and parallel to the plane Ff = mg sin :
(61)
The maximum value of Ff is N , so
so the maximum value of
8.2
Ff = N = mg cos
(62)
mg cos tan
(63) (64)
is when = mg sin = :
Role of friction in accelerating a car
Forces are as shown for a rear-wheel drive car in …g 9. The frictional force between the rear wheels and
Figure 9: Rear-wheel driven vehicle the ground is Ff , and this force provides the force needed to accelerate the car, Ff = ma.
9
Kinematical relations
Before considering other one-dimensional problems we need to develop some other general aspects of mechanics.
9.1
Work
Force F is applied to a body. If point of application of the force, i.e. body moves a distance dr as in …g 10, the work done by the force is de…ned to be dW = F dr = (F cos ) dr
(65)
where F cos is component of force in direction of motion of the body. Hence work is a scalar quantity. For …nite displacements of a particle from position r1 to r2 as in …g 10 the work done by the force is Z r2 W = F dr (66) r1
Note that F may vary with position. 9