Concept explainers
A uniformly loaded square crate is released from rest with its comer D directly above A; it rotates about A until its comer B strikes the floor, and then rotates about B. The floor is sufficiently rough to prevent slipping and the impact at B is perfectly plastic. Denoting by
(a)
The angular velocity of the crate immediately after B strikes the floor.
Answer to Problem 17.118P
The angular velocity of the square box after striking B on the floor will be
Explanation of Solution
Given:
Square box which is uniformly loaded is released on the floor when its corner D is directly above the A. square box tends to rotate till it strikes the floor. The floor is made anti-slipping and impact at B is perfectly plastic.
Concept:
According to impulse momentum principle,
Calculation:
Let’s consider,
M = mass of a square box.
C = length of the side.
Moment of inertia =
We can say,
Taking moment at A,
Conclusion:
The angular velocity of the square box after striking B on the floor will be
(b)
The fraction of kinetic energy lost during the impact.
Answer to Problem 17.118P
The fractions of energy lost during impact conditions are.
Explanation of Solution
Given:
Square box which is uniformly loaded is released on the floor when its corner D is directly above the A. square box tends to rotate till it strikes the floor. The floor is made anti-slipping and impact at B is perfectly plastic.
Calculation:
Kinetic energy before impact,
Similarly kinetic energy after impact,
Combining E1 and E2 to find fraction of energy cost,
Conclusion:
The fraction of energy lost during impact conditions is
(c)
The angle through which the crater will rotate after B strikes the floor.
Answer to Problem 17.118P
Angle made by corner A of square box and floor will be 1.500
Explanation of Solution
Given:
Square box which is uniformly loaded is released on the floor when its corner D is directly above the A. square box tends to rotate till it strikes the floor. The floor is made anti-slipping and impact at B is perfectly plastic.
Concept:
As per law of conservation of energy before impact,
And that of after impact,
Before impact,
After impact,
As,
But
Therefore, from geometry,
Equating both equations of h3
Conclusion:
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Chapter 17 Solutions
Vector Mechanics For Engineers
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