In figure, two blocks are separated by a uniform strut attached to each block with frictionless pins. Block $A$ weighs $400\,N$, block $B$ weighs $300\,N$, and the strut $A B$ weigh $200\,N$. If $\mu=0.25$ under $B$, determine the minimum coefficient of friction under $A$ to prevent motion.
Difficult
Download our app for free and get startedPlay store
(a)

Consider $F BD$ of structure.

Applying equilibrium equations,

$Av + Bv =200 N$

$A _{ H }= B _{ H}{ \ldots \text { (ii) }}$

From F BD of block B,

$B _{ H }+ F _{ B } \cos 60^{\circ}- N _{ B } \sin 60^{\circ}=0$

$N_B \cos 60^{\circ}-B_V-300+F_V \sin 60^{\circ}=0$

$F _{ B }=0.25 N _{ B }$

$B _{ H }-0.74 N _{ B }=0 \ldots \text {.(iii) }$

$- B _{ V }+0.71 N _{ B }=300$

$F _{ A }- A _{ H }=0$

$N _{ A }- A _{ V }=400$

$F _{ A }=\mu_{ A } N _{ A }$

$\therefore \mu_{ A } N _{ A }- A _{ H }=0$.

On solving above equations, we get

$N _{ A }=650 N , F _{ A }=260 N , F _{ A }=\mu_{ A } N _{ A }$

$\therefore \mu_{ A }=\frac{260}{250}=0.4$

art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Similar Questions

  • 1
    The upper portion of an inclined plane of inclination $\alpha $ is smooth and the lower portion is rough. A particle slides down from rest from the top and just comes to rest at the foot. If the ratio of the smooth length to rough length is $m : n$ , the coefficient of friction is
    View Solution
  • 2
    When a bicycle is in motion, the force of friction exerted by the ground on the two wheels is such that it acts
    View Solution
  • 3
    If the overbridge is concave instead of being convex, the thrust on the road at the lowest position will be
    View Solution
  • 4
    A uniform rope lies on a horizontal table so that a part of it hangs over the edge. The rope begins to slide down when the length of the hanging part is $25\%$ of the entire length. The coefficient of friction between the rope and the table is
    View Solution
  • 5
    Two blocks $A$ and $B$ of masses $5 \,kg$ and $3 \,kg$ respectively rest on a smooth horizontal surface with $B$ over $A$. The coefficient of friction between $A$ and $B$ is $0.5$. The maximum horizontal force (in $kg$ wt.) that can be applied to $A$, so that there will be motion of $A$ and $B$ without relative slipping, is
    View Solution
  • 6
    What is the maximum value of the force $F$ such that the block shown in the arrangement does not move ....... $N$
    View Solution
  • 7
    A block of mass $5\,kg$ is placed at rest on a table of rough surface. Now, if a force of $30\,N$ is applied in the direction parallel to surface of the table, the block slides through a distance of $50\,m$ in an interval of time $10\,s$. Coefficient of kinetic friction is (given, $g =10\,ms ^{-2}$)
    View Solution
  • 8
    A block of mass $1 \,kg$ is projected from the lowest point up along the inclined plane. If $g=10 \,ms ^{-2}$, the retardation experienced by the block is ............. $ms ^ {-2}$
    View Solution
  • 9
    A force $f$ is acting on a block of mass $m$. Coefficient of friction between block and surface is  $\mu$. The block can be pulled along the surface if :-
    View Solution
  • 10
    A block is moving on an inclined plane making an angle $45^{\circ}$ with the horizontal and the coefficient of friction is $\mu$. The force required to just push it up the inclined plane is $3$ times the force required to just prevent it from sliding down. If we define $N=10 \ \mu$, then $N$ is
    View Solution