Question

Consider a 14 tyre truck, whose only rear 8 wheels are power driven (means only these 8 wheels can produce an acceleration ). These 8 wheels are supporting approximately half of the load . If the coefficient of friction between road and each tyre is 0.6 , then what could be the maximum attainable acceleration by this truck ?

Answer 1

Hint: Here, we will use the relation between the forces that are acting on the blocks and by substituting the given values we will get the required maximum attainable acceleration by the truck. Further, we will study about the basics of frictional force.

Formula used:
$\eqalign{& f = \mu N \cr
  & f = ma \cr} $

Complete step by step solution:
There are forces that come into action when a body or object comes in motion, friction is one of those forces. This opposes the motion of an object or body.
In the question it is given that 8 wheels carry half the load, which is given by:
$N = \dfrac{{Mg}}{2}$
  Here, acceleration is provided by friction f, given by:
$\eqalign{& f = \mu N \cr
& \Rightarrow f = \mu \dfrac{{Mg}}{2} \cr} $
$\eqalign{& \Rightarrow ma = \mu \dfrac{{Mg}}{2} \cr} $
$\eqalign{& \Rightarrow a = \mu \dfrac{{Mg}}{2} \cr} $
  $\eqalign{& \therefore a = 3m/{s^2} \cr} $
Therefore, we get the result of the maximum attainable acceleration by the given truck by the above equation.

Additional Information: As we know that the friction force can be defined as the force exerted by a surface when an object moves across it or even makes an effort to move across the surface. There are three types of friction force - sliding friction, rolling friction and static friction. It can be said that the friction force often opposes the motion of an object.
Static friction comes into action on objects when they are resting on a surface. For example, if we are hiking in the woods, there is a presence of static friction between our shoes and the trail each time we put down our foot. Without this friction, our feet would slip out and thereby, making it difficult to walk.
Sliding friction is friction that comes in action on objects when they are sliding over another surface. As we know that the sliding friction is weaker than the static friction. That is the reason that it is easier to slide a piece of furniture over the floor after we start it moving than it is to get it moving in the first place.
The last one is rolling friction is friction that comes in action on objects when they are rolling over another surface. Rolling friction is much weaker than sliding friction and static friction. This is the reason that most forms of ground transportation use wheels, including bicycles, cars, 4-wheelers, roller skates, scooters, and skateboards, as these wheels make it easier to travel with facing less frictional force.

Note: Frictional force is a force that opposes the motion of any object. There are many practical examples of frictional force. We should also remember that various kinds of lubricants are used to overcome the frictional force like- grease, oil etc.