Explanation Given: The maximum and minimum distance from center of the Venus is shown in Figure (1). The mass of the Venus M v = 0.816 ( 5.976 × 10 24 kg ) . The gravitational constant is G = 66.73 × 10 − 12 m 3 / kg ⋅ s 2 From Figure (1) write the value for minimum distance O A . r p = 8 Mm 10 6 m 1 Mm = 8 ( 10 6 ) m The minimum distance from the centre of Venus is O A = r p . From Figure (1) write the value for maximum distance O A ' . r a = 8 Mm + 18 Mm 10 6 m 1 Mm = 26 ( 10 6 ) m The maximum distance from the centre of Venus is O A ' = r a . Write the expression for the minimum distance from the centre of Venus. r a = r 0 2 G M ( r 0 υ 0 2 ) − 1 (I) Here, minimum distance from the center of Venus is r 0 and the initial speed of the rocket υ 0 and the gravitational constant is G and mass of the Venus is M . Write the expression for the velocity of rocket in circular orbit. ( υ A ' ' ) = G M v O A ' (II) Here, distance from the center of Venus is O A ' , and the velocity of rocket in circular orbit is ( υ A ' ' ) , the gravitational constant is G and mass of the Venus is M v . Since, O A = r p and O A ' ' = r a . From figure (I) write the expression for the altitude h . h = r p υ p = r a υ a υ A = υ A ( O A ) O A ' (III) Here, h is constant at any positions of the orbit , the speed of the rocket at apogee is υ a , the speed of the rocket at perigee is υ p , r p is the minimum distance from the center of earth or perigee and r a is the orbit maximum distance from the center of earth or apogee. Since, O A = r p . Write the expression for time period of circular orbit. T C = 2 π ( O A ) υ A ' ' (IV) Here, the time period is T , satellite around the circular orbit of radius is r 0 , altitude is h , and velocity of satellite is υ s . Since, O A = r p and O A ' ' = r a . From figure (I) write the expression for period of elliptical orbit. T e = π r p υ p ( r p + r a ) r p r a T e = π O A υ A ( O A + O A ' a ) O A × O A ' (V) Here, period of elliptical orbit is T e , r p is minimum distance from the center of Venus or perigee and r a is the maximum distance from the center of Venus or apogee. Conclusion: Since, r 0 = r p and υ 0 = υ p . Substitute r p for r 0 and υ p for υ 0 in Equation (I). r a = r 0 2 G M v ( r 0 υ 0 2 ) − 1 r a = r p 2 G M v ( r p υ p 2 ) − 1 2 G M v ( r p υ p 2 ) M = r p r a + 1 2 G M v ( r p υ p 2 ) = r p + r a r a υ p = 2 G M v r a r p ( r p + r a ) (VI). Since, υ p = υ A , r p = O A and r a = O A ' . Substitute υ A for υ p , [ 26 ( 10 6 ) m ] for r a , [ 8 ( 10 6 ) m ] for r p , 66.73 × 10 − 12 m 3 / kg ⋅ s 2 for G and 0

Engineering Mechanics: Dynamics (14th Edition)

14th Edition

ISBN: 9780133915389

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 13.7, Problem 128P

To determine

(a) The speed of the rocket at point A' .

(b) the required speed rocket must attain at A after braking.

(c) The periods of both the circular orbit and elliptical orbit.

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Chapter 13.7, Problem 127P

Chapter 13.7, Problem 129P

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(read image) Answer: A = 1192 N

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(read image) Answer: vC = 0.965 ft/sec right

Chapter 13 Solutions

Engineering Mechanics: Dynamics (14th Edition)

Ch. 13.4 - In each case, determine its velocity when t = 2 s...Ch. 13.4 - In each case, determine its velocity at s = 8 m if...Ch. 13.4 - Determine the initial acceleration of the 10-kg...Ch. 13.4 - Write the equations of motion in the x and y...Ch. 13.4 - The motor winds n the cable with a constant...Ch. 13.4 - If motor M exerts a force of F = (10t2 + 100) N on...Ch. 13.4 - A spring of stiffness k = 500 N/m is mounted...Ch. 13.4 - The spring has a stiffness k = 200 N/m and is...Ch. 13.4 - Block B rests upon a smooth surface. If the...Ch. 13.4 - The 6-lb particle is subjected to the action of...

Ch. 13.4 - The two boxcars A and B have a weight of 20 000 lb...Ch. 13.4 - If the coefficient of kinetic friction between the...Ch. 13.4 - If the 50-kg crate starts from rest and achieves a...Ch. 13.4 - If blocks A and B of mass 10 kg and 6 kg...Ch. 13.4 - The 10-lb block has a speed of 4 ft/s when the...Ch. 13.4 - The 10-lb block has a speed of 4 ft/s when the...Ch. 13.4 - The speed of the 3500-lb sports car is plotted...Ch. 13.4 - The conveyor belt is moving at 4 m/s. If the...Ch. 13.4 - The conveyor belt is designed to transport...Ch. 13.4 - Determine the time needed to pull the cord at B...Ch. 13.4 - Cylinder B has a mass m and is hoisted using the...Ch. 13.4 - Block A has a weight of 8 lb and block B has a...Ch. 13.4 - The 2-Mg truck is traveling at 15 m/s when the...Ch. 13.4 - The motor lifts the 50-kg crate with an...Ch. 13.4 - The 75-kg man pushes on the 150-kg crate with a...Ch. 13.4 - The coefficient of kinetic friction is k, and the...Ch. 13.4 - A 40-lb suitcase slides from rest 20 ft down the...Ch. 13.4 - Solve Prob. 13-18 if the suitcase has an initial...Ch. 13.4 - If the coefficient of kinetic friction between...Ch. 13.4 - The conveyor belt delivers each 12-kg crate to the...Ch. 13.4 - The 50-kg block A is released from rest. Determine...Ch. 13.4 - If the supplied force F = 150 N, determine the...Ch. 13.4 - A 60-kg suitcase slides from rest 5 m down the...Ch. 13.4 - Solve Prob. 13-24 if the suitcase has an initial...Ch. 13.4 - The 1.5 Mg sports car has a tractive force of F =...Ch. 13.4 - The conveyor belt is moving downward at 4 m/s. If...Ch. 13.4 - At the instant shown the 100-lb block A is moving...Ch. 13.4 - Determine the velocity of the 200-lb crate when t...Ch. 13.4 - Determine the velocity of the 400-kg crate A when...Ch. 13.4 - The tractor is used to lift the 150-kg load B with...Ch. 13.4 - If the tractor travels to the right with an...Ch. 13.4 - Block A and B each have a mass m. Determine the...Ch. 13.4 - The 4-kg smooth cylinder is supported by the...Ch. 13.4 - The coefficient of static friction between the...Ch. 13.4 - If the spring is unstretched when s = 0 and the...Ch. 13.4 - Neglecting the mass of the rope and pulley, and...Ch. 13.4 - Determine the force in the cable when t = 5 s, if...Ch. 13.4 - An electron of mass m is discharged with an...Ch. 13.4 - The 400-lb cylinder at A is hoisted using the...Ch. 13.4 - What is their velocity at this instant?Ch. 13.4 - Block A has a mass mA and is attached to a spring...Ch. 13.4 - A parachutist having a mass m opens his parachute...Ch. 13.4 - Neglect the mass of the motor and pulleys.Ch. 13.4 - If the force exerted on cable AB by the motor is F...Ch. 13.4 - Blocks A and B each have a mass m. Determine the...Ch. 13.4 - Blocks A and Beach have a mass m. Determine the...Ch. 13.4 - If the board AC pushes on the block at an angle ...Ch. 13.4 - If a horizontal force P = 12lb is applied to block...Ch. 13.4 - A freight elevator, including its load, has a mass...Ch. 13.4 - The block A has a mass mA and rests on the pan B,...Ch. 13.5 - P13-5.Set up the n, t axes and write the equations...Ch. 13.5 - P13-6.Set up the n, b, t axes and write the...Ch. 13.5 - The block rests at a distance of 2 m from the...Ch. 13.5 - Prob. 8FP Ch. 13.5 - A pilot weighs 150 lb and is traveling at a...Ch. 13.5 - The sports car is traveling along a 30 banked road...Ch. 13.5 - If the 10-kg ball has a velocity of 3m/ s when it...Ch. 13.5 - The motorcycle has a mass of 0.5 Mg and a...Ch. 13.5 - Prob. 52P Ch. 13.5 - Prob. 53P Ch. 13.5 - The 2-kg block B and 15-kg cylinder A are...Ch. 13.5 - Determine the maximum constant speed at which the...Ch. 13.5 - Cartons having a mass of 5 kg are required to move...Ch. 13.5 - Prob. 57P Ch. 13.5 - Prob. 58P Ch. 13.5 - Prob. 59P Ch. 13.5 - Prob. 60P Ch. 13.5 - At the instant B = 60, the boys center of mass G...Ch. 13.5 - A girl having a mass of 25 kg sits at the edge of...Ch. 13.5 - The pendulum bob B has a weight of 5 lb and is...Ch. 13.5 - The pendulum bob B has a mass m and is released...Ch. 13.5 - Determine the constant speed of the passengers on...Ch. 13.5 - A motorcyclist in a circus rides his motorcycle...Ch. 13.5 - The vehicle is designed to combine the feel of a...Ch. 13.5 - The 0.8-Mg car travels over the hill having the...Ch. 13.5 - The 0.8-Mg car travels over the hill having the...Ch. 13.5 - When it reaches the curved portion AB, it is...Ch. 13.5 - Determine the resultant normal and frictional...Ch. 13.5 - If he rotates about the z axis with a constant...Ch. 13.5 - Determine the maximum speed at which the car with...Ch. 13.5 - Determine the maximum constant speed at which the...Ch. 13.5 - The box has a mass m and slides down the smooth...Ch. 13.5 - Prove that if the block is released from rest at...Ch. 13.5 - The cylindrical plug has a weight of 2 lb and it...Ch. 13.5 - When crossing an intersection, a motorcyclist...Ch. 13.5 - The airplane, traveling at a constant speed of 50...Ch. 13.5 - The 2-kg pendulum bob moves in the vertical plane...Ch. 13.5 - The 2-kg pendulum bob moves in the vertical plane...Ch. 13.5 - If it has a speed of 1.5 m/s when y = 0.2 m,...Ch. 13.5 - The ball has a mass m and is attached to the cord...Ch. 13.6 - If the attached spring has a stiffness k = 2...Ch. 13.6 - Determine the constant angular velocity of the...Ch. 13.6 - If = ( t2) rad, where t is in seconds, determine...Ch. 13.6 - The 2-Mg car is traveling along the curved road...Ch. 13.6 - The 0.2-kg pin P is constrained to move in the...Ch. 13.6 - If the cam is rotating at a constant rate of 6...Ch. 13.6 - Determine the magnitude of the resultant force...Ch. 13.6 - Determine the magnitude of the unbalanced force...Ch. 13.6 - Rod OA rotates counterclockwise with a constant...Ch. 13.6 - The boy of mass 40 kg is sliding down the spiral...Ch. 13.6 - Using a forked rod, a 0.5-kg smooth peg P is...Ch. 13.6 - The arm is rotating at a rate of = 4 rad/s when ...Ch. 13.6 - If arm OA rotates with a constant clockwise...Ch. 13.6 - Determine the normal and frictional driving forces...Ch. 13.6 - A smooth can C, having a mass of 3 kg, is lifted...Ch. 13.6 - Prob. 96P Ch. 13.6 - Prob. 97P Ch. 13.6 - The particle has a mass of 0.5 kg and is confined...Ch. 13.6 - A car of a roller coaster travels along a track...Ch. 13.6 - The 0.5-lb ball is guided along the vertical...Ch. 13.6 - The ball of mass misguided along the vertical...Ch. 13.6 - Using a forked rod, a smooth cylinder P, having a...Ch. 13.6 - The pilot of the airplane executes a vertical loop...Ch. 13.6 - The collar has a mass of 2 kg and travels along...Ch. 13.6 - The particle has a mass of 0.5 kg and is confined...Ch. 13.6 - Solve Prob. 13-105 If the arm has an angular...Ch. 13.6 - The forked rod is used to move the smooth 2-lb...Ch. 13.6 - Prob. 108P Ch. 13.6 - Rod OA rotates counterclockwise at a constant...Ch. 13.6 - Solve Prob. 13-109 if motion is in the vertical...Ch. 13.7 - If his speed is a constant vP = 80 ft/s, determine...Ch. 13.7 - The earth has an orbit with eccentricity 0.0167...Ch. 13.7 - Prob. 114P Ch. 13.7 - Determine the speed of a satellite launched...Ch. 13.7 - Prob. 116P Ch. 13.7 - Prove Keplers third law of motion. Hint: Use Eqs....Ch. 13.7 - Prob. 118P Ch. 13.7 - Prob. 119P Ch. 13.7 - Determine the constant speed of satellite S so...Ch. 13.7 - Prob. 121P Ch. 13.7 - Prob. 122P Ch. 13.7 - Prob. 123P Ch. 13.7 - Prob. 124P Ch. 13.7 - The rocket is traveling around the earth in free...Ch. 13.7 - Prob. 127P Ch. 13.7 - Prob. 128P Ch. 13.7 - Prob. 129P Ch. 13.7 - Prob. 130P Ch. 13.7 - The rocket is traveling around the earth in free...Ch. 13.7 - Prob. 132P Ch. 13.7 - Prob. 3CP Ch. 13.7 - If the trailer has a mass of 250 kg and coasts 45...Ch. 13.7 - The coefficient of kinetic friction between the...Ch. 13.7 - Block B rests on a smooth surface. If the...Ch. 13.7 - If the motor draws in the cable at a rate of v =...Ch. 13.7 - The ball has a mass of 30 kg and a speed v = 4 m/s...Ch. 13.7 - If the coefficient of static friction between the...Ch. 13.7 - If at the instant it reaches point A it has a...

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(a) The speed of the rocket at point A ' . (b) the required speed rocket must attain at A after braking. (c) The periods of both the circular orbit and elliptical orbit.

Solution Summary: The author calculates the maximum and minimum distance from the center of the Venus.

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(a) The speed of the rocket at point A' .

(b) the required speed rocket must attain at A after braking.

(c) The periods of both the circular orbit and elliptical orbit.

Want to see the full answer?

Chapter 13 Solutions

(a) The speed of the rocket at point A ' . (b) the required speed rocket must attain at A after braking. (c) The periods of both the circular orbit and elliptical orbit.

Solution Summary: The author calculates the maximum and minimum distance from the center of the Venus.

Concept explainers

Videos

(a) The speed of the rocket at point A' . (b) the required speed rocket must attain at A after braking. (c) The periods of both the circular orbit and elliptical orbit.

Want to see the full answer?

Chapter 13 Solutions

(a) The speed of the rocket at point A' .

(b) the required speed rocket must attain at A after braking.

(c) The periods of both the circular orbit and elliptical orbit.