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engineering
introduction mechanical engineering

Questions and Answers of Introduction Mechanical Engineering

A machine with a mass of \(50 \mathrm{~kg}\) is mounted on springs of equivalent stiffness \(6.10 \times 10^{4} \mathrm{~N} / \mathrm{m}\) and subject to a harmonic force of \(370 \sin 35 t
A machine with a mass of \(30 \mathrm{~kg}\) is mounted on springs with an equivalent stiffness of \(4.8 \times 10^{4} \mathrm{~N} / \mathrm{m}\). During operation, it is subject to a force of \(200
A \(5 \mathrm{~kg}\) block is mounted on a helical coil spring such that the system's natural frequency is \(50 \mathrm{rad} / \mathrm{s}\). The block is subject to a harmonic excitation of amplitude
A 50-kg turbine is mounted on four parallel springs, each with a stiffness of \(3 \times 10^{5} \mathrm{~N} / \mathrm{m}\). When the machine operates at \(40 \mathrm{~Hz}\), its steady-state
A system with an equivalent mass of \(30 \mathrm{~kg}\) has a natural frequency of \(120 \mathrm{rad} / \mathrm{s}\) and a damping ratio of 0.12 and is subject to a harmonic excitation of amplitude
A \(30-\mathrm{kg}\) block is suspended from a spring with a stiffness of \(300 \mathrm{~N} / \mathrm{m}\) and attached to a dashpot of damping coefficient of \(120 \mathrm{~N} \cdot \mathrm{s} /
What is the amplitude of steady-state oscillation of the \(30 \mathrm{~kg}\) block of the system of Figure P4.16? 4 10 N/m 40 kg FIGURE P4.16 2000 sin 1001 N 10 cm Ip = 3 kg-m 20 cm 30 kg 2700 N s/m
If \(\omega=16.5 \mathrm{rad} / \mathrm{s}\), what is the maximum value of \(M_{0}\) such that the disk of Figure P4.17 rolls without slip? 4000 N/m w 10 cm Mo sin cot 50 N s/m = 0.12 FIGURE P4.17
If \(M_{0}=2 \mathrm{~N} \cdot \mathrm{m}\), for what values of \(\omega\) will the disk of Figure P4.17 roll without slip? 4000 N/m w 50 N s/m FIGURE P4.17 10 cm Mo sin cot 20-kg thin disk =0.12
For what values of \(d\) will the steady-state amplitude of angular oscillations be less than \(1^{\circ}\) for the rod of Figure P4.19? 1000 sin 50r m+ FIGURE P4.19 d uyu 4 x 10 N/m 20-kg slender
A 30-kg compressor is mounted on an isolator pad of stiffness \(6 \times 10^{5} \mathrm{~N} / \mathrm{m}\). When subject to a harmonic excitation of magnitude \(350 \mathrm{~N}\) and frequency \(100
A thin disk with a mass of \(5 \mathrm{~kg}\) and a radius of \(10 \mathrm{~cm}\) is connected to a torsional damper of coefficient \(4.1 \mathrm{~N} \cdot \mathrm{s} \cdot \mathrm{m} /
A 50-kg machine tool is mounted on an elastic foundation. An experiment is run to determine the stiffness and damping properties of the foundation. When the tool is excited with a harmonic force of
A machine with a mass of \(30 \mathrm{~kg}\) is placed on an elastic mounting of unknown properties. An engineer excites the machine with a harmonic force with a magnitude of \(100 \mathrm{~N}\) at a
A 80-kg machine tool is placed on an elastic mounting. The phase angle is measured as \(35.5^{\circ}\) when the machine is excited at \(30 \mathrm{~Hz}\). When the machine is excited at \(60
A \(100-\mathrm{kg}\) machine tool has a \(2-\mathrm{kg}\) rotating component. When the machine is mounted on an isolator and its operating speed is very large, the steady-state vibration amplitude
A \(1000 \mathrm{~kg}\) turbine with a rotating unbalance is placed on springs and viscous dampers in parallel. When the operating speed is \(20 \mathrm{~Hz}\), the observed steady-state amplitude is
A \(120-\mathrm{kg}\) fan with a rotating unbalance of \(0.35 \mathrm{~kg} \cdot \mathrm{m}\) is to be placed at the midspan of a \(2.6-\mathrm{m}\) simply supported beam. The beam is made of steel
Solve Chapter Problem 4.27 assuming the damping ratio of the beam is 0.04 .Data From Chapter Problem 4.27:A \(120-\mathrm{kg}\) fan with a rotating unbalance of \(0.35 \mathrm{~kg} \cdot \mathrm{m}\)
A \(620-\mathrm{kg}\) fan has a rotating unbalance of \(0.25 \mathrm{~kg} \cdot \mathrm{m}\). What is the maximum stiffness of the fan's mounting such that the steady-state amplitude is \(0.5
During flight a 75-g particle becomes stuck to one of the blades, \(25 \mathrm{~cm}\) from the axis of rotation. What is the steady-state amplitude of vibration caused by the resulting rotating
Determine the steady–state amplitude of vibration if one of the blades in Figure P4.30 snaps off during flight.Refer to the following situation: The tail rotor section of the helicopter of Figure
Whirling is a phenomenon that occurs in a rotating shaft when an attached rotor is unbalanced. The motion of the shaft and the eccentricity of the rotor cause an unbalanced inertia force, pulling the
A \(30-\mathrm{kg}\) rotor has an eccentricity of \(1.2 \mathrm{~cm}\). It is mounted on a shaft and bearing system whose stiffness is \(2.8 \times 10^{4} \mathrm{~N} / \mathrm{m}\) and damping ratio
An engine flywheel has an eccentricity of \(0.8 \mathrm{~cm}\) and mass \(38 \mathrm{~kg}\). Assuming a damping ratio of 0.05 , what is the necessary stiffness of the bearings to limit its whirl
It is proposed to build a \(6-\mathrm{m}\) smokestack on the top of a \(60-\mathrm{m}\) factory. The smokestack will be made of steel \(\left(ho=7850 \mathrm{~kg} / \mathrm{m}^{3}\right)\) and will
What is the steady-state amplitude of oscillation due to vortex shedding of the smokestack of Chapter Problem. P4.35 if the wind speed is \(22 \mathrm{mph}\) ?Data From Chapter Problem 4.35:It is
A factory is using the piping system of Figure P4.37 to discharge environmentally safe waste-water into a small river. The velocity of the river is estimated as \(5.5 \mathrm{~m} / \mathrm{s}\).
Determine the amplitude of steady-state vibration for the systems shown in Figures P4.38. Use the indicated generalized coordinate. 3 x 104 N/m 100 N s/m 2.8 kg TX 1.5x10 N/m FIGURE P4.38 0.02 sin
Determine the amplitude of steady-state vibration for the systems shown in Figures P4.39. Use the indicated generalized coordinate. 1 105 N/m 0.01 sin 250t m FIGURE P4.39 3 m 1 m 5 kg 400 N. s/m
Determine the amplitude of steady-state vibration for the systems shown in Figures P4.40. Use the indicated generalized coordinate. 0.08 sin 200t m FIGURE P4.40 115 kg E-210 x 10 N/m 1.5 m X 1-4.6
Determine the amplitude of steady-state vibration for the systems shown in Figures P4.41. Use the indicated generalized coordinate. 50 cm FIGURE P4.41 m = 4 kg -0.035 sin 10 m
Determine the amplitude of steady-state vibration for the systems shown in Figures P4.42. Use the indicated generalized coordinate. 0.1 sin 300t rad -1.1 m- G=80 10 N/m x 106m4 J = 4.6 10 6 m4
A \(40 \mathrm{~kg}\) machine is attached to a base through a spring of stiffness \(2 \times 10^{4} \mathrm{~N} / \mathrm{m}\) in parallel with a dashpot of damping coefficient \(150 \mathrm{~N}
A 5-kg rotor-balancing machine is mounted on a table through an elastic foundation of stiffness \(3.1 \times 10^{4} \mathrm{~N} / \mathrm{m}\) and damping ratio 0.04 . Transducers indicate that the
During a long earthquake the one-story frame structure of Figure P4.45 is subject to a ground acceleration of amplitude \(50 \mathrm{~mm} / \mathrm{s}^{2}\) at a frequency of \(88 \mathrm{rad} /
What is the required column stiffness of a one-story structure to limit its acceleration amplitude to \(2.1 \mathrm{~m} / \mathrm{s}^{2}\) during an earthquake whose acceleration amplitude is \(150
In a rough sea, the heave of a ship is approximated as harmonic of amplitude \(20 \mathrm{~cm}\) at a frequency of \(1.5 \mathrm{~Hz}\). What is the acceleration amplitude of a \(20-\mathrm{kg}\)
In the rough sea of Chapter Problem 4.47, what is the required stiffness of an elastic foundation of damping ratio 0.05 to limit the acceleration amplitude of a \(5-\mathrm{kg}\) radio set to \(1.5
Consider the one degree-of-freedom model of a vehicle suspension system of Figure P4.49. Consider a motorcycle of mass \(250 \mathrm{~kg}\). The suspension stiffness is \(70,000 \mathrm{~N} /
For the motorcycle of Chapter Problem 4.49 determine(a) the "frequency response" of the motorcycle's suspension system by plotting the amplitude of acceleration versus motorcycle speed and(b)
What is the minimum static deflection of an undamped isolator that provides 75 percent islolation to a \(200-\mathrm{kg}\) washing machine at \(5000 \mathrm{rpm}\) ?
What is the maximum allowable stiffness of an isolator of damping ratio 0.05 that provides 81 percent isolation to a \(40-\mathrm{kg}\) printing press operating at \(850 \mathrm{rpm}\) ?
When set on a rigid foundation and operating at \(800 \mathrm{rpm}\), a 200-kg machine tool provides a harmonic force with a magnitude of \(18,000 \mathrm{~N}\) to the foundation. An engineer has
A 150-kg engine operates at \(1500 \mathrm{rpm}\).(a) What percent isolation is achieved if the engine is mounted on four identical springs each of stiffness \(1.2 \times 10^{5} \mathrm{~N} /
A \(150 \mathrm{~kg}\) engine operates at speeds between 1000 and \(2000 \mathrm{rpm}\). It is desired to achieve at least 85 percent isolation at all speeds. The only readily available isolator has
Cork pads with a stiffness of \(6 \times 10^{5} \mathrm{~N} / \mathrm{m}\) and a damping ratio of 0.2 are used to isolate a \(40-\mathrm{kg}\) machine tool from its foundation. The machine tool
A 100-kg machine operates at \(1400 \mathrm{rpm}\) and produces a harmonic force of magnitude \(80,000 \mathrm{~N}\). The magnitude of the force transmitted to the foundation is to be reduced to
A \(10-\mathrm{kg}\) laser flow-measuring device is used on a table in a laboratory. Because of operation of other equipment, the table is subject to vibration. Accelerometer measurements show that
Rough seas cause a ship to heave with an amplitude of \(0.4 \mathrm{~m}\) at a frequency of \(20 \mathrm{rad} / \mathrm{s}\). Design an isolation system with a damping ratio of 0.13 such that a \(45
A sensitive computer is being transported by rail in a boxcar. Accelerometer measurements indicate that when the train is traveling at its normal speed of \(85 \mathrm{~m} / \mathrm{s}\) the dominant
A \(200 \mathrm{~kg}\) engine operates at \(1200 \mathrm{rpm}\). Design an isolator such that the transmissibility ratio during start-up is less than 4.6 and the system achieves 80 percent isolation.
A \(150 \mathrm{~kg}\) machine tool operates at speeds between 500 and \(1500 \mathrm{rpm}\). At each speed a harmonic force of magnitude \(15,000 \mathrm{~N}\) is produced. Design an isolation
A \(200 \mathrm{~kg}\) testing machine operates at \(500 \mathrm{rpm}\) and produces a harmonic force of magnitude \(40,000 \mathrm{~N}\). An isolation system for the machine consists of a damped
A 150-kg washing machine has a rotating unbalance of \(0.45 \mathrm{~kg} \cdot \mathrm{m}\). The machine is placed on isolators of equivalent stiffness \(4 \times 10^{5} \mathrm{~N} / \mathrm{m}\)
A 54-kg air compressor operates at speeds between 800 and \(2000 \mathrm{rpm}\) and has a rotating unbalance of \(0.23 \mathrm{~kg} \cdot \mathrm{m}\). Design an isolator with a damping ratio of 0.15
A \(1000 \mathrm{~kg}\) turbomachine has a rotating unbalance of \(0.1 \mathrm{~kg} \cdot \mathrm{m}\). The machine operates at speeds between 500 and \(750 \mathrm{rpm}\). What is the maximum
A motorcycle travels over a road whose contour is approximately sinusoidal, \(y(z)=0.2 \sin (0.4 z) \mathrm{m}\) where \(z\) is measured in meters. Using a SDOF model, design a suspension system with
A suspension system is being designed for a \(1000 \mathrm{~kg}\) vehicle. A first model of the system used in the design process is a spring of stiffness \(k\) in parallel with a viscous damper of
A \(20 \mathrm{~kg}\) block is connected to a spring of stiffness \(1 \times 10^{5} \mathrm{~N} / \mathrm{m}\) and placed on a surface which makes an angle of \(30^{\circ}\) with the horizontal. A
A \(40 \mathrm{~kg}\) block is connected to a spring of stiffness \(1 \times 10^{5} \mathrm{~N} / \mathrm{m}\) and slides on a surface with a coefficient of friction 0.2 . When a harmonic force of
Determine the steady-state amplitude of motion of the \(5-\mathrm{kg}\) block. The coefficient of friction between the block and surface is 0.11 . (See Figure P4.72 .) y(t) 2.7 x 10 sin 180t m w 2 x
Determine the steady-state amplitude of motion of the \(5-\mathrm{kg}\) block. The coefficient of friction between the block and surface is 0.11 . (See Figure P4.73.) y(t) 3.2 x 10 sin 220 m 1 10
Use the equivalent viscous damping approach to determine the steady-state response of a system subject to both viscous damping and Coulomb damping.
The area under the hysteresis curve for a particular helical coil spring is \(0.2 \mathrm{~N} \cdot \mathrm{m}\) when subject to a \(350 \mathrm{~N}\) load. The spring has a stiffness of \(4 \times
When a free-vibration test is run on the system of Figure P4.76, the ratio of amplitudes on successive cycles is 2.8 to 1 . Determine the response of the pump when it has an excitation force of
When a free-vibration test is run on the system of Figure P4.76, the ratio of amplitudes on successive cycles is 2.8 to 1 . When operating, the engine has a rotating unbalance of magnitude \(0.25
When the pump at the end of the beam of Figure P4.76 operates at \(1860 \mathrm{rpm}\), it is noted that the phase angle between the excitation and response is \(18^{\circ}\). What is the
A schematic of a single-cylinder engine mounted on springs and a viscous damper is shown in Figure P4.79. The crank rotates about \(O\) with a constant speed \(\omega\). The connecting rod of mass
Using the results of Problem P4.79, determine the maximum steady-state response of a single-cylinder engine with \(m_{r}=1.5 \mathrm{~kg}, m_{p}=1.7 \mathrm{~kg}, r=5.0 \mathrm{~cm}, l=15.0
A 5-kg rotor-balancing machine is mounted to a table through an elastic foundation of stiffness \(10,000 \mathrm{~N} / \mathrm{m}\) and damping ratio 0.04 . Use of a transducer reveals that the
During operation a \(100-\mathrm{kg}\) press is subject to the periodic excitations shown. The press is mounted on an elastic foundation of stiffness \(1.6 \times 10^{5} \mathrm{~N} / \mathrm{m}\)
During operation a \(100-\mathrm{kg}\) press is subject to the periodic excitations shown. The press is mounted on an elastic foundation of stiffness \(1.6 \times 10^{5} \mathrm{~N} / \mathrm{m}\)
During operation a \(100-\mathrm{kg}\) press is subject to the periodic excitations shown. The press is mounted on an elastic foundation of stiffness \(1.6 \times 10^{5} \mathrm{~N} / \mathrm{m}\)
During operation a \(100-\mathrm{kg}\) press is subject to the periodic excitations shown. The press is mounted on an elastic foundation of stiffness \(1.6 \times 10^{5} \mathrm{~N} / \mathrm{m}\)
During operation a \(100-\mathrm{kg}\) press is subject to the periodic excitations shown. The press is mounted on an elastic foundation of stiffness \(1.6 \times 10^{5} \mathrm{~N} / \mathrm{m}\)
Use of an accelerometer of natural frequency \(100 \mathrm{~Hz}\) and damping ratio 0.15 reveals that an engine vibrates at a frequency of \(20 \mathrm{~Hz}\) and has an acceleration amplitude of
An accelerometer with a natural frequency of \(200 \mathrm{~Hz}\) and damping ratio of 0.7 is used to measure the vibrations of a system whose actual displacement is \(x(t)=1.6 \sin 45.1 t
An accelerometer with a natural frequency of \(200 \mathrm{~Hz}\) and damping ratio of 0.2 is used to measure the vibrations of an engine operating at \(1000 \mathrm{rpm}\). What is the percent error
When a machine tool is placed directly on a rigid floor, it provides an excitation of the form\[ F(t)=(4000 \sin 100 t+5100 \sin 150 t) \mathrm{N} \]to the floor. Determine the natural frequency of
Use the force shown in Figure P4.91 as an approximation to the force provided by the punch press during its operation. Rework Example 4.17 for the excitation.Data From Example 4.17:The 500-kg punch
A \(550-\mathrm{kg}\) industrial sewing machine has a rotating unbalance of \(0.24 \mathrm{~kg} \cdot \mathrm{m}\). The machine operates at speeds between 2000 and \(3000 \mathrm{rpm}\). The machine
The system of Figure P4.93 is subject to the excitation\(F(t)=1000 \sin 25.4 t+800 \sin (48 t+0.35)-300 \sin (100 t+0.21) \mathrm{N}\)What is the output in \(\mathrm{mm} / \mathrm{s}^{2}\) of an
What is the output, in \(\mathrm{mm}\), of a seismometer with a natural frequency of \(2.5 \mathrm{~Hz}\) and a damping ratio of 0.05 placed at point \(A\) for the system of Figure P4.93? 4.8 104
A \(20 \mathrm{~kg}\) block is connected to a moveable support through a spring of stiffness \(1 \times 10^{5} \mathrm{~N} / \mathrm{m}\) in parallel with a viscous damper of damping coefficient
An accelerometer has a natural frequency of \(80 \mathrm{~Hz}\) and a damping coefficient of \(8.0 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}\). When attached to a vibrating structure, it measures an
Vibrations of a \(30 \mathrm{~kg}\) machine occur at \(150 \mathrm{rad} / \mathrm{s}\) with an amplitude of \(0.003 \mathrm{~mm}\).(a) Design an energy harvester with a damping ratio of 0.2 that
An energy harvester is being designed to harvest the vibrations form a \(200 \mathrm{~kg}\) machine that has a rotating unbalance of \(0.1 \mathrm{~kg} \cdot \mathrm{m}\) which operates at \(1000
An energy harvester is being designed for a vehicle with a simplified suspension system similar to that in the benchmark examples. The harvester, which is to be mounted on the vehicle, is to harvest
How much energy is harvested over one period by the energy harvester of Problem 4.99 if the vehicle is traveling at \(50 \mathrm{~m} / \mathrm{s}\) over a road whose contour is shown in Figure
An energy harvester is being designed to harvest energy from a MEMS system. The harvester consists of a micro-cantilever beam vibrating in a viscous liquid such that its damping ratio is 0.2 . The
The one-dimensional displacement of a particle is\[ x(t)=0.5 e^{-0.2 t} \sin 5 t \mathrm{~m} \](a) What is the maximum displacement of the particle?(b) What is the maximum velocity of the
The one-dimensional displacement of a particle is\[ x(t)=0.5 e^{-0.2 t} \sin (5 t+0.24) \mathrm{m} \](a) What is the maximum displacement of the particle?(b) What is the maximum velocity of the
At the instant shown in Figure P1.3, the slender rod has a clockwise angular velocity of \(5 \mathrm{rad} / \mathrm{s}\) and a counterclockwise angular acceleration of \(14 \mathrm{rad} /
A \(t=0\), a particle of mass \(1.2 \mathrm{~kg}\) is traveling with a speed of \(10 \mathrm{~m} / \mathrm{s} \mathrm{that} \mathrm{is}\) increasing at a rate of \(0.5 \mathrm{~m} / \mathrm{s}^{2}\).
The machine of Figure P1.5 has a vertical displacement \(x(t)\). The machine has a component which rotates with a constant angular speed \(\omega\). The center of mass of the rotating component is a
The rotor of Figure P1.6 consists of a disk mounted on a shaft. Unfortunately, the disk is unbalanced, and the center of mass is a distance \(e\) from the center of the shaft. As the disk rotates,
A 2 ton truck is traveling down an icy, \(10^{\circ}\) hill at \(50 \mathrm{mph}\) when the driver sees a car stalled at the bottom of the hill \(250 \mathrm{ft}\) away. As soon as he sees the
The contour of a bumpy road is approximated by\[ y(x)=0.03 \sin (0.125 x) \mathrm{m} \]What is the amplitude of the vertical acceleration of the wheels of an automobile as it travels over this road
The helicopter of Figure P1.9 has a horizontal speed of \(110 \mathrm{ft} / \mathrm{s}\) and a horizontal acceleration of \(3.1 \mathrm{ft} / \mathrm{s}^{2}\). The main blades rotate at a constant

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