Concept explainers
For the system of particles of Prob. 14.13, determine (a) the position
Fig. P14.13
(a)
Find the position vector of the mass center of the system.
Answer to Problem 14.14P
The position vector of the mass center of the system is
Explanation of Solution
Given information:
The mass of the particles A is
The mass of the particles B is
The mass of the particles C is
The position vector is
The mass center is G.
Calculation:
Find the position vectors from point O to each satellite in meters.
Refer to figure P14.13 in the textbook.
Express the position vector point A as follows:
Express the position vector point B as follows:
Express the position vector point C as follows:
Determine the mass center G of the system using the relation:
Here,
Substitute
Thus, the position vector of the mass center of the system is
(b)
Find the linear momentum of the system.
Answer to Problem 14.14P
The linear momentum of the system is
Explanation of Solution
Calculation:
Express the linear momentum of particle A as follows:
Express the linear momentum of particle B as follows:
Express the linear momentum of particle C as follows:
Find the linear momentum of the system using the relation:
Substitute
Thus, the linear momentum of the system is
(c)
Find the angular momentum of the system about G and also verify this problem and to problem 14.13 satisfy the Equation given in problem 14.27.
Answer to Problem 14.14P
The angular momentum of the system about G is
Explanation of Solution
Calculation:
Find the position vector from the particles
Here,
Substitute
Find the position vector from the particles
Here,
Substitute
Find the position vector from the particles
Here,
Substitute
Calculate the angular momentum about point G using the relation:
Here,
Substitute
Thus, the angular momentum of the system about G is
Find the value of
Substitute
Show that the
Express the angular momentum about point O as follows:
Substitute
Hence, the
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Chapter 14 Solutions
VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
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