What should be the minimum force P to be appl | vedclass

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(A) Let the tension in the string be $P$. Since the string passes over a pulley attached to the block,the force pulling the block up the incline is th

Vedclass · Accepted Answer

$Mg 	an(	heta/2)$

Vedclass · Answer

(A) Let the tension in the string be $P$. Since the string passes over a pulley attached to the block,the force pulling the block up the incline is the sum of the tension components along the incline.The force exerted by the string on the block along the incline is $F = P + P \cos 	heta = P(1 + \cos 	heta)$.The component of the gravitational force acting down the incline is $Mg \sin 	heta$.For the block to just begin to move up,the force pulling it up must equal the gravitational force component pulling it down:$P(1 + \cos 	heta) = Mg \sin 	heta$$P = \frac{Mg \sin 	heta}{1 + \cos 	heta}$Using trigonometric identities $\sin 	heta = 2 \sin(	heta/2) \cos(	heta/2)$ and $1 + \cos 	heta = 2 \cos^2(	heta/2)$:$P = \frac{Mg \cdot 2 \sin(	heta/2) \cos(	heta/2)}{2 \cos^2(	heta/2)}$$P = Mg 	an(	heta/2)$

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