains.)The reason locomotives are built to be so heavy is for traction.The upward normal force of the rails on the wheels, F N , cancelsthe downward force of gravity, F W , so ignoring plus and minussigns, these two forces are equal in absolute value, F N = F W .Given this amount of normal force, the maximum force of static154 Chapter 3 Conservation of Momentum