Concept explainers
The kinetic energy of the space probe after its collision with the meteorite.
Answer to Problem 18.54P
The kinetic energy of the space probe after its collision with the meteorite is
Explanation of Solution
Given information:
The weight of the space probe is
Write the expression of the mass of the meteorite.
Here, weight of the meteorite is
Write the expression of the mass of the space probe.
Here, weight of the meteorite is
Write the expression of angular momentum of the meteorite about
Here, the distance of point A is
Write the Expression of the moment of inertia along x-axis.
Here, the radius of gyration of the space probe along x-axis is
Write the Expression of the moment of inertia along the y-axis.
Here, the radius of gyration of the space probe along y-axis is
Write the Expression of the moment of inertia along z-axis.
Here, the radius of gyration of the space probe along z-axis is
Write the expression of angular momentum of space probe.
Here, moment of inertia along x-axis is
Substitute
Here, angular velocity along x-axis is
Write the expression of kinetic energy of the space probe.
Substitute
Calculation:
Substitute
Substitute
Write the expression that shows the relation between linear momentum of meteorite and the space probe.
Here, the initial velocity along x-axis is
Substitute
Substitute
Substitute
Substitute
The angular momentum of the space probe is
Write the expression of the relation between
Substitute
Compare x-component of Equation (IX) on both side.
Compare y-component of Equation (XIV) on both side.
Compare z-component of Equation (XIV) on both side.
Substitute
Substitute
Conclusion:
Thus, the kinetic energy is
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Chapter 18 Solutions
Vector Mechanics For Engineers
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