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
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 13.2, Problem 13.85P
(a) Determine the kinetic energy per unit mass that a missile must have after being fired from the surface of the earth if it is to reach an infinite distance from the earth. (b) What is the initial velocity of the missile (called the escape velocity)? Give your answers in SI units and show that the answer to part b is independent of the firing angle.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A 35 g steel ball is held by a ceiling-mounted electromagnet 3.4 m above the floor. A compressed-air cannon sits on the floor, 5.0 m to one side of the point directly under the ball. When a button is pressed, the ball drops and, simultaneously, the cannon fires a 25 g plastic ball. The two balls collide 1.2 m above the floor.
What was the launch speed of the plastic ball?
Oblique Impact
To analyze an oblique impact using the conservation of momentum and coefficient of restitution.
When an oblique impact occurs between two smooth particles, the particles move away from each other with velocity vectors that have unknown directions and unknown magnitudes. If the y axis is within the plane of contact and the x axis is the line of impact, the impulsive forces of deformation and restitution act only along the line of impact (the x axis). Momentum of the system is conserved along the line of impact (the x axis):
∑m(vx)1=∑m(vx)2
The coefficient of restitution, e, relates the relative-velocity components of the particles along the line of impact (the x axis):
e=(vBx)2−(vAx)2(vAx)1−(vBx)1
The momenta of both particles A and B are conserved in the plane of contact (the y axis) because no impulse acts on either particle in this plane. Therefore, the y component of the velocities before and after the collisions remains unchanged:
(vy)1=(vy)2
As shown,…
Oblique Impact
To analyze an oblique impact using the conservation of momentum and coefficient of restitution.
When an oblique impact occurs between two smooth particles, the particles move away from each other with velocity vectors that have unknown directions and unknown magnitudes. If the y axis is within the plane of contact and the x axis is the line of impact, the impulsive forces of deformation and restitution act only along the line of impact (the x axis). Momentum of the system is conserved along the line of impact (the x axis):
∑m(vx)1=∑m(vx)2
The coefficient of restitution, e, relates the relative-velocity components of the particles along the line of impact (the x axis):
e=(vBx)2−(vAx)2(vAx)1−(vBx)1
The momenta of both particles A and B are conserved in the plane of contact (the y axis) because no impulse acts on either particle in this plane. Therefore, the y component of the velocities before and after the collisions remains unchanged:
Immediately after the collision,…
Chapter 13 Solutions
Vector Mechanics for Engineers: Dynamics
Ch. 13.1 - Block A is traveling with a speed v0 on a smooth...Ch. 13.1 - A 400-kg satellite is placed in a circular orbit...Ch. 13.1 - A 1-Ib stone is dropped down the “bottomless pit”...Ch. 13.1 - A baseball player hits a 5.1-oz baseball with an...Ch. 13.1 - A 500-kg communications satellite is in a circular...Ch. 13.1 - Prob. 13.5PCh. 13.1 - In an ore-mixing operation, a bucket full of ore...Ch. 13.1 - Determine the maximum theoretical speed the may be...Ch. 13.1 - A 2000-kg automobile starts from rest at point A...Ch. 13.1 - A package is projected up a 15° incline at A with...
Ch. 13.1 - A 1.4-kg model rocket is launched vertically from...Ch. 13.1 - Packages are thrown down an incline at A with a...Ch. 13.1 - Packages are thrown down an incline at A with a...Ch. 13.1 - Boxes are transported by a conveyor belt with a...Ch. 13.1 - Boxes are transported by a conveyor belt with a...Ch. 13.1 - A 1200-kg trailer is hitched to a 1400-kg car. The...Ch. 13.1 - A trailer truck enters a 2 percent uphill grade...Ch. 13.1 - The subway train shown is traveling at a speed of...Ch. 13.1 - The subway train shown is travelling at a speed of...Ch. 13.1 - Blocks A and B weigh 25 Ib and 10 Ib,...Ch. 13.1 - The system shown is at rest when a constant 30-lb...Ch. 13.1 - Car B is towing car A at a constant speed of 10...Ch. 13.1 - The system shown is at rest when a constant 250-N...Ch. 13.1 - The system shown is at rest when a constant 250-N...Ch. 13.1 - Two blocks A and B, of mass 4 kg and 5 kg....Ch. 13.1 - Four 3-kg packages are held in place by friction...Ch. 13.1 - A 3-kg block rests on top of a 2-kg block...Ch. 13.1 - Solve Prob. 13.26. assuming that the 2-kg block is...Ch. 13.1 - People with mobility impairments can gain great...Ch. 13.1 - A 7.5-lb collar is released from rest in the...Ch. 13.1 - A 10-kg block is attached to spring A and...Ch. 13.1 - A 5-kg collar A is at rest on top of, but not...Ch. 13.1 - A piston of mass m and cross-sectional area A is...Ch. 13.1 - An uncontrolled automobile travelling at 65 mph...Ch. 13.1 - Two types of energy-absorbing fenders designed to...Ch. 13.1 - Nonlinear springs are classified as hard or soft,...Ch. 13.1 - A meteor starts from rest at a very great distance...Ch. 13.1 - Express the acceleration of gravity gh, at an...Ch. 13.1 - Prob. 13.38PCh. 13.1 - The sphere at A is given a downward velocity v0 of...Ch. 13.1 - The sphere at Ais given a downward velocity v0and...Ch. 13.1 - A bag is gently pushed off the top of a wall at A...Ch. 13.1 - A roller coaster starts from rest at A, rolls down...Ch. 13.1 - In Prob. 13.42. determine the range of values of h...Ch. 13.1 - A small block slides at a speed v on a horizontal...Ch. 13.1 - A small block slides at a speed v=8 ft/s on a...Ch. 13.1 - A chairlift is designed to transport 1000 skiers...Ch. 13.1 - Prob. 13.47PCh. 13.1 - The velocity of the lift of Prob. 13.47 increases...Ch. 13.1 - (a) A 120-lb woman rides a 15-lb bicycle up a...Ch. 13.1 - Prob. 13.50PCh. 13.1 - Prob. 13.51PCh. 13.1 - Prob. 13.52PCh. 13.1 - Prob. 13.53PCh. 13.1 - The elevator E has a weight of 6600 lb when fully...Ch. 13.2 - Two small balls A and B with masses 2m and m,...Ch. 13.2 - A small blocks is released from rest and slides...Ch. 13.2 - Prob. 13.55PCh. 13.2 - A loaded railroad car of mass m is rolling at a...Ch. 13.2 - A 750-g collar can slide along the horizontal rod...Ch. 13.2 - A 4-Ib collar can slide without friciton along a...Ch. 13.2 - A 4-Ib collar can slide without friction along a...Ch. 13.2 - A 500-g collar can slide without friction on the...Ch. 13.2 - For the adapted shuffleboard device in Prob 13.28....Ch. 13.2 - An elastic cable is to be designed for bungee...Ch. 13.2 - Prob. 13.63PCh. 13.2 - A 2-kg collar is attached to a spring and slides...Ch. 13.2 - Prob. 13.65PCh. 13.2 - A thin circular rod is supported in a vertical...Ch. 13.2 - Prob. 13.67PCh. 13.2 - A spring is used to stop a 50-kg package that is...Ch. 13.2 - Prob. 13.69PCh. 13.2 - Prob. 13.70PCh. 13.2 - Prob. 13.71PCh. 13.2 - Prob. 13.72PCh. 13.2 - A 10-lb collar is attached to a spring and slides...Ch. 13.2 - An 8-oz package is projected upward with a...Ch. 13.2 - If the package of Prob. 13.74 is not to hit the...Ch. 13.2 - A small package of weight W is projected into a...Ch. 13.2 - Prob. 13.77PCh. 13.2 - The pendulum shown is released from rest at A and...Ch. 13.2 - Prob. 13.79PCh. 13.2 - Prob. 13.80PCh. 13.2 - Prob. 13.81PCh. 13.2 - Prob. 13.82PCh. 13.2 - Prob. 13.83PCh. 13.2 - Prob. 13.84PCh. 13.2 - (a) Determine the kinetic energy per unit mass...Ch. 13.2 - Prob. 13.86PCh. 13.2 - Prob. 13.87PCh. 13.2 - How much energy per pound should be imparted to a...Ch. 13.2 - Knowing that the velocity of an experimental space...Ch. 13.2 - Prob. 13.90PCh. 13.2 - Prob. 13.91PCh. 13.2 - Prob. 13.92PCh. 13.2 - Prob. 13.93PCh. 13.2 - Prob. 13.94PCh. 13.2 - Prob. 13.95PCh. 13.2 - Prob. 13.96PCh. 13.2 - Prob. 13.97PCh. 13.2 - Prob. 13.98PCh. 13.2 - Prob. 13.99PCh. 13.2 - Prob. 13.100PCh. 13.2 - Prob. 13.101PCh. 13.2 - Prob. 13.102PCh. 13.2 - Prob. 13.103PCh. 13.2 - Prob. 13.104PCh. 13.2 - Prob. 13.105PCh. 13.2 - Prob. 13.106PCh. 13.2 - Prob. 13.107PCh. 13.2 - Prob. 13.108PCh. 13.2 - Prob. 13.109PCh. 13.2 - Prob. 13.110PCh. 13.2 - Prob. 13.111PCh. 13.2 - Prob. 13.112PCh. 13.2 - Prob. 13.113PCh. 13.2 - Prob. 13.114PCh. 13.2 - Prob. 13.115PCh. 13.2 - A spacecraft of mass mdescribes a circular orbit...Ch. 13.2 - Prob. 13.117PCh. 13.2 - Prob. 13.118PCh. 13.3 - A large insect impacts the front windshield of a...Ch. 13.3 - The expected damages associated with two types of...Ch. 13.3 - The initial velocity of the block in position A is...Ch. 13.3 - Prob. 13.F2PCh. 13.3 - Prob. 13.F3PCh. 13.3 - Car A was traveling west at a speed of 15 m/s and...Ch. 13.3 - Prob. 13.F5PCh. 13.3 - A 35.000-Mg ocean liner has an initial velocity of...Ch. 13.3 - Prob. 13.120PCh. 13.3 - A sailboat weighing 980 lb with its occupants is...Ch. 13.3 - A truck is hauling a 300-kg log out of a ditch...Ch. 13.3 - The coefficients of friction between the load and...Ch. 13.3 - Steep safety ramps are built beside mountain...Ch. 13.3 - Baggage on the floor of the baggage car of a...Ch. 13.3 - Prob. 13.126PCh. 13.3 - Prob. 13.127PCh. 13.3 - Prob. 13.128PCh. 13.3 - Prob. 13.129PCh. 13.3 - Prob. 13.130PCh. 13.3 - Prob. 13.131PCh. 13.3 - The system shown is at rest when a constant 150-N...Ch. 13.3 - Prob. 13.133PCh. 13.3 - Prob. 13.134PCh. 13.3 - A 60-g model rocket is fired vertically. The...Ch. 13.3 - Prob. 13.136PCh. 13.3 - A crash test is performed between an SUV A and a...Ch. 13.3 - Prob. 13.138PCh. 13.3 - Prob. 13.139PCh. 13.3 - A 1.6 2-oz golf ball is hit with a golf club and...Ch. 13.3 - The triple jump is a track-and-field event in...Ch. 13.3 - Prob. 13.142PCh. 13.3 - Prob. 13.143PCh. 13.3 - A 28-g steel-jacketed bullet is fired with a...Ch. 13.3 - A 25-ton railroad car moving at 2.5 mi/h is to be...Ch. 13.3 - At an intersection, car B was traveling south and...Ch. 13.3 - The 650-kg hammer of a drop-hammer pile driver...Ch. 13.3 - Prob. 13.148PCh. 13.3 - Prob. 13.149PCh. 13.3 - Prob. 13.150PCh. 13.3 - Prob. 13.151PCh. 13.3 - Prob. 13.152PCh. 13.3 - A 1-az bullet is traveling with velocity of 1400...Ch. 13.3 - In order to test the resistance of a chain to...Ch. 13.4 - A 5 -kg ball A strikes a 1-kg ball B that is...Ch. 13.4 - F6 A sphere with a speed v0 rebounds after...Ch. 13.4 - An 80-Mg railroad engine A coasting at 6.5 km/h...Ch. 13.4 - Prob. 13.F8PCh. 13.4 - Prob. 13.F9PCh. 13.4 - Block A of mass mA strikes ball B of mass mB with...Ch. 13.4 - Prob. 13.155PCh. 13.4 - Collars A and B, of the same mass m, are moving...Ch. 13.4 - One of the requirements for tennis balls to be...Ch. 13.4 - Prob. 13.158PCh. 13.4 - Prob. 13.159PCh. 13.4 - Packages in an automobile parts supply house are...Ch. 13.4 - Three steel spheres of equal mass are suspended...Ch. 13.4 - Prob. 13.162PCh. 13.4 - Prob. 13.163PCh. 13.4 - Two identical billiard balls can move freely on a...Ch. 13.4 - Prob. 13.165PCh. 13.4 - A 600-g ball A is moving with a velocity of...Ch. 13.4 - Two identical hockey pucks are moving on a hockey...Ch. 13.4 - Prob. 13.168PCh. 13.4 - Prob. 13.169PCh. 13.4 - The Mars Pathfinder spacecraft used large airbags...Ch. 13.4 - A girl throws a ball at an inclined wall from a...Ch. 13.4 - Rockfalls can cause major damage to roads and...Ch. 13.4 - Prob. 13.173PCh. 13.4 - cars of the same mass run head-on into each other...Ch. 13.4 - Prob. 13.175PCh. 13.4 - Prob. 13.176PCh. 13.4 - After having been pushed by an airline employee,...Ch. 13.4 - Blocks A and B each weigh 0.8 lb and block C...Ch. 13.4 - A 5-kg sphere is dropped from a height of y=2 m to...Ch. 13.4 - Prob. 13.180PCh. 13.4 - Prob. 13.181PCh. 13.4 - Block A is released from rest and slides down the...Ch. 13.4 - Prob. 13.183PCh. 13.4 - A test machine that kicks soccer balls has a 5-lb...Ch. 13.4 - Prob. 13.185PCh. 13.4 - Prob. 13.186PCh. 13.4 - A 2-kg sphere moving to the right with a velocity...Ch. 13.4 - When the rope is at an angle of a=30 , the 1-Ib...Ch. 13.4 - Prob. 13.189PCh. 13 - A 32,000-Ib airplane lands on an aircraft carrier...Ch. 13 - A 2-oz pellet shot vertically from a spring-loaded...Ch. 13 - A satellite describes an elliptic orbit about a...Ch. 13 - Prob. 13.193RPCh. 13 - Prob. 13.194RPCh. 13 - A 300-g block is released from rest after a spring...Ch. 13 - A kicking-simulation attachment goes on the front...Ch. 13 - A 300-g collar A is released from rest, slids down...Ch. 13 - Prob. 13.198RPCh. 13 - Prob. 13.199RPCh. 13 - Prob. 13.200RPCh. 13 - The 2-Ib ball at A is suspended by an inextensible...
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.Similar questions
- V = 12Msqrt(gL)/5m . If you come up with this answer, the website is showing its wrong so try again pleasearrow_forwardA projectile object reaches a height of 303 m, if it is fired straight up using a spring-loaded gun. Using the same gun, what is the maximum height (m) that can be reached by the projectile if it fired at an angle of 19 ° from the vertical?arrow_forwardWhich of the following law states "The rate of change of momentum is directly proportional to the impressed force, and takes place in the same direction, in which the force acts"? Select one: O Newton's Second Law of Motion O Newton's First Law of Motion O Newton's Law of Collision of Elastic bodies O Law of conservation of Momentumarrow_forward
- 113 Blocks on a spring. Two blocks with masses m₁ and m₂ are connected by a spring and are free to slide on a frictionless horizontal surface. The blocks are pulled apart along an x axis and then released from rest. At any later time, (a) what fraction frac₁ of the total kinetic energy of the system will block 1 have and (b) what fraction fracz will block 2 have? (c) If m₁ > m2,which block has more kinetic energy? 中arrow_forwardA projectile is fired from a cannon with an initial velocity of 1000 m/s and at an angle of 30° from the horizontal. What distance from the cannon will the projectile strike the ground if the point of impact is 1500 m below the point of release?arrow_forwardThe 3 kg object A and the 5 kg object B undergo oblique impact as shown in Figure P5. The coefficient of restitution between the objects is 0.6. The magnitude of the velocity of A is 10 m/s, while the magnitude of the velocity of B is 5 m/s just before impact. The angle theta =36.9?. What is the magnitude of the velocity of each particle after impact?arrow_forward
- 1. Space probes may be separated from their launchers by exploding bolts. (They bolt away from one another.) Suppose a 4100-kg satellite uses this method to separate from the 1200-kg remains of its launcher, and that 3000 J of kinetic energy is supplied to the two parts. Assume that the satellite and launcher are at rest before separation and the direction of the satellite's velocity after separation is positive. Gravity is negligible compared to the force of explosion. Consider: Let the subscripts i and f denote the initial and final velocities and the subscripts s and/ denote the satellite and the launcher, respectively. How many knowns are there and how many unknowns? satellite launcher Before launch Vsf satellite launcher V₁ After launcharrow_forwardPlease can you answer part D with full working outarrow_forwardM= 2,500 kg m= 800 kgarrow_forward
- Solve the problem. I have attached a sample solution for your reference/help.pls solve it.arrow_forward3. A 15-kg rock is dropped from rest on the earth and reaches the ground in 1.75 s. When it is dropped from the same height on Saturn's satellite Enceladus, it reaches the ground in 18.6 s. (a) What is the acceleration due to gravity on Enceladus? (b) How long will it take for the rock to reach the ground on Earth if it was released 100 m above the Earth's surface? (c) Same question in (b) but in Enceladus.arrow_forwardA 22-gg bullet traveling 250 m/sm/s penetrates a 2.0 kgkg block of wood and emerges going 125 m/sm/s . Part A If the block is stationary on a frictionless surface when hit, how fast does it move after the bullet emerges? Express your answer to two significant figures and include the appropriate units.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Dynamics - Lesson 1: Introduction and Constant Acceleration Equations; Author: Jeff Hanson;https://www.youtube.com/watch?v=7aMiZ3b0Ieg;License: Standard YouTube License, CC-BY