A cylinder is placed on a rough plank,which i | vedclass

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Question

(B) Let the mass of the cylinder be $m$,radius be $R$,and moment of inertia be $I$. Let the friction force between the cylinder and the plank be $f$.

Vedclass · Accepted Answer

Friction force acts in the forward direction on the cylinder.

Vedclass · Answer

(B) Let the mass of the cylinder be $m$,radius be $R$,and moment of inertia be $I$. Let the friction force between the cylinder and the plank be $f$. For the cylinder,the force $f$ acts in the forward direction at the point of contact,causing it to accelerate and rotate. The acceleration of the center of mass is $a = f/m$ and the angular acceleration is $\alpha = (fR)/I$. For pure rolling on the plank,the acceleration of the point of contact on the cylinder must match the acceleration of the plank. The acceleration of the contact point on the cylinder is $a_p = a + R\alpha = f/m + (fR^2)/I$. The plank is pulled by force $F$ and experiences a backward friction force $f$ from the cylinder. Its acceleration is $a_{plank} = (F - f)/M_{plank}$. Since the plank is being pulled forward,the cylinder tends to slip backward relative to the plank. To oppose this relative motion,the friction force $f$ acts in the forward direction on the cylinder (and backward on the plank). Thus,the correct direction of friction on the cylinder is forward.

$A$ cylinder is placed on a rough plank,which in turn is placed on a smooth surface. The plank is pulled with a constant force $F$. Indicate the correct direction of the friction force acting on the cylinder.

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