When the force applied on block A is F=2 F1 it is found that...

When the force applied on block $A$ is $F=2 F_{1}$ it is found that the block $B$ just begins to slide on $A$. What is the value of coefficient of friction $\mu ?$
(a) $\frac{\sqrt{3}}{5}$
(b) $\frac{1}{\sqrt{3} \times 1}$
(c) $\frac{1}{\sqrt{3}}$
(d) $\sqrt{3}$

Key Concepts

Coefficient of Friction

The coefficient of friction is a dimensionless number that characterizes the interaction between two surfaces in contact. It quantitatively relates the maximum static frictional force to the normal force, providing a measure of how much frictional resistance to sliding exists between the surfaces before relative motion occurs.

Relative Motion and Inertial Frames

In dynamics problems involving more than one block, understanding relative motion becomes essential. Analyzing the motion from a non-inertial frame attached to one of the accelerating bodies can involve pseudo-forces and help explain how and when one block begins to slide over another.

Newton's Second Law

Newton's Second Law is the cornerstone of dynamics, stating that the net force acting on an object equals its mass multiplied by its acceleration. In problems involving multiple blocks and applied forces, using this law helps determine the acceleration of each block and the net force responsible for overcoming frictional resistance.

Static Friction

Static friction is the force that resists the initiation of motion between two surfaces in contact. Its maximum value is found by multiplying the coefficient of static friction by the normal force. In scenarios where a block just begins to slide, the applied force reaches this maximum threshold, signifying the transition from static to kinetic behavior.

Transcript

00:01 In this question, they have given that the system consists of mass a 40 kilogram and mass b 15 kilogram and a force capital f is applied parallel to the smooth inclined plane.

00:14 So we have to answer in this question that when the force applied on the block a is capital f is equal to to f1 where f1 is the frictional force between a and b.

00:28 So we have to find that what is the value of coefficient? of friction mu that is present in between the blocks a and b if it is found that the block b just begins to slide on a so now how can i solve this question so let's say i'm drawing this i'm redraw this diagram let's say this is our inclined plane right and this is 30 degree so i can say in this direction my a x acceleration and an x direction and in this direction there will be a y and the angle is 30 degree right now if i have to find the f1 so i can easily write that f1 will be equal to because it is the frictional force so it will be equal to total mass of these two blocks that will be equal to 40 plus 15 multiply by g and multiply by sine 30 degree because it is the component of this f1 right so f1 will be equal to 55 g is 10 so i will multiply this with 10 multiplied by sign 30 is 1 divided by 2 so from this i can say f1 will be equal to 275 newton this is f1 now if i find the f capital f capital f is equal to 2 f1 so it will be equal to 5 50 newton so f will be equal to 5 50 newton now we have to find the coefficient of friction so for this first we have to find the acceleration right now how can we find the acceleration acceleration will be equal to difference in this forces that will be 550 minus 275 because it is acting in a positive direction divided by the total mass that will be 55.

02:29 So according to this, the acceleration will be equal to 5 meter per second square.

02:35 This is the acceleration...

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