Engineering Mechanics: Dynamics Study (Book and Pearson eText)
14th Edition
ISBN: 9780134116990
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 21.4, Problem 54P
To determine
The normal and frictional force disk exerts on the ground.
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using the theorem of three moments, find all the reactions and supports, I need the calculations only
Q.5: (10 Marks) Select the correct answer (choose 10 only)
1. The forward whirling speed is ......... the static structure tilting speed.
(a) Less than
(b) Higher than
(c) equal to
2. The divergence between the forward and backward whirling speeds increases as:
(a) The rotating speed increase (b) the polar moment of inertia increases
(c) Both (a) and (b)
(d) do not change
3. Increasing the system natural frequency can be done by:
(a) add masses (b) adding braces and supports (c) increase damping
4. The amplitude of vibration due to external force can be reduced by:
(a) Increasing damping (b) Decreasing damping (c) Increasing mass
5. Tuned absorbers are used to:
(a) Shift the natural frequency (b) increase damping (c) Increase stiffness
6. Accelerometers sensors contains:
г
(a) Piezoelectric materials (b) Magnet and coil (c) coil only
7. Increasing the stiffness of the system causes:
(a) Less transmitted force (b) more transmitted force (c) Transmitted force does not
change
8. The…
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
Chapter 21 Solutions
Engineering Mechanics: Dynamics Study (Book and Pearson eText)
Ch. 21.1 - Show that the sum of the moments of inertia of a...Ch. 21.1 - Determine the moment of inertia of the cone with...Ch. 21.1 - Determine moment of inertia Iy of the solid formed...Ch. 21.1 - Determine the moments of inertia Ix and Iy of the...Ch. 21.1 - The density of the material is . Express the...Ch. 21.1 - Prob. 6PCh. 21.1 - Prob. 7PCh. 21.1 - Prob. 8PCh. 21.1 - The weight of the cone is 15 lb, the height is h =...Ch. 21.1 - The density of the material is .
Ch. 21.1 - Prob. 11PCh. 21.1 - Determine the moment of inertia Ixx of the...Ch. 21.1 - Determine the product of inertia Iyz of the...Ch. 21.1 - Prob. 14PCh. 21.1 - Prob. 15PCh. 21.1 - Determine the moment of inertia of the rod about...Ch. 21.1 - Prob. 17PCh. 21.1 - Prob. 18PCh. 21.1 - Prob. 19PCh. 21.1 - Prob. 20PCh. 21.1 - Prob. 21PCh. 21.3 - If a body contains no planes of symmetry, the...Ch. 21.3 - Prob. 23PCh. 21.3 - Prob. 24PCh. 21.3 - The large gear has a mass of 5 kg and a radius of...Ch. 21.3 - Prob. 26PCh. 21.3 - Prob. 27PCh. 21.3 - Prob. 28PCh. 21.3 - Prob. 29PCh. 21.3 - Prob. 30PCh. 21.3 - Prob. 31PCh. 21.3 - Prob. 32PCh. 21.3 - The 20-kg sphere rotates about the axle with a...Ch. 21.3 - The 200-kg satellite has its center of mass at...Ch. 21.3 - Prob. 35PCh. 21.3 - Prob. 36PCh. 21.3 - Prob. 37PCh. 21.3 - Prob. 38PCh. 21.3 - Prob. 39PCh. 21.3 - Prob. 40PCh. 21.4 - Derive the scalar form of the rotational equation...Ch. 21.4 - Prob. 42PCh. 21.4 - Prob. 43PCh. 21.4 - Prob. 44PCh. 21.4 - The disk has a weight of 15 lb. Neglect the weight...Ch. 21.4 - Prob. 46PCh. 21.4 - Prob. 47PCh. 21.4 - Prob. 48PCh. 21.4 - Prob. 49PCh. 21.4 - Prob. 50PCh. 21.4 - Prob. 51PCh. 21.4 - The 5-kg circular disk is mounted off center on a...Ch. 21.4 - Prob. 53PCh. 21.4 - Prob. 54PCh. 21.4 - Prob. 55PCh. 21.4 - The 4-kg slender rod AB is pinned at A and held at...Ch. 21.4 - Prob. 57PCh. 21.4 - Prob. 58PCh. 21.4 - Prob. 59PCh. 21.4 - Show that the angular velocity of a body, in terms...Ch. 21.4 - Prob. 61PCh. 21.6 - The gyroscope consists of a uniform 450-g disk D...Ch. 21.6 - Prob. 63PCh. 21.6 - Prob. 64PCh. 21.6 - Prob. 65PCh. 21.6 - When viewed from the front of the airplane, the...Ch. 21.6 - Prob. 67PCh. 21.6 - Prob. 68PCh. 21.6 - Prob. 69PCh. 21.6 - Prob. 70PCh. 21.6 - Prob. 71PCh. 21.6 - Prob. 72PCh. 21.6 - Prob. 73PCh. 21.6 - Prob. 74PCh. 21.6 - Prob. 75PCh. 21.6 - Prob. 76PCh. 21.6 - Prob. 77PCh. 21.6 - Prob. 78P
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- 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. 45.27arrow_forwardUniversity 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…arrow_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_forward
- 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_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_forwardCalculate the force in cable AB and the angle θ for the support system shown. Round your final answers to two decimal places.arrow_forward
- 1.53 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_forwardCORRECT AND DETAILED HANDWRITTEN SOLUTION WITH FBD ONLY. I WILL UPVOTE THANK YOU. CORRECT ANSWER IS ALREADY PROVIDED. 20: A 2022 Porsche 911 (992) GT3 is crossing a 20 ft bridge. The specification of the car is shown below.Determine the maximum shear (in lb) and moment (in lb-ft) on the bridge. ANS: Vmax = 2,680.850 lb ; Mmax = 11,233.13 lb-ftarrow_forward
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