Question

The 40kg uniform slender rod AB rests in the position shown when the constant couple moment of M is applied. Determine the magnitude of the moment M, so that 2 seconds after the start of the motion, the velocity of the center, G, will be 4 m/s. Neglect the mass of the rollers. The bar moves in the horizontal plane.

Problem 6 (25 pts) The 40-kg uniform slender rod AB rests in the position shown when the constant couple moment of M is applied. Determine the magnitude of the moment, M, so that, 2-seconds after the start of the motion, the velocity of the center, G, will be 4 m/s. Neglect the mass of the rollers. The bar moves in the horizontal plane. 0.75 m 0.75 m

Answer 1

Let the position of the roller be as shown in the figure above at any time 't'.

L/2 i NL/2) cos θ L/2 Lcos0

Let it is making an angle $\theta$ with the horizontal.

Position of the center, G from O = r=

0.75 m COS+

According to the principle of angular impulse and momentum,

$\int_{T_2}^{T_1}M_Gdt=H_{G_2}-H_{G_1}$

Thus, $\int_{0}^{2}Mdt=\left [ (mv_Gr_G)_2-(mv_Gr_G)_1 \right ]$

MẦdt-40(4×0.75-0×0.75)

40 × 4 × 0.75 -m (2 -0)