Question

The slender 15 kg bar is initially at rest and standing in the vertical position when the bottom end A is displaced slightly to the right. If the track in which it moves is smooth, determine the speed at which end A strikes the corner D. The bar is constrained to move in the vertical plane. Neglect the mass of the cord BC.

Answer 1

Answer:

Explanation:

Given Parameters

Mass of slender, m = 15kg

Length of AB, a = 4.5m

Initial velocity of slender, $v_1$ = 0m/s

we draw the initial condition of slender as shown in the attached file 1

Now consider the instantaneous center at C

Write the expression to calculate the kinetic energy at initial position ($K.E_1$)

$K.E_1 = \frac{1}{2}m{v_1}^2$

substitute the values in the above expression

$K.E_1 = 0$

Write the expression to calculate the Potential energy at initial position ($P.E_1$)

$P.E_1 = mgh_1$

here, $h_1(\frac{4.5}{2})$ is the position of the center of mass in initial position

Substitute the values in the above expression

$P.E_1 = 15 \times 9.81 \times \frac{4.5}{2}$

= 331.088Nm

the condition of the slender at the final position is as shown in the second file attached

check other files for extra details