Explanation Given information: The mass of satellite is 1200 kg , the initial angular velocity is ω 0 = ( 0.050 rad / s ) i + ( 0.075 rad / s ) k , the radius of gyration of the satellite are k x = 1.120 m , k y = 1.200 m , and k z = 0.900 m and the thrust produced by each jet is 50 N . Write the expression for the moment of inertia about x axis. I x = m k x 2 ...... (I) Write the expression for the moment of inertia about y axis. I y = m k y 2 ...... (II) Write the expression for the moment of inertia about z axis. I z = m k z 2 ...... (III) The initial angular velocity of components. ω x = 0.05 rad / s ω y = 0 ω z = 0.075 rad / s Write the expression for the initial angular momentum. ( H G ) 1 = I x ( ω x ) 1 i + I y ( ω y ) 1 j + I z ( ω z ) 1 k ..... (IV) The final angular velocity of components. ω x = 0 ω y = 0 ω z = 0 ...... (V) Write the expression for the final angular momentum. ( H G ) 2 = I x ( ω x ) 2 i + I y ( ω y ) 2 j + I z ( ω z ) 2 k ...... (VI) Write the position vector A with respect of G . r A / G = ( 1.2 i + 1.8 k ) m ..... (VII) Write the position vector B with respect of G . r B / G = ( 1.2 i − 1.6 k ) m ...... (VIII) Write the principle of impulse and momentum. ( H G ) 1 + r A / G ( F Δ t ) A j + r B / G ( F Δ t ) B j = ( H G ) 2 ..... (IX) Write the expression for the operating time of jet A . Δ t A = ( F Δ t ) A F ...... (X) Here, the thrust force is F .the momentum at point A is ( F Δ t ) A . Write the expression for the operating time of jet B . Δ t B = ( F Δ t ) B F ...... (XI) Here, the thrust force is F .the momentum at point A is ( F Δ t ) A . Calculation: Substituting 1200 kg for m and 1.12 m for k x in Equation (I): I x = 1200 kg × ( 1 .12 m ) 2 = 1200 kg × 1.2544 m 2 = 1505.28 kg ⋅ m 2 Substituting 1200 kg for m and 1.2 m for k y in Equation (II): I y = 1200 kg × ( 1 .2 m ) 2 = 1200 kg × 1.44 m 2 = 1728 kg ⋅ m 2 Substituting 1200 kg for m and 0.9 m for k z in Equation (III): I z = 1200 kg × ( 0.9 m ) 2 = 1200 kg × 0.81 m 2 = 972 kg ⋅ m 2 Substituting 1505.28 kg ⋅ m 2 for I x , 1728 kg ⋅ m 2 for I y , 972 kg ⋅ m 2 for I z , 0.05 rad / s for ( ω x ) 1 , 0 for ( ω y ) 1 and 0.075 rad / s for ( ω z ) 1 in Equation (IV): ( H G ) 1 = [ 1505 To determine (b) The change in velocity of mass center.

12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Chapter 18.1, Problem 18.35P

To determine

(a)

The operating timer of jet A.

The operating time of jet B.

To determine

(b)

The change in velocity of mass center.

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Chapter 18.1, Problem 18.34P

Chapter 18.1, Problem 18.36P

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