Simple Nature - Light and Matter

Maximum acceleration of a car example 25

.Rubber on asphalt givesμk ≈0.4 andμs≈0.6. What is the

upper limit on a car’s acceleration on a flat road, assuming that

the 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 verti-

cally. The vertical forces acting on the car should cancel out. The

earth makes a downward gravitational force on the car whose

absolute value ismg, so the road apparently makes an upward

normal force of the same magnitude,Fn=mg.

Now what about the horizontal motion? As is always true, the co-

efficient of static friction is greater than the coefficient of kinetic

friction, so the maximum acceleration is obtained with static fric-

tion, i.e., the driver should try not to burn rubber. The maximum

force of static friction isFs,max = μsFn =μsmg. The maximum

acceleration isa=Fs/m=μsg≈6 m/s^2. This is true regard-

less of how big the tires are, since the experimentally determined

relationshipFs,max=μsFnis independent of surface area.

self-check E

Find the direction of each of the forces in figure k. .Answer, p. 1055

k/1. The cliff’s normal force on
the climber’s feet. 2. The track’s
static frictional force on the wheel
of the accelerating dragster. 3.
The ball’s normal force on the
bat.

Locomotives example 26

Looking at a picture of a locomotive, l, we notice two obvious

things that are different from an automobile. Where a car typi-

cally has two drive wheels, a locomotive normally has many —

ten in this example. (Some also have smaller, unpowered wheels

in front of and behind the drive wheels, but this example doesn’t.)

Also, cars these days are generally built to be as light as possi-

ble for their size, whereas locomotives are very massive, and no

effort seems to be made to keep their weight low. (The steam

locomotive in the photo is from about 1900, but this is true even

for 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,FN, cancels

the downward force of gravity,FW, so ignoring plus and minus

signs, these two forces are equal in absolute value,FN = FW.

158 Chapter 3 Conservation of Momentum