Concept explainers
The uniform rods AB and BC are of mass 3 kg and 8 kg, respectively, and collar C has a mass of 4 kg. Knowing that at the instant shown the velocity of collar C is 0.9 m/s downward, determine the velocity of point B after rod AB has rotated through 90°.
Fig. P17.45
Find the velocity of point B after rod AB has rotated through
Answer to Problem 17.45P
The velocity of point B after rod AB has rotated through
Explanation of Solution
Given information:
The mass
The mass
The mass
The velocity
Calculation:
Refer the system shown.
Find the length
Find the mass moment of inertia
Substitute 3 kg for
Find the mass moment of inertia
Substitute 8 kg for
Consider the position 1 of the system as shown.
Sketch the position 1 as shown in Figure (1).
Refer Figure (1).
Since
Find the velocity
Here,
Substitute 0.9 m/s for
Consider rod AB rotates about point A.
Find the angular velocity of rod AB
Substitute 0.9 m/s for
Find the velocity of rod AB using the kinematics.
Substitute 150 mm for
Find the kinetic energy
Substitute 3 kg for
Refer Figure (1),
Consider the datum is a level line through point A.
Find the potential energy
Substitute
Substitute 3 kg for
Consider the position 2 of the system when the rod AB has rotated
Sketch the position 2 as shown in Figure (2).
Consider rod AB rotates about point A.
Find the angular velocity of rod AB
Substitute 150 mm for
Find the velocity of rod AB using the kinematics.
Substitute 150 mm for
Consider the point C is the instantaneous center of rod BC. Therefore the velocity at point C at position 2
Find the angular velocity of rod BC
Substitute 390 mm for
Find the velocity of rod AB using the kinematics.
Substitute 390 mm for
Find the kinetic energy
Substitute 3 kg for
Refer Figure (1).
Consider the datum is a level line through point A.
Find the potential energy
Substitute
Substitute 3 kg for
Consider the conservation of energy equation:
Find the velocity of point B
Substitute
Substitute
Thus, velocity of point B after rod AB has rotated through
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