(C) The maximum acceleration $a_{\max}$ that the block of mass $m$ can have without slipping is determined by the static friction force $f_{s, \max} =

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(C) The maximum acceleration $a_{\max}$ that the block of mass $m$ can have without slipping is determined by the static friction force $f_{s, \max} = \mu_s N = \mu_s mg$.Using Newton's second law for block $m$: $f_{s, \max} = m a_{\max} \implies \mu_s mg = m a_{\max} \implies a_{\max} = \mu_s g$.Given $\mu_s = 0.5$ and $g = 9.8 \; m/s^2$,we have $a_{\max} = 0.5 \times 9.8 = 4.9 \; m/s^2$.For the two blocks to move together,the entire system must move with an acceleration $a \le a_{\max}$.Applying Newton's second law to the combined system of mass $(m + M)$:$F = (m + M) a_{\max} = (2 + 8) \times 4.9 = 10 \times 4.9 = 49 \; N$.

Class 11 Physics Newton's Laws of Motion and Friction Block on Block System, psudo force and Constrained Motion In Friction

Medium

$A$ system of two blocks of masses $m = 2 \; kg$ and $M = 8 \; kg$ is placed on a smooth table as shown in the figure. The coefficient of static friction between the two blocks is $0.5$. The maximum horizontal force $F$ that can be applied to the block of mass $M$ so that the blocks move together will be $\dots \; N$.

JEE MAIN 2022 All JEE MAIN

A
$9.8$
B
$39.2$
C
$49$
D
$78.4$

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Class 11

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Newton's Laws of Motion and Friction

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Block on Block System, psudo force and Constrained Motion In Friction

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The coefficient of static friction between two blocks is $0.5$ and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is $\ldots \ldots N$. (take $g=10 \, m/s^2$)

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$A$ block $A$ of mass $100\, kg$ rests on another block $B$ of mass $200\, kg$ and is tied to a wall as shown in the figure. The coefficient of friction between $A$ and $B$ is $0.2$ and that between $B$ and the ground is $0.3$. The minimum force $F$ required to move the block $B$ is........ $N$. $(g = 10\, m/s^2)$

Medium

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Two blocks $A$ and $B$ of masses $6 \, kg$ and $3 \, kg$ rest on a smooth horizontal surface as shown in the figure. If the coefficient of friction between $A$ and $B$ is $0.4$,find the maximum horizontal force $F$ that can be applied to block $A$ such that they move together without separation. (in $, N$)

Medium

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Imagine a situation in which the horizontal surface of block $M_0$ is smooth and its vertical surface is rough with a coefficient of friction $\mu$. Identify the correct statement$(s)$.

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In the arrangement shown in the figure,the coefficient of friction between the two blocks is $0.5$. The force of friction between the two blocks is (Assume that the $4 \,kg$ block is placed on a smooth horizontal surface.) (Acceleration due to gravity $= 10 \,ms^{-2}$.) (in $\,N$)

MediumAP EAMCET 2019

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The coefficient of static friction between two blocks is $0.5$ and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is $\ldots \ldots N$. (take $g=10 \, m/s^2$)

Imagine a situation in which the horizontal surface of block $M_0$ is smooth and its vertical surface is rough with a coefficient of friction $\mu$. Identify the correct statement$(s)$.

In the arrangement shown in the figure,the coefficient of friction between the two blocks is $0.5$. The force of friction between the two blocks is (Assume that the $4 \,kg$ block is placed on a smooth horizontal surface.) (Acceleration due to gravity $= 10 \,ms^{-2}$.) (in $\,N$)

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