Question

A plank of mass M=8kg with a bar of mass m​=2kg placed on its rough surface, lies on a smooth floor of an elevator ascending g/4. The coefficient of friction is μ=1/5 between the masses . A horizontal force F = 30 N is applied to the plank. Then the acceleration of bar and the plank in the reference frame of elevator are

Answer 1

In this question, first we will use the basic formula of frictional force and then we will find the acceleration of bar and plank by putting the given values in the equation. This will give us the required answer. Further we will study the basics of force and friction.
Formula used:
$a = \dfrac{f}{m}$

Complete step by step solution:
Here, if the frictional force between the plank and bar is represented by f, then:
$f = \mu N$
$\because N = 20 + \dfrac{{2g}}{4} = 25N$
\eqalign{ & \Rightarrow f = 25 \times \dfrac{1}{5} \cr & \therefore f = 5N \cr}
Therefore, the frictional force is 5N.
Now, to find the acceleration of the bar, which is given by the ratio of frictional force f and mass m:
\eqalign{& a = \dfrac{5}{2} \cr & \therefore a = 2.5m/{s^2} \cr}
Now, we need to find the acceleration of the plank, which is given by:
\eqalign{ & {a_1} = 30 - \dfrac{5}{8} \cr & \therefore {a_1} = \dfrac{{25}}{8}m/{s^2} \cr}
Therefore, we have the values of acceleration due to bar and acceleration due to plank as above.

Additional information:
Force is simply any push or pull. The S.I unit of force is Newton represented by N. The acceleration is defined as the increase in the velocity of an object. The acceleration is measured in meters per Second Square.
There are three laws of motions given by Newton. These laws of motion relate an object's motion to the forces acting on it.
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