(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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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 $\mu$. Find the value$(s)$ of $F$ for which $M$ and $m$ are stationary with respect to $M_0$.

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Block $A$ of mass $100 \ kg$ is kept above another block $B$ of mass $300 \ kg$. Block $A$ is tied to the wall $C$ with a horizontal string. The coefficient of friction between $A$ and $B$ is $0.35$ and that between $B$ and the horizontal surface is $0.5$. Find the horizontal force $P$ necessary to move the block $B$. (in $N$)

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The acceleration of the $10\, kg$ block when $F = 30\, N$ is applied as shown in the figure is ........ $m/s^2$.

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$A$ pen of mass $m$ is lying on a piece of paper of mass $M$ placed on a rough table. If the coefficients of friction between the pen and paper and the paper and the table are $\mu_1$ and $\mu_2$,respectively,then the minimum horizontal force with which the paper has to be pulled for the pen to start slipping is given by:

KVPY 2010

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When $F = 2 \text{ N}$, what is the frictional force between the $5 \text{ kg}$ block and the ground (in $\text{ N}$)?

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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 $\mu$. Find the value$(s)$ of $F$ for which $M$ and $m$ are stationary with respect to $M_0$.

The acceleration of the $10\, kg$ block when $F = 30\, N$ is applied as shown in the figure is ........ $m/s^2$.

When $F = 2 \text{ N}$, what is the frictional force between the $5 \text{ kg}$ block and the ground (in $\text{ N}$)?

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