Question

A small body is released from the rest on a fixed smooth inclined plane at t=0. Velocity versus time graphs of the body us as shown in the figure. The angle of inclination of the plane with the horizontal is:

Answer 1

Here, we use the relation between the angles of inclination of particles to find the angle of inclination of the plane with the horizontal. Further, by substituting the given values we get the required result. Also, we will study the angle of inclination and basic frictional force, due to which an object cannot move smoothly.
Formula used:
$a = \tan \theta$
$g\sin \theta = a$

Complete step by step solution:
As we know that the angle of inclination is an angle between the line and the x-axis.
Here, inclination a of the particle is given as:
$a = \tan \theta = \dfrac{{10}}{2} = 5$
Now, to find the angle of inclination of the plane with the horizontal we have the relation:
$g\sin \theta = a$
Here, $\theta$ is the required angle of inclination of the plane with the horizontal.
Substituting the given values in above equation we get:
\eqalign{& \sin \theta = \dfrac{a}{g} \cr & \Rightarrow \sin \theta = \dfrac{5}{{10}} = \dfrac{1}{2} \cr & \therefore \theta = {30^ \circ } \cr}

Therefore, we get the required angle of inclination of plane with the horizontal i.e., $\theta = {30^ \circ }$.

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. An object cannot move smoothly when there is a presence of frictional force. 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:
The value of angle of inclination is always between zero degrees to 180 degrees, it is never greater than this. 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.