Concept explainers
(a)
The component
(a)
Answer to Problem 18.34P
The component
Explanation of Solution
Given information:
The weight of the space probe
The radius of gyration along x axis
The radius of gyration along y axis
The radius of gyration along z axis
The weight of the meteorite (w) is 5 oz.
The angular velocity
The change in velocity of the mass center of the probe
The width of the side panel from center to point A (b) is 9 ft.
The length of the panel from center to point A (l) is 0.75 ft.
The speed is reduced by 25 percent.
Calculation:
Calculate the mass of the space probe
Here, g is the acceleration due to gravity.
Substitute
Calculate the mass of the meteorite (m) using the formula:
Substitute
Write the relative position vector
Substitute 9 ft for b and 0.75 ft.
Write the expression for the velocity
Calculate the initial liner momentum of the meteorite using the relation:
Substitute
Calculate the moment about origin
Substitute
The speed is reduced to 25 percent.
Calculate the final liner momentum of the meteorite using the relation:
Substitute
Calculate the final linear momentum of meteorite and its moment about the origin using the relation:
Substitute
The initial linear momentum of the space probe
Calculate the final linear momentum of the space probe using the relation:
Substitute
Substitute -0.675 in./s for
Calculate the final angular momentum of the space probe
Substitute
Write the expression for the conservation of linear momentum of the probe plus the meteorite as follows:
Substitute
Equate the i component from the Equation (1).
Equate j component from the Equation (1).
Equate k component from the Equation (1).
Write the expression for the conservation of angular momentum about the origin as follows:
Substitute
Equate i component from the Equation (2).
Equate k component from the Equation (2).
Substitute –4,840 ft/s for
Thus, the component
(b)
The relative velocity
(b)
Answer to Problem 18.34P
The relative velocity
Explanation of Solution
Given information:
The weight of the space probe
The radius of gyration along x axis
The radius of gyration along y axis
The radius of gyration along z axis
The weight of the meteorite (w) is 5 oz.
The angular velocity
The change in velocity of the mass center of the probe
The width of the side panel from center to point A (b) is 9 ft.
The length of the panel from center to point A (l) is 0.75 ft.
The speed is reduced by 25 percent.
Calculation:
Find the velocity along z direction:
Equate j component from the equation (2).
Substitute -2160 ft/s for
Calculate the relative velocity
Substitute -2160 ft/s for
Thus, the relative velocity
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Chapter 18 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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