A fender is mounted on a automobile though dampers (to absorb collision energy) andsprings (so that the fender can recover after low-speed collisions). During a crash-test, theautomobile is moving at 2 m/s when its fender strikes a concrete barrier. The vehiclemass, m, is 1,000 kg. (In comparison, the fender itself is essentially massless.) Thesprings that mount the fender have a stiffness, k, of 1,000,000 N/m.ymbarrier1) Write a differential equation for the deflection of the springs when the fender is incontact with the barrier.2) If the damping coefficient, c, is 30,000 N-s/m, what is the damping ratio of themass-spring-damper system when the fender is in contact with the barrier?3) For that damping coefficient, make a reasonably accurate sketch (with properlylabeled axes) of the time-course of the force exerted on the barrier, starting fromthe moment of first contact.4) Is there any value of the damping coefficient, c, that would yield no rebound ofthe vehicle from the barrier? If so, what is it? If not, why not?

Given Data Speed of the automobile is 2 m/s Mass of the vehicle is 1000 kg Stiffness of the spring…

ugn damp springs (so that the fender can recover after low-speed collisions). During a crash-test, the automobile is moving at 2 m/s when its fender strikes a concrete barrier. The vehicle mass, m, is 1,000 kg. (In comparison, the fender itself is essentially massless.) The springs that mount the fender have a stiffness, k, of 1,000,000 N/m. y m barrier 1) Write a differential equation for the deflection of the springs when the fender is in contact with the barrier.

ugn damp springs (so that the fender can recover after low-speed collisions). During a crash-test, the automobile is moving at 2 m/s when its fender strikes a concrete barrier. The vehicle mass, m, is 1,000 kg. (In comparison, the fender itself is essentially massless.) The springs that mount the fender have a stiffness, k, of 1,000,000 N/m. y m barrier 1) Write a differential equation for the deflection of the springs when the fender is in contact with the barrier.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: T Blackboard @ Texas Tech Univers x E MasteringEngineering - Spring 2 x E MasteringEngineering…

A: Given data :- h = 4 m Fc = 400 N FE = 350 N FB = 400 N Find :- FR = ?

Q: Problem Statement: A crate is initially at rest on a sloped surface, when a force is applied: F(t) =…

Q: At the instant 0 = 40 ° , the slotted guide is moving upward with an acceleration of 3 m/s and a…

Q: An object of mass m = 0.2 kg is hung from a spring whose spring constant is 80 Nm-1. The body is…

A: Ans.1 The equation of the motion is this is a free oscillation motion or underdamped

Q: The spring constant shown is k and the masses are ma and mg . The horizontal bar is smooth. At the…

Q: You have to design a structure of a thin rectangular beam supporting a lamp with a mass of 20 kg as…

A: Given , Mass of the lamp ,m = 20 kg Modulus of elasticity of the beam , E =200 GPa. Length of the…

Q: Suppose the block has a weight of 80 lb and the force F is being supplied by a motor which is…

A: Weight of block=80lbdistance(d)=6ftspeed of motor=Draw the free-body diagram of the system.

Q: Find the value of the spring constant k. The amplitude of the driving force is 0.505 N ar force is…

A: At resonance, frequency of oscillation becomes equal to natural frequency.

Q: A. A car's body has mass 100 slugs. This mass is supported by the car's 4 shock absorbers. The shock…

Q: Draw and discuss the FBD for the following system. • Label all forces and directions. • How many…

A: The free-body diagram of the mass A in the given system is shown below.Here, we have two unkown to…

Q: In your report you must include: (a) The free body diagram of the rudder. (b) If the maximum…

Q: Don't Use Chat GPT Will Upvote

A: Step 1:Step 2:Step 3: Step 4:

Q: 2) As shown in the figure, a uniform rod of length I and mass m is supported by a pin at one end and…

A: This question is about topic of rotational motion. Here the rod is tied with string and hinged at…

Q: A 68 kg mass is supported by the three springs as shown. The initial displacement is 15 cm downward…

A: MassEquivalent spring constant

Q: The equation of motion for a vibrating system with viscous damping is ÿ + 2Çwný + wñy = 0. If the…

A: Vibratory systems include mechanisms for storing potential energy (springs), kinetic energy…

Q: 2. Consider an engineering mechanics analysis of cellular mechanosensing via focal adhesions shown…

Q: The cable of the 1600 kg elevator cab in the figure snaps when the cab is at rest at the first…

Q: The bicyclist encounters a incline in the road. (Eigure 3) To maintain a constant velocity, the…

Q: 62. •A 5-kg object is constrained to move along a straight line. Its initial speed is 12 m/s in one…

Q: An object with a mass of 0.5 kg is released from a distance of 2 m, the spring coefficient k = 100 N…

A: Given Data: The mass of the object is m = 0.5 kg. The spring coefficient is k= 100 N/m. The initial…

Q: A steel cylindrical violin string that plays the "E" note: Length = 360 mm • Diameter = 0.25 mm…

Q: ki= 15 N/m; k2 = 10 N/m; m, k3 = 12 N/m; %3D C1 Ci =1 N.s/m; m2 K3 c2= 2 N.s/m; C3 = 2 N.s/m; m3 mi…

A: Given : To find : Equation of motion

Q: 4. A spring with stiffness constant k = 2000 N/m attached to a platform launched a mass of 2kg…

Q: Q4/Thin rod positioned between two walls that are held at constant temperatures. Heat flows through…

Q: Consider a mass-spring system hanging vertically. The mass is 0.15 kg and the spring constant is 0.3…

Q: 1. The heat equation describes the flow of thermal energy (heat) in materials. The temperature V…

Question

A fender is mounted on a automobile though dampers (to absorb collision energy) and
springs (so that the fender can recover after low-speed collisions). During a crash-test, the
automobile is moving at 2 m/s when its fender strikes a concrete barrier. The vehicle
mass, m, is 1,000 kg. (In comparison, the fender itself is essentially massless.) The
springs that mount the fender have a stiffness, k, of 1,000,000 N/m.
y
m
barrier
1) Write a differential equation for the deflection of the springs when the fender is in
contact with the barrier.
2) If the damping coefficient, c, is 30,000 N-s/m, what is the damping ratio of the
mass-spring-damper system when the fender is in contact with the barrier?
3) For that damping coefficient, make a reasonably accurate sketch (with properly
labeled axes) of the time-course of the force exerted on the barrier, starting from
the moment of first contact.
4) Is there any value of the damping coefficient, c, that would yield no rebound of
the vehicle from the barrier? If so, what is it? If not, why not?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

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

Find expressions for the coefficients an and bn for a plucked 50 cm string fixed at the ends with initial velocity 10 m/s at the midpoint. A an = (-1)"80/[(nn)2], b = (-1)"80/[w₁(nπ{(2n+1)π² B C D an = 0, b2n=+1 = (-1)2n+180/[wn{(2n+1)m}² a2n+1 = -(-1)2n+180/[(2n+1)}²], b₁ = 0 an = 0, bn = (-1)^80/[w,(nn)²]
My question and answer is in the image. Can you please check my work? A 2 kg mass is attached to a spring with spring constant 50 N/m. The mass is driven by an external force equal tof(t) = 2 sin(5t). The mass is initially released from rest from a point 1 m below the equilibrium position. (Use theconvention that displacements measured below the equilibrium position are positive.)(a) Write the initial-value problem which describes the position of the mass. 2y"+50y=2cos(5t) (b) Find the solution to your initial-value problem from part (a). (1+(1/2)tcos(t))cos(5t)-(1/2)tcos(t) (c) Circle the letter of the graph below that could correspond to the solution. B (d) What is the name for the phenomena this system displays? Resonance
Solve the problem quick & carefully On a sheet of paper with FBD , Don't copy which might be wrong.
Drop-load (III) context We want to lower a suspended load in a controlled way, so that it hits the ground with a speed whose modulus is not too great. To do this, the suspended load (B) is connected by a rope passing through a pulley to another mass (A), which can move on an inclined surface. Information The masses of charges A and B are known.The pulley is a solid cylinder (or disc) of mass mp and radius R which can turn without friction.The surface on which mass A is placed is horizontal.There is friction between mass A and the surface on which it is placed, the coefficient of friction is uc.Mass A is on a surface tilted by an angle delta.The rope attached to mass A is perfectly parallel to the surface on which the mass is placed. Modelization Create a model for the acceleration of mass B given the known parameters of the problem that are relevant. Mass of load A: 70kg; Mass of the suspended load (B): 82kg; Pulley mass (mp): 52kg Pulley radius: 0.46m Coefficient of friction: 0.12…
IMAGES NOTES DISCUSS UNITS STATS Part Description Ans A 4.0 kg mass is connected to a spring (k=155 N/m) and is sliding on a horizontal frictionless surface. The mass is given an initial displacement of +19 cm and released with an initial velocity A. Format of -26 cm/s. Determine the acceleration of the spring at t=2.4 seconds. (include units with answer) 2 Type here to search
Physics 121 Spring 2021 - Document #11: Homework #04 & Reading Assignment page 4 of 8 Problem 1: Gnome Ride - This from a Previous Exam I. A Gnome of given mass M goes on the Gnome Ride as follows: He stands on a horizontal platform that is connected to a large piston so that the platform is driven vertically with a position as a function of time according to the following equation: y(t) = C cos(wt) Here w is a constant given angular frequency, C is a given constant (with appropriate physical units) and y represents the vertical position, positive upward as indicated. Part (a) - What is the velocity of the Gnome at time t = 0? Explain your work. Present your answer in terms of the given parameters Part (b) – What is the net force on the Gnome at time t = 0? Explain your work. Present your answer in terms of the given parameters Part (c) – What is the Normal Force on the Gnome at time t = 0? Explain your work. Present your answer in terms of the given parameters Some Possibly Useful…
An object attached to the end of a vertical helical spring bounces with a frequency of 2.1 Hz. If the spring constant is 5.9 N/m, what is the mass of the object?
Answer the following question part a and part b A) The 4 kg disk shown in Figure Q1 is initially at rest. A force of F = 50 N is applied to the thin, inextensible cable wrapped round the disk diameter d = 156 mm. Calculate the work done on the disk after it has turned through 8.8 revolutions. [Answer in J] 30 Q1 b) Assuming that the 8 kg disk in previous part is initially at rest and a force of F = 67 N is applied to the thin, inextensible cable wrapped round the disk diameter d = 177 mm. Find the angular velocity of the disk after it has turned through 8.1 revolutions. [Answer in rad / s]
See the attached image1) A long rod in the shape of a circular cone is rotating with constant angular velocity c about an axis located at the left end of the rod as shown in the figure below. The bar has length L, major and minor diameters D and d, respectively, and its material has linear elastic behavior with modulus of elasticity E. The values of the problem parameters must be defined by the student a) From the balance of a differential member of the bar, derive the differential equation of balance for the bar. Solve the equation analytically to obtain the bar displacement field, U(X). Give the expression for the displacement at the free end of the member. b) Implement a computational code in MATLAB (or any other software) to solve this problem with "n" two-node bar finite elements. c) Run different simulations by increasing the number of finite elements in each simulation. At each simulation, obtain the displacement of the free end of the member. Graphically compare your results…
HEAT TRANSFER CASE: I want to know what temperature in (°F) the cylinder will have inside. It's a heat transfer problem. what is T2 ? HEAT TRANSFER They gave me an answer all squashed together that i can't make sense of it. If you could help me makes sense of it thank you!
Please show the work to understand the process. AI generated steps have been wrong.
a) A two-degree-of-freedom coupled pendulum model is shown in Figure Q1a. The parameters of the model are: k=100 N/m; m=10 kg and L=1 m. The equations of motion of the system are given below. J₁ä + (mgL + kĽ² ) 8₁ - kľ² 0₁₂ = 0 J₁₂+(mgL+kĽ²)₂-kĽ² 0₁ = 0 i) Calculate the natural frequencies. ii) Draw the mode shapes. m Figure Q1a. b) In the above system discuss the implications of the following changes in coupling stiffness. i) k is reduced considerably to 0.1 N/m. ii) k is increased considerably to 1x105 N/m. c) Draw a schematic of modal test arrangement of a beam using instrumented impact hammer. d) Why is it necessary to measure force in a modal test?