Concept explainers
A system consists of three identical 19.32-lb particles A, B, and C. The velocities of the particles are, respectively, vA = vA j, vB = vBi, and vC = vCk, and the magnitude of the linear momentum L of the system is 9 lb · s. Knowing that HG = HO, where HG is the angular momentum of the system about its mass center G and HO is the angular momentum of the system about O, determine (a) the velocities of the particles, (b) the angular momentum of the system about O.
Fig. P14.11 and P14.12
(a)
Find the velocity of particles.
Answer to Problem 14.12P
The velocity of particle A is
The velocity of particle B is
The velocity of particle C is
Explanation of Solution
Given information:
The velocity of particles is as follows:
The linear momentum (L) of the system is
Calculation:
The mass of three particles is equal.
Determine the weight of the identical particle.
Here, W is weight of each particle and g is acceleration due to gravity.
Substitute
Write the position vectors for the particles based on the given coordinate system:
Determine position vector
Here,
Substitute
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
Express the angular momentum about point O as follows:
Calculate the angular momentum about point G using the relation:
Here,
Subtract the angular momentum
L is parallel to
Substitute
Find the velocity of particles using the relation as follows:
Substitute
Resolve the components and solve
Find the velocity of particle A using the Equation:
Thus, the velocity of particle A is
Find the velocity of particle B using the Equation:
Thus, the velocity of particle B is
Find the velocity of particle C using the Equation:
Thus, the velocity of particle C is
(b)
Find the angular momentum of the system about O.
Answer to Problem 14.12P
The angular momentum of the system about O is
Explanation of Solution
Calculation:
Calculate the angular momentum about point H using the relation:
Here,
Substitute
Thus, the angular momentum of the system about O is
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Chapter 14 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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