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.

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

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

The wall of a furnace has a thickness of 5 cm and thermal conductivity of 0.7 W/m-°C. The inside surface is heated by convection with a hot gas at 402°C and a heat transfer coefficient of 37 W/m²-°C. The outside surface has an emissivity of 0.8 and is exposed to air at 27°C with a heat transfer coefficient of 20 W/m²-ºC. Assume that the furnace is inside a large room with walls, floor and ceiling at 27°C. Show the thermal circuit and determine the heat flux through the furnace wall. h₁ T₁ k -L T. sur ho E

Turbomachienery . GIven: vx = 185 m/s, flow angle = 60 degrees, R = 0.5, U = 150 m/s, b2 = -a3, a2 = -b3 Find: velocity triangle , a. magnitude of abs vel leaving rotor (m/s) b. flow absolute angles (a1, a2, a3) 3. flow rel angles (b2, b3) d. specific work done e. use code to draw vel. diagram Use this code for plot % plots Velocity Tri. in Ch4 function plotveltri(al1,al2,al3,b2,b3) S1L = [0 1]; V1x = [0 0]; V1s = [0 1*tand(al3)]; S2L = [2 3]; V2x = [0 0]; V2s = [0 1*tand(al2)]; W2s = [0 1*tand(b2)]; U2x = [3 3]; U2y = [1*tand(b2) 1*tand(al2)]; S3L = [4 5]; V3x = [0 0]; V3r = [0 1*tand(al3)]; W3r = [0 1*tand(b3)]; U3x = [5 5]; U3y = [1*tand(b3) 1*tand(al3)]; plot(S1L,V1x,'k',S1L,V1s,'r',... S2L,V2x,'k',S2L,V2s,'r',S2L,W2s,'b',U2x,U2y,'g',... S3L,V3x,'k',S3L,V3r,'r',S3L,W3r,'b',U3x,U3y,'g',...... 'LineWidth',2,'MarkerSize',10),... axis([-1 6 -4 4]), ... title('Velocity Triangle'), ... xlabel('x'),ylabel('y'), grid

To save fuel during the heating season it is suggested that glass windows be covered at night with a 1.2 cm layer of polystyrene. Estimate the percent savings in energy and discuss the feasibility of this idea. Show the thermal circuit with and without the insulation panel. Consider a typical case of 0.2 cm thick window glass with inside and outside heat transfer coefficients of 6 and 32 W/m²-ºC. Lg←←Lp h T₁ T。 g kp insulation panel

Chapter 18 Solutions

Vector Mechanics for Engineers: Dynamics

Ch. 18.1 - Prob. 18.1P Ch. 18.1 - A thin rectangular plate of weight 15 Ib rotates...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.