Concept explainers
Values of
Answer to Problem 13.111P
Values of
Explanation of Solution
Given information:
The altitude of the space vehicle at point A, ha = 225mi.
The altitude of the space vehicle at point B, hb = 40mi.
Radius of earth, R = 3960mi.
Calculation:
The radius of the orbit at point A,
The radius of the orbit at point B,
Velocity in circular orbit at point A,
The kinetic energy at point A,
Potential energy at point A,
The kinetic energy at point B,
Potential energy at point B,
Law of conservation of energy,
Conservation of angular momentum between A and B,
Now from equation 1, putting the value of vb.
From equation 2
The energy expenditure,
The energy expenditure at point A,
Additional energy at point A,,
Kinetic energy at point A,
Potential energy at point A,
The kinetic energy at point B,
Potential energy at point B,
Law of conservation of energy,
Conservation of angular momentum between A and B,
Want to see more full solutions like this?
Chapter 13 Solutions
Vector Mechanics For Engineers
- Gravitational Slingshot Often in designing orbits for satellites, people use what is termed a "gravitational slingshot effect." The idea is as follows: A satellite of mass m; and speed v,i circles around a planet of mass m, that is moving with speed v in the opposite direction. See the diagram below: Although the satellite never touches the planet, this interaction can still be treated as a collision because of the gravitational interaction between the planet and satellite during the slingshot. Since gravity is a conservative force, the collision is elastic. Use an x-axis with positive pointing to the right. Solve for the unknowns below algebraically first, then use the following values for the parameters. m, = 2.40E+24 kg m; = 880 kg Viz = 3.050E+3 m/s Vpiz = -6.10E+3 m/s Solve for the final velocity of the satellite after the collision.arrow_forwardFor a perfectly elastic collision, u1+v1=u2+v2, or alternatively, u2−u1=v1−v2. If object 2 is initially at rest, then u2=0. Then v1−v2=−u1. However, for a partially elastic collision the relative velocity after the collision will have a smaller magnitude than the relative velocity before the collision. We can express this mathematically as v1−v2=−ru1, where r (a number less than one) is called the coefficient of restitution. For some kinds of bodies, the coefficient r is a constant, independent of v1 and v2. Show that in this case the final kinetic energy of the motion relative to the center of mass is less than the initial kinetic energy of this motion by a factor of r2. Furthermore, derive expressions for v1 and v2 in terms of u1 and r.arrow_forwardThree identical point masses of m =0.2 (kg) are moving at a constant velocity v =20 (m/s) equidistant from each other on a circular orbit of radius R = 0.3 (m). What is the total angular momentum (kg.m²/s) of the three point masses relative to point A at the moment shown in the figure. Point A is 2R away from the center. m 2R m a: m A) 0.9 В) 1.2 С) 1.8 D) 3.0 E) 3.6arrow_forward
- The pilot of an airplane carrying a package of mail to a remote outpost wishes to release the package at the right moment to hit the recovery location A. What angle θ with the horizontal should the pilot’s line of sight to the target make at the instant of release? The airplane is flying horizontally at an altitude of 178 m with a velocity of 239 km/h.arrow_forwardThree identical point masses of m = 0.1 (kg) are moving at a constant velocity v=10 (m/s) equidistant from each other on a circular orbit of radius R = 0.4 (m). What is the total angular momentum (kg.m²/s) of the three point masses relative to point A at the moment shown in the figure. Point A is 2R away from the center. m 2R A m R m A) 0.9 В) 1.2 С) 1.8 D) 3.0 E) 3.6arrow_forwardA Japanese spacecraft Hayabusa-2 landed on an asteroid Ryugu on 21st February 2019 in an attempt to collect a sample of rock from the surface. This mission will help to understand the history of the formation of our solar system. Prior to close approach, Hayabusa-2 fired its rocket to move from rest in free space. Right down the rocket equation of motion and determine at its maximum momentum, the fraction of its mass to the original mass Mo.arrow_forward
- A rocketship has 9 modules each with a mass of 15 200 kg and moves at a speed of 7.0 km/s. One of the modules is explosively propelled away from the rocketship at a speed of 1350 km/h with respect to the rocketship, opposite in direction from the original travel direction of the rocket ship.What is the resulting change in the speed of the rocketship?arrow_forwardRequired information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A 75-Mg boxcar A is moving in a railroad switchyard with a velocity of 12.5 km/h toward cars Band C, which are both at rest with their brakes off at a short distance from each other. Car Bis a 30-Mg flatcar supporting a 40-Mg container, and car Cis a 70-Mg boxcar. As the cars hit each other, they get automatically and tightly coupled. v km/h A C В NOP Determine the velocity of car A immediately after each of the two couplings, assuming that the container slides after the first coupling but hits a stop before the second coupling occurs. km/h →. The velocity of car A after the first coupling is | The velocity of car A after the second coupling is km/h +.arrow_forwardA 40-Mg boxcar A is moving in a railroad switchyard with a velocity of 9 km/h toward cars B and C , which are both at rest with their brakes off at a short distance from each other. Car B is a 25-Mg flatcar supporting a 30-Mg container, and car C is a 35-Mg boxcar. As the cars hit each other they get automatically and tightly coupled. Determine the velocity of car A immediately after each of the two couplings, assuming that the container (a) does not slide on the flatcar, (b) slides after the first coupling but hits a stop before the second coupling occurs, (c) slides and hits the stop only after the second coupling has occurred.arrow_forward
- Three identical point masses of m = 0.3 (kg) are moving at a constant velocity v =10 (m/s) equidistant from each other on a circular orbit of radius R= 0.2 (m). What is the total angular momentum (kg.m/s) of the three point masses relative to point A at the moment shown in the figure. Point A is 2R away from the center. m 2R m marrow_forwardIn Prob. 13.109, a space vehicle was in a circular orbit at an altitude of 225 mi above the surface of the earth. To return to earth it decreased its speed as it passed through A by firing its engine for a short interval of time in a direction opposite to the direction of its motion. Its resulting velocity as it reached point B at an altitude of 40 mi formed an angle fB = 60° with the vertical. An alternative strategy for taking the space vehicle out of its circular orbit would be to turn it around so that its engine pointed away from the earth and then give it an incremental velocity DvA toward the center O of the earth. This would likely require a smaller expenditure of energy when firing the engine at A, but might result in too fast a descent at B. Assuming that this strategy is used, use computational software to determine the values of fB and vB for an energy expenditure ranging from 5 to 100 percent of that needed in Prob. 13.109. 13.109. A space vehicle is in a circular…arrow_forwardA satellite is in a circular orbit around Mars. It has a constant altitude and constant speed. The acceleration of the satellite is: tangential - direction opposite to the velocity radial - directed towards Mars O radial - directed away from Mars tangential - along the velocity zeroarrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY