(A) The surface exerts two forces on the block: the normal force $(N)$ acting vertically upwards and the kinetic frictional force $(f_{k})$ acting hor

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(A) The surface exerts two forces on the block: the normal force $(N)$ acting vertically upwards and the kinetic frictional force $(f_{k})$ acting horizontally opposite to the direction of motion.$1$. The normal force is $N = mg$.$2$. The kinetic frictional force is $f_{k} = \mu_{k} N = \mu_{k} mg$.$3$. The net force $(F_{net})$ exerted by the surface is the vector sum of the normal force and the frictional force:$F_{net} = \sqrt{N^{2} + f_{k}^{2}}$$F_{net} = \sqrt{(mg)^{2} + (\mu_{k} mg)^{2}}$$F_{net} = \sqrt{(mg)^{2} (1 + \mu_{k}^{2})}$$F_{net} = mg \sqrt{1 + \mu_{k}^{2}}$$F_{net} = mg(1 + \mu_{k}^{2})^{1/2}$Therefore,option $A$ is correct.

Class 11 Physics Newton's Laws of Motion and Friction Kinetic Friction and Motion on Rough Horizontal Surface

Medium

$A$ block of mass $m$ is moving on a rough horizontal surface. The coefficient of kinetic friction between the block and the surface is $\mu_{k}$. The net force exerted by the surface on the block is (where $g$ is the acceleration due to gravity).

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A
$mg(1+\mu_{k}^{2})^{1/2}$
B
$[mg(1+\mu_{k})]^{1/2}$
C
$mg(1+\mu_{k}^{2})$
D
$mg(1+\mu_{k})^{1/2}$

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Class 11

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Newton's Laws of Motion and Friction

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Kinetic Friction and Motion on Rough Horizontal Surface

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$A$ block of mass $10 \ kg$ is moving on a rough surface with a velocity $v = 4 \ m/s$ to the left. An external force $F = 20 \ N$ is applied to the right as shown in the figure. The coefficient of kinetic friction is $\mu = 0.6$. The frictional force acting on the block is ...... $N$.

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On a rough horizontal surface,a body of mass $2 \, kg$ is given a velocity of $10 \, m/s$. If the coefficient of friction is $0.2$ and $g = 10 \, m/s^2$,the body will stop after covering a distance of ........ $m$.

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$A$ block of mass $m$ rests on a rough horizontal surface as shown in the figure. The coefficient of friction between the block and the surface is $\mu$. $A$ force $F = mg$ acting at an angle $\theta$ with the vertical side of the block pulls it. In which of the following cases can the block be pulled along the surface?

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$A$ small body slips,subject to the force of friction,from point $A$ to point $B$ along two curved surfaces of equal radius,first along route $1$,then along route $2$. Friction does not depend on the speed and the coefficient of friction on both routes is the same. In which case will the body's speed at $B$ be greater?

Medium

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$A$ car is moving along a straight horizontal road with a speed $v_0$. If the coefficient of friction between the tyres and the road is $\mu$,the shortest distance in which the car can be stopped is

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$A$ block of mass $m$ is moving on a rough horizontal surface. The coefficient of kinetic friction between the block and the surface is $\mu_{k}$. The net force exerted by the surface on the block is (where $g$ is the acceleration due to gravity).

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$A$ block of mass $10 \ kg$ is moving on a rough surface with a velocity $v = 4 \ m/s$ to the left. An external force $F = 20 \ N$ is applied to the right as shown in the figure. The coefficient of kinetic friction is $\mu = 0.6$. The frictional force acting on the block is ...... $N$.

On a rough horizontal surface,a body of mass $2 \, kg$ is given a velocity of $10 \, m/s$. If the coefficient of friction is $0.2$ and $g = 10 \, m/s^2$,the body will stop after covering a distance of ........ $m$.

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