A bead of mass 2kg is fitted onto a rod with a length of 8m and can move on it with friction having the coefficient of friction 0.5. At the initial moment the bead is in the middle of the rod. The rod

Question

A bead of mass 2kg is fitted onto a rod with a length of 8m and can move on it with friction having the coefficient of friction 0.5. At the initial moment the bead is in the middle of the rod. The rod moves translationally in a horizontal plane with an acceleration $1 m / sec^{2}$ in the direction forming an angle 37° with the rod in gravity free region. Find the time (in sec) when the bead will leave the rod.

diagram

TestHub · Accepted Answer

Pseudo force on the bead: 2 N at 37° to the rod. $N = 2 sin 3 7^{\circ} = 1.2 N$ , $f = μ N = 0.6 N$ .

$a_{re l} = \frac{2 cos 3 7 ^{\circ} - 0.6}{2} = 0.5 m / s^{2}$ ; covers 4 m: $4 = \frac{1}{2} (0.5) t^{2} \Rightarrow t = 4 s$ .

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