Concept explainers
The uniform rectangular block shown is moving along a frictionless surface with a velocity
Fig. P17.115
Find the magnitude of the velocity
Answer to Problem 17.115P
The magnitude of the velocity
Explanation of Solution
Given information:
The length
The width
Calculation:
Write the equation of centroidal moment of inertia
Find the one half of the diagonal distance
Substitute 200 mm for a and 100 mm for b.
Before impact, let
Here, magnitude of velocity of the rectangular block is
After impact, the rectangular block rotates about small obstruction at B. Therefore,
Let
Find the equation of velocity
Consider the principle of impulse and momentum.
Sketch the impulse and momentum diagram of the rectangular block as shown in Figure (1).
Take moment about B (positive sign in clockwise direction).
Substitute
Substitute
Sketch the free body diagram of the rectangular block after impact (position 2) and final position (position 3) as shown in Figure (2).
Write the equation of velocity
Refer Figure (2),
Find the angle
Substitute 200 mm for a and 100 mm for b.
Find the distance (h).
Substitute 0.1118 m for d and
At position 3, the angular velocity
Write the equation of the potential energy
Write the equation of the kinetic energy
Substitute
Substitute
Write the equation of the potential energy
The kinetic energy of the system at final position
Consider the conservation of energy.
Substitute
Substitute 200 mm for a, 100 mm for b, 0.1118 m for d,
Find the the magnitude of the velocity
Substitute 200 mm for a, 100 mm for b, and
Thus, the magnitude of the velocity
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