Concept explainers
For the system of particles of Prob. 14.13, determine (a) the position
(a)
The position vector of the mass centre, G of the system.
Answer to Problem 14.14P
Explanation of Solution
Given information:
Mass of A
Mass of B
Mass of C
Velocity of A
Velocity of B
Velocity of C
We can find the position vectors at centre O with the help of figure at points A, B and C.
Position vector at A,
Position vector at B,
Position vector at C,
The position vector at mass centre G is,
Conclusion:
The position vector of the given system is,
(b)
The linear momentum of the system.
Answer to Problem 14.14P
Explanation of Solution
Given information:
Mass of A
Mass of B
Mass of C
Velocity of A
Velocity of B
Velocity of C
The linear momentum of each particle,
Linear momentum of particle A,
Linear momentum of particle B,
Linear momentum of particle C,
Now, total linear momentum of the system,
Conclusion:
Linear moment of the system,
(c)
The angular momentum of system about point ‘G’. And also to show that the answer is verify the equation
Answer to Problem 14.14P
Explanation of Solution
Given information:
Mass of A
Mass of B
Mass of C
Velocity of A
Velocity of B
Velocity of C
We can find the position vectors at centre O with the help of figure at points A, B and C.
Position vector at A,
Position vector at B,
Position vector at C,
The position vector at mass centre G is,
Position vector relative to the mass centre,
Now, angular momentum about G,
Now, we show that this answer is verified the given formula:
Now, the angular momentum about G is added in the above obtained equation:
Now, Angular moment of all the particles about point O,
Hence the above obtained values verify the equation:
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Chapter 14 Solutions
Vector Mechanics For Engineers
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