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,

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 18.1, 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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 18.1, Problem 18.34P

Chapter 18.1, Problem 18.36P

Students have asked these similar questions

Two identical giant flywheels are on 2 identical slopes at an angle alpha = 20 deg. One flywheel is rolling on its inside shaft of diameter d1 = 3 ft, and the second flywheel is rolling without slipping on its outside diameter d2 = 5 ft. They are both released from rest. The weight of the flywheel is W = 8 lbs Knowing that flywheel 1 attains a speed of v = 7.0 ft/s in t = [t] s, (if t doesn't show take any t between 5 and 10 sec) find the radius of gyration of the flywheels, following those steps: b. Find omega final c. Find the angular impulse at the point of contact between the shaft and the slope. d. Write the formula to find the final momentum. e. Solve for k, using the principle of angular impulse and momentum

Denoting, respectively, by w, HO and T the angular velocity, the angular momentum, and the kinetic energy of a rigid body with a fixed point O, (a) ) prove that ) show that the angle 0 between w and HO will always be acute.

A 48-kg advertising panel of length 2a = 2.4 m and width 2b = 1.6 m is kept rotating at a constant rate w1 about its horizontal axis by a small electric motor attached at A to frame ACB. This frame itself is kept rotating at a constant rate w2 about a vertical axis by a second motor attached at C to the column CD. Knowing that the panel and the frame complete a full revolution in 6 s and 12 s, respectively, express, as a function of the angle 0, the dynamic reaction exerted on column CD by its support at D.

Chapter 18 Solutions

Vector Mechanics For Engineers

Ch. 18.1 - Prob. 18.1P 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 the...Ch. 18.1 - Prob. 18.5P Ch. 18.1 - A solid rectangular parallelepiped of mass m has a...Ch. 18.1 - Solve Prob. 18.6, assuming that the solid...Ch. 18.1 - Prob. 18.8P Ch. 18.1 - Determine the angular momentum HD of the disk of...Ch. 18.1 - Prob. 18.10P

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.