A body of mass 5 ,kg is placed on a rough hor | vedclass

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(B) Let the mass of the body be $m = 5 \,kg$,the angle of pulling force be $	heta = 45^{\circ}$,and the coefficient of static friction be $\mu = \fra

Vedclass · Accepted Answer

$\frac{25}{\sqrt{2}} \,N$

Vedclass · Answer

(B) Let the mass of the body be $m = 5 \,kg$,the angle of pulling force be $	heta = 45^{\circ}$,and the coefficient of static friction be $\mu = \frac{1}{3}$.Let $F$ be the applied force. The components of $F$ are $F \cos 	heta$ (horizontal) and $F \sin 	heta$ (vertical upward).The normal reaction $N$ is given by $N = mg - F \sin 	heta$.The limiting friction is $f_L = \mu N = \mu(mg - F \sin 	heta)$.For the body to slide,the horizontal component of the force must be equal to the limiting friction: $F \cos 	heta = \mu(mg - F \sin 	heta)$.Rearranging for $F$: $F(\cos 	heta + \mu \sin 	heta) = \mu mg$.$F = \frac{\mu mg}{\cos 	heta + \mu \sin 	heta}$.Substituting the values: $F = \frac{(1/3) 	imes 5 	imes 10}{\cos 45^{\circ} + (1/3) \sin 45^{\circ}} = \frac{50/3}{\frac{1}{\sqrt{2}} + \frac{1}{3\sqrt{2}}} = \frac{50/3}{\frac{3+1}{3\sqrt{2}}} = \frac{50}{3} 	imes \frac{3\sqrt{2}}{4} = \frac{50\sqrt{2}}{4} = \frac{25\sqrt{2}}{2} = \frac{25}{\sqrt{2}} \,N$.

$A$ body of mass $5 \,kg$ is placed on a rough horizontal surface of coefficient of static friction $\frac{1}{3}$. The least pulling force to be applied on the body at an angle $45^{\circ}$ with the horizontal to slide it,is . . . . . . $\left(g=10 \,ms^{-2}\right)$

Similar Questions

$A$ block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined at an angle $\theta$ to the vertical. The minimum value of the coefficient of friction between the block and the surface for which the block will remain in equilibrium is

Which of the following is true about the coefficient of static friction $(\mu_s)$ and the coefficient of kinetic friction $(\mu_k)$?

The maximum value of static friction is called:

The maximum force of friction is called:

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