Question

Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration 'a' perpendicular to the axis of the cylinder. What is F_friction at point P ? It is assumed that the cylinder does not slip.

• A. $\text{Ma}$
• B. $\frac{\text{Ma}}{2}$
• C. $\frac{\text{Ma}}{3}$
• D. $\text{Mg}$

Answer 1

Answer: (C)

For no slipping at P
$\text{a}_{1} + \text{α} R = \text{a} \, \, \, \rightarrow $ (1)

$\text{f} = \left(\text{Ma}\right)_{1} = \text{M} \left(\text{a} - \text{α} R\right) \, \, \, \rightarrow $ (2)
$\text{f. R} = \text{I} \cdot \text{α} = \frac{\text{MR}^{2}}{2} \cdot \text{α} \, \, \, \rightarrow $ (3)
Solve the equations (2) and (3)
$\text{f} = \frac{\text{Ma}}{3}$ ​