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
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Chapter 13.2, Problem 13.82P
To determine
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To determine
(b)
That the work done by
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Q.1: (15 Marks)
Find the first three natural frequencies and mode shapes of the axial and torsional
vibration for a steel shaft free at both ends, having a length of 3 m. Find the subsequent
axil motion if the shaft is subjected to the following initial conditions, given that E = 210
GPa, G=80 GPa, p = 7800 kg/m³:
f(x)=0
v(x) = {1
2.8
Q.4: (15 Marks)
A uniform rotor of mass 500 kg and diametral moment of inertia of 20 kg.m², is supported
by identical short bearings of stiffness 1 MN/m in the horizontal and vertical directions. If
the distance between the bearings is 0.6 m:
(a) What is the corresponding polar moment of inertia if the backward whirling speed is
80% of the static structure tilting natural frequency?
(b) Determine the forward whirling speed.
45.27
University of Babylon
Collage of Engineering/
Al-Musayab
Department of Automobiles
Mid Examination/ Stage: 3rd
Subject: Theory of Vehicles
Date: 14 \ 4 \2025
Time: 1.5 Hours
2025-2024
Q1: The arms of a Porter governor are 250 mm long. The upper arms are pivoted on
the axis of revolution, but the lower arms are attached to a sleeve at a distance of 50
mm from the axis of rotation. The weight on the sleeve is 600 N and the weight of
each ball is 80 N. Determine the equilibrium speed when the radius of rotation of the
balls is 150 mm. If the friction is equivalent to a load of 25 N at the sleeve, determine
the range of speed for this position.
Q2: In a loaded Proell governor shown in Figure below each ball weighs 3 kg and
the central sleeve weighs 25 kg. The arms are of 200 mm length and pivoted about
axis displaced from the central axis of rotation by 38.5 mm, y=238 mm, x=303.5
mm, CE 85 mm, MD 142.5 mm. Determine the equilibrium speed.
Fe
mg
E
M
2
Q3: In a spring loaded Hartnell type…
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...
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- Q.2: (15 Marks) = 1400 For the following system, determine the first natural frequency using Dunkerley's equation, Given that the disk has moment of inertia J = 2 kg.m², the shaft has G = 20 GPa, p kg/m³, polar moment of cross-sectional area of the shaft Ip = 8×108 m². 500 mm 220 mm k=200 N/m FOF m=1 kg 14.14 56.56. W слarrow_forwardQ.2: (15 Marks) = 1400 For the following system, determine the first natural frequency using Dunkerley's equation, Given that the disk has moment of inertia J = 2 kg.m², the shaft has G = 20 GPa, p kg/m³, polar moment of cross-sectional area of the shaft Ip = 8×108 m². 500 mm 220 mm k=200 N/m FOF m=1 kg 14.14 56.56. W слarrow_forwardQ1: In Figure below, pinion A having 15 teeth is fixed to motor shaft. Za-20, Z-15, where B and C are a compound gear wheel. Wheel E is keyed to the machine shaft. Arm F rotates about the same shaft on which A is fixed and carries the compound wheel B, C. If the motor runs at 1200 rpm counter-clockwise, find (a) the speed of the machine shaft and (b) ratio of the reduction gear. C B D Q1: A compound epicyclic gear is shown diagrammatically in Figure below. The gears A, D and E are free to rotate on the axis P. The compound gear B and C rotate together on the axis Q at the end of arm F. All the gears have equal pitch. The number of external teeth on the gears A, B and C are 18, 45 and 21 respectively. The gears D and E are annular gears. The gear A rotates at 100 r.p.m. in the anticlockwise direction and the gear D rotates at 450 r.p.m. clockwise. Find the speed and direction of the arm and the gear E. D E A P F LL B Carrow_forward
- Calculate the force in cable AB and the angle θ for the support system shown. Round your final answers to two decimal places.arrow_forward1.53 In the steel structure shown, a 6-mm-diameter pin is used at C and 10-mm-diameter pins are used at B and D. The ultimate shearing stress is 150 MPa at all connections, and the ultimate normal stress is 400 MPa in link BD. Knowing that a factor of safety of 3.0 is desired, determine the largest load P that can be applied at A. Note that link BD is not reinforced around the pin holes. Front view D D 6 mm 18 mm B A B Side view 160 mm 120 mm A B Top viewarrow_forwardCORRECT AND DETAILED HANDWRITTEN SOLUTION WITH FBD ONLY. I WILL UPVOTE THANK YOU. CORRECT ANSWER IS ALREADY PROVIDED. 16: Determine (a) the maximum bending stress, (b)the maximum shearing stress, (c) compressive bending stress atthe roller support, and (d) the shearing stress 1 in below the topsurface of the beam at the location 1 ft to the right of the rollersupport in the simply supported beam shown in Fig. 8-70.ANS: (a) 21,945.313 lb/in2; (b) 1656.25 lb/in2; (c) 10,000 lb/in2; (d) 190.972 lb/in2arrow_forward
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