(C) For the block,the forces are balanced as follows:$T \cos 37^{\circ} = f$$N + T \sin 37^{\circ} = Mg$Since $f = \mu N$,we have $T \cos 37^{\circ} =

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(C) For the block,the forces are balanced as follows:$T \cos 37^{\circ} = f$$N + T \sin 37^{\circ} = Mg$Since $f = \mu N$,we have $T \cos 37^{\circ} = \mu (Mg - T \sin 37^{\circ})$.Substituting the values $M = 100 \, kg$,$\mu = 1/3$,$\cos 37^{\circ} = 4/5$,and $\sin 37^{\circ} = 3/5$:$T(4/5) = (1/3)(100g - T(3/5))$$12T/5 = 100g - 3T/5$$15T/5 = 100g \implies 3T = 100g \implies T = 100g/3$.For the person,the upward force is $T = 100g/3$ and the downward force is $mg = 25g$.The equation of motion is $T - mg = ma_{\max}$.$100g/3 - 25g = 25a_{\max}$$(100g - 75g)/3 = 25a_{\max}$$25g/3 = 25a_{\max}$$a_{\max} = g/3$.

Class 11 Physics Newton's Laws of Motion and Friction Mix Examples-Newton's Laws of Motion and Friction

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$A$ block of mass $M = 100 \, kg$ is pulled by a force $T$ at an angle of $37^{\circ}$ with the horizontal. The coefficient of friction between the block and the ground is $\mu = 1/3$. $A$ person of mass $m = 25 \, kg$ is standing on a platform and pulls the block with the force $T$. Find the maximum upward acceleration $a_{\max}$ of the person such that the block just starts to move.

A
$\frac{4g}{3}$
B
$\frac{g}{2}$
C
$\frac{g}{3}$
D
$\frac{3g}{4}$

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Newton's Laws of Motion and Friction

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Mix Examples-Newton's Laws of Motion and Friction

Two masses $m_1 = 5 \ kg$ and $m_2 = 10 \ kg$,connected by an inextensible string over a frictionless pulley,are arranged as shown in the figure. The coefficient of friction of the horizontal surface is $0.15$. The minimum mass $m$ that should be placed on top of $m_2$ to stop the motion is ........ $kg$. (in $.3$)

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The masses of blocks $A$ and $B$ are $m$ and $M$ respectively. Between $A$ and $B$,there is a constant frictional force $F$ and $B$ can slide on a smooth horizontal surface. $A$ is set in motion with velocity $v_0$ while $B$ is at rest. What is the distance moved by $A$ relative to $B$ before they move with the same velocity?

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An object of mass $10 \,kg$ is projected from the ground with a speed of $40 \,m/s$ at an angle of $60^{\circ}$ with the horizontal. The rate of change of momentum of the object one second after projection in $SI$ units is ........ [Take $g = 9.8 \,m/s^2$]

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In the figure,two blocks are connected by a uniform strut attached to each block with frictionless pins. Block $A$ weighs $400 \, N$,block $B$ weighs $300 \, N$,and the strut $AB$ weighs $200 \, N$. If $\mu = 0.25$ under block $B$,determine the minimum coefficient of friction under block $A$ to prevent motion.

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$A$ metal block is resting on a rough wooden surface. $A$ horizontal force applied to the block is increased uniformly with time,i.e.,$F = kt$. Which of the following curves correctly represents the velocity $v$ of the block as a function of time $t$?

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An object of mass $10 \,kg$ is projected from the ground with a speed of $40 \,m/s$ at an angle of $60^{\circ}$ with the horizontal. The rate of change of momentum of the object one second after projection in $SI$ units is ........ [Take $g = 9.8 \,m/s^2$]

$A$ metal block is resting on a rough wooden surface. $A$ horizontal force applied to the block is increased uniformly with time,i.e.,$F = kt$. Which of the following curves correctly represents the velocity $v$ of the block as a function of time $t$?

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