(a) Explanation Given Information: The mass ( m ) of the satellite is 2500 kg. The height ( h ) of the satellite is 2.4 m. The base side ( B ) of the satellite is 1.2 m. The radii of gyration about x ( k x ) , y ( k y ) and z ( k z ) axis are 0.9 m, 0.98 m and 0.9 m respectively. The satellite is equipped with a main thrusters ( F ) is 500 N. The thrusters in A ( F A ) , B ( F B ) , C ( F C ) and D ( F D ) are 20 N. The thrusters ( Δ t ) A and B are activated for 2 sec. The satellite ( ω 0 ) is spinning at the rate of 36 rev/h . Calculation: Calculate the angular velocity ( ω 0 ) : ω 0 = 36 rev/h ( 2 π rev ) ( 1 h 3 , 600 sec ) = 0.062832 rad/s Calculate the moment of inertia ( I x ) about x axis: I x = m k x 2 Substitute 2500 kg for m and 0.9 m for k x . I x = 2500 × ( 0.9 ) 2 = 2025 kg ⋅ m 2 Calculate the moment of inertia I y about y axis: I y = m k y 2 Substitute 2,500 kg for m and 0.98 m for k y . I y = 2500 × ( 0.98 ) 2 = 2401 kg ⋅ m 2 Calculate the moment of inertia I z about z axis: I z = I x = 2025 kg ⋅ m 2 Calculate the initial angular moment ( H G ) 0 of the system about the mass centre. ( H G ) 0 = I y ω 0 j Substitute 0.062832 rad/s for ω 0 and 2401 kg ⋅ m 2 for I y . ( H G ) 0 = 2401 × 0.062832 j = ( 150.86 kg ⋅ m 2 / s ) j Show the distance a and b as in Figure (1). Calculate the value of ( a ) in Figure (1): a = B 2 Substitute 1.2 m for B . a = 1.2 2 = 0.6 m Calculate the value of ( b ) in Figure (1): b = a + B cos 45 ° Substitute 1.2 m for B and 0.6 m for a . b = 0.6 + 1.2 cos 45 ° = 1.4485 m Calculate the moment ( M G ) about the mass centre: M G = − b ( F A + F B ) i Substitute 1.4485 m for b and 20 N for F A and F B . M G = − 1.4485 ( 20 + 20 ) i = − ( 57.941 N ⋅ m ) i Calculate the angular moment ( H G ) of the system after 2 sec about the mass centre. H G = ( H G ) 0 + M G ( Δ t ) Substitute − ( 57.941 N ⋅ m ) i for M G , 2 sec for Δ t and ( 150.86 kg ⋅ m 2 / s ) j for ( H G ) 0 (b) To determine The rate ( φ ˙ ) of precession. (c) To determine The rate ( ψ ˙ ) of spin.

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

12th Edition

ISBN: 9781260916942

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 18, Problem 18.155RP

(a)

To determine

The precession axis of the satellite.

(b)

To determine

The rate (φ˙) of precession.

(c)

To determine

The rate (ψ˙) of spin.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 18, Problem 18.154RP

Chapter 18, Problem 18.156RP

Students have asked these similar questions

PUNTO 4. calculate their DoF using Gruebler's formula. PUNTO 5. Ground

PUNTO 2. PUNTO 3. calculate their DoF using Gruebler's formula. III IA

calculate their DoF using Gruebler's formula. PUNTO 6. PUNTO 7. (Ctrl)

Chapter 18 Solutions

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

Ch. 18.1 - A thin, homogeneous disk of mass m and radius r...Ch. 18.1 - Prob. 18.2P Ch. 18.1 - Prob. 18.3P Ch. 18.1 - A homogeneous disk of weight W = 6 lb rotates at...Ch. 18.1 - A homogeneous disk of mass m = 8 kg rotates at the...Ch. 18.1 - A solid rectangular parallelepiped of mass m has a...Ch. 18.1 - Prob. 18.8P Ch. 18.1 - Determine the angular momentum HD of the disk of...Ch. 18.1 - Prob. 18.10P Ch. 18.1 - Determine the angular momentum HO of the disk of...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The precession axis of the satellite.

Solution Summary: The author explains the satellite's precession axis, the radii of gyration, and the thrusters.

Concept explainers

Videos

The precession axis of the satellite.

The rate (φ˙) of precession.

The rate (ψ˙) of spin.

Want to see the full answer?

Chapter 18 Solutions