Explanation Given information: The gross weight of the spacecraft is W 0 = 11 , 600 lb . The change in velocity is v 1 − v 0 = 360 ft / s . The fuel consumed rate is W = 1 , 000 lb . Calculation: Calculate the weight of the spacecraft ( W 1 ) as shown below. W 1 = W 0 − W Substitute 11 , 600 lb for W 0 and 1 , 000 lb for W . W 1 = 11 , 600 − 1 , 000 = 10 , 600 lb Sketch the Free Body Diagram of the spacecraft as shown in Figure 1. Refer to Figure 1. Apply the conservation of momentum to the fuel plus the fuel as shown below. m v = ( m − Δ m ) ( v + Δ v ) + ( Δ m ) ( v + Δ v − u ) m v = m v + m Δ v − Δ m v − Δ m Δ v + Δ m v + Δ m Δ v − Δ m u m Δ v − u Δ m = 0 Divide both sides of the Equation into Δ t as shown below. m Δ v Δ t − u Δ m Δ t = 0 m Δ v Δ t = u Δ m Δ t Δ v Δ t = u m Δ m Δ t Substitute − d m d t for Δ m Δ t . d v d t = − u m d m d t Integrate both sides of the Equation and apply the limits as shown below

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

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

Publisher: McGraw-Hill Education

See similar textbooks

Videos

Question

Chapter 14.3, Problem 14.97P

To determine

The relative velocity of the fuel ejected.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.3, Problem 14.96P

Chapter 14.3, Problem 14.98P

Students have asked these similar questions

Problem 11.2 Two swimmers A and B, of mass 75 kg and 50 kg, respectively, dive off the end of a 200-kg boat. Each swimmer has a relative horizontal velocity of 3 m/s when leaving the boat. If the boat is initially at rest, determine its final velocity, assuming that (a) the two swimmers dive simultaneously, (b) swimmer A dives first, (c) swimmer B dives first. Answers: all velocities will be between 0.75 m/s <|V|< 1.4 m/s

The rocket used to launch the 540-kg spacecraft of Prob. 14.95 is redesigned to include two stages A and B , each of mass 9.5 Mg, including 8.9 Mg of fuel. The fuel is again consumed at a rate of 225 kg/s and ejected with a relative velocity of 3600 m/s. Knowing that when stage A expels its last particle of fuel, its casing is released and jettisoned, determine (a) the speed of the rocket at that instant, (b) the maximum speed imparted to the spacecraft.Reference to Problem 14.95:

The rocket engines of a spacecraft are fired to increase its velocity by 450 ft/s. Knowing that 1200 lb of fuel is ejected at a relative velocity of 5400 ft/s, determine the weight of the spacecraft after the firing.

Chapter 14 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 14.1 - A 30-g bullet is fired with a horizontal velocity...Ch. 14.1 - Two identical 1350-kg automobiles A and B are at...Ch. 14.1 - Prob. 14.3P Ch. 14.1 - Prob. 14.4P Ch. 14.1 - Two swimmers A and B, of weight 190 lb and 125 lb,...Ch. 14.1 - A 180-lb man and a 120-lb woman stand side by side...Ch. 14.1 - A 40-Mg boxcar A is moving in a railroad...Ch. 14.1 - Two identical cars A and B are at rest on a...Ch. 14.1 - A 20-kg base satellite deploys three...Ch. 14.1 - For the satellite system of Prob. 14.9, assuming...

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 relative velocity of the fuel ejected.

Solution Summary: The author explains the relative velocity of the fuel ejected and the change in velocity.

Videos

The relative velocity of the fuel ejected.

Want to see the full answer?

Chapter 14 Solutions