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

Step-by-step 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 = (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((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 * 9.81 * (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