Question

Two fixed frictionless inclined planes making an angle 30 degree and 60 degree with the vertical are shown in the figure. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B?

Answer 1

Hint: Here, we will use the relation between the forces that is acting on the blocks and by substituting the given values we will get the required relative acceleration of block A with respect to block B. Furthermore, we will study the basics of friction and its types.

Formula used:
$mg\sin \theta = ma$

Complete answer:
The two blocks are on fixed frictionless inclined planes. Here, we get a relation between the forces acting of the block which is given by:
$mg\sin \theta = ma$
$\therefore a = g\sin \theta $
Here, a is along the inclined plane.
So, the vertical component of acceleration will be given by:
$g{\sin ^2}\theta $
Now, relative vertical acceleration of A with respect to B will be given by:
$\eqalign{
  & g[{\sin ^2}{60^ \circ } - {\sin ^2}{30^ \circ }] \cr
  & \Rightarrow \dfrac{g}{2} \cr
  & \therefore 4.9m/{s^2} \cr} $
Therefore, the relative vertical acceleration of A with respect to B is given by $4.9m/{s^2}$

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.