Question

The 10-kg slender bar AB, shown in the figure, has a length of 2 m. A block of negligible mass, pinned freely to end A, is confined to move along the smooth circular groove with its centre at O. End B rests on the floor for which the coefficient of kinetic friction

μ
k
=
0.4
. If the bar is released from rest when
θ
=
30
∘
,

(a) Identify the type of ensuing motion of the bar,

(b) Draw the free body, kinematic and kinetic diagrams for the bar,

(c) Set up a global reference axes system, and write down the relevant kinetic and kinematic relationships with respect to reference axes system, and

(d) Determine the angular acceleration of the bar and the reaction forces at ends A and B.

Answer 1

• (a) The ensuing motion of the bar is a combination of rotational and translational motion.

• (b) The free body diagram (FBD) for the bar includes the weight acting downward at the center of mass, the normal reaction force at end B perpendicular to the floor, and the friction force at end B opposing the motion.

• (c) Set up a global reference axis system with a horizontal axis in the direction of motion and a vertical axis upward. The relevant relationships are θ = θ0 + ω0t + (1/2)αt^2 for kinematics and ΣF = ma for kinetics.

• (d) The angular acceleration (α) of the bar and the reaction forces at ends A and B cannot be determined without additional information such as the mass distribution and the location of the pivot point.

Step-by-step explanation: