Problem $4$

The uniform slender bar ABC weighs $6$ lb and is initially at rest with end $A,$ bearing against the stop in the horizontal guide. When a constant couple $M=72$lbin is applied to end $C,$ the bar rotates causing end $A$ to strike the side of the vertical guide with a velocity of $10f\frac{t}{sec}.$ The mass of the rollers may be neglected. Note: Moment of inertia of a slender bar is: $\frac{?}{\text{b}\text{a}\text{r}}(I)=\frac{1}{12}m{l}^2$

Calculate the change in gravitational potential energy, $V_g.$

Calculate the work done by the moment $M$

Write down the relativity equation of velocities between points A and $B$ and thus determine the final velocity of the center of the mass of the bar $\frac{?}{\text{b}\text{a}\text{r}}(v)$ and its angular velocity $.$

Determine change in the kinetic energy.

Calculate the loss of energy $E$ due to friction in the guides and rollers.