Two small disks A and B of mass 3 kg and 1.5 kg, respectively, may slide on a horizontal, frictionless surface. They are connected by a cord, 600 mm long, and spin counterclockwise about their mass center G at the rate of 10 rad/s. At t = 0, the coordinates of G are
Fig. P14.53 and P14.54
(a)
Find the velocity of A and B after the cord breaks.
Answer to Problem 14.53P
The velocity of A after the cord breaks is
The velocity of B after the cord breaks is
Explanation of Solution
Given information:
The mass
The mass
The cord length AB is
The rate of spin
The coordinates of G,
The velocity
The distance b is
Calculation:
Sketch the disk A and B as shown in Figure 1.
Refer to Figure 1.
The small disks A and B of mass
At location G,
Find the total mass (m) using the relation as follows:
Substitute
Substitute
Find the linear momentum using the relation as follows:
Substitute
Find the angular moment about G using the equation as follows:
Substitute
Find the angular moment about G using the equation as follows:
Refer problem 14.27,
Substitute
Find the kinetic energy
Refer to equation 14.29 in section 14.2A Kinetic energy of a System of particles in the textbook.
Substitute
Sketch the system as shown in Figure 2.
Write the conservation of linear momentum as follows:
Substitute
Substitute
Equate the coefficient i as follows:
Equate the coefficient j as follows:
Express the conservation of energy as follows:
Find the velocity
Substitute
Substitute
Apply the quadratic formula as follows:
Substitute 1 for a, 1.92 for b, and
Thus, the velocity of A after the cord breaks is
Find the velocity
Substitute
The velocity
Find the velocity
Thus, the velocity of B after the cord breaks is
(b)
Find the distance a from the y axis to the path of A.
Answer to Problem 14.53P
The distance a from the y axis to the path of A is
Explanation of Solution
Calculation:
Find the distance a from the y axis to the path of A using the relation:
Substitute
Substitute
Thus, the distance a from the y axis to the path of A is
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Chapter 14 Solutions
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