Concept explainers
Two small disks A and B of mass 2 kg and 1 kg, respectively, may slide on a horizontal and frictionless surface. They are connected by a cord of negligible mass and spin about their mass center G. At t = 0, G is moving with the velocity
(a)
The initial velocity,
Answer to Problem 14.54P
Explanation of Solution
Given information:
Mass of the disk A,
Mass of the disk B,
At t=0,
Co-ordinates of G are
Velocity of A,
Velocity,
Distance
Firstly, calculate for initial condition:
The free body diagram for initial condition is as follows:
The distance G from points A and B,
And,
Now, considering linear momentum,
Hence, angular momentum of both the disc about G,
Now, kinetic energy of the component is,
Calculation:
Using conservation of mass of linear momentum,
(b)
The length of cord initially connecting the two disks.
Answer to Problem 14.54P
Explanation of Solution
Given information:
Mass of the disk A,
Mass of the disk B,
At t=0,
Co-ordinates of G are
Velocity of A,
Velocity,
Distance
Firstly, calculate for initial condition:
The free body diagram for initial condition is as follows:
The distance G from points A and B,
And,
Now, considering linear momentum,
Hence, angular momentum of both the disc about G,
Now, kinetic energy of the component is,
Calculation:
Using conservation of mass of linear momentum,
Conservation of angular momentum of both the disc about point O,
Now, applying law of conservation of energy:
Dividing equation (2) by equation (1);
Now, substituting the value of ? in equation (1);
(c)
The rate in rad/s at which the disks were spinning about G.
Answer to Problem 14.54P
Explanation of Solution
Given information:
Mass of the disk A,
Mass of the disk B,
At t=0,
Co-ordinates of G are
Velocity of A,
Velocity,
Distance
Firstly, calculate for initial condition:
The free body diagram for initial condition is as follows:
The distance G from points A and B,
And,
Now, considering linear momentum,
Hence, angular momentum of both the disc about G,
Now, kinetic energy of the component is,
Calculation:
Using conservation of mass of linear momentum,
Conservation of angular momentum of both the disc about point O,
Now, applying law of conservation of energy:
Dividing equation (2) by equation (1);
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Chapter 14 Solutions
Vector Mechanics for Engineers: Dynamics
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