The figure shows a mass-pulley system. It consists of a pulley which is connected to the inertial frame through a frictionless revolute joint. The pulley has two sheaves, one with radius r=50 mm and the other with radius R=100mm. The sheaves are rigidly coupled together. The moment of inertia of the pulley is 1=0.03 kg m². A mass M-8 kg is suspended from the smaller sheave the pulley. A damper with damping coefficient C is connected between the mass and the inertial frame. A spring with stiffness k links the larger sheave to the inertial frame. The undamped natural frequency of the system is a = 50 rad/s and the damping ratio is = 0.6. 1. k www R M Focos(12t) Figure: Mass pulley system Calculate the stiffness, k, of the spring and the damping coefficient, C.

The figure shows a mass-pulley system. It consists of a pulley which is connected to the inertial frame through a frictionless revolute joint. The pulley has two sheaves, one with radius r=50 mm and the other with radius R=100mm. The sheaves are rigidly coupled together. The moment of inertia of the pulley is 1=0.03 kg m². A mass M-8 kg is suspended from the smaller sheave the pulley. A damper with damping coefficient C is connected between the mass and the inertial frame. A spring with stiffness k links the larger sheave to the inertial frame. The undamped natural frequency of the system is a = 50 rad/s and the damping ratio is = 0.6. 1. k www R M Focos(12t) Figure: Mass pulley system Calculate the stiffness, k, of the spring and the damping coefficient, C.

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: PROBLEM 3 3 Mechanical system consists of solid body 1 of mass mm which is connected by non-elastic…

Q: Consider the Bar/Rollers/Wire system of the figure. The Bar and Rollers assembly weighs 60 lbs, with…

A: Given data weight of bar and rollers assembly (w) = 60 lbs To determine 1) draw a free body…

Q: English: A train carriage consists of a car body and two axles with wheels. The car body has a mass…

A: F = ma so we have to determine the velocity once it has travelled 0.2 m under constant accn.

Q: m A solid sphere of mass 3m and radius 2R has a rope tied around it. The free end is wrapped around…

A: Given: Mass of sphere = 3m Radius of sphere = 2R Mass of pulley = m Radius of pulley = R Mass of…

Q: A bar is attached to the spring at the point C. The left end of the bar is pin supported and can…

Q: Determine the reactions at the pin support and the applied moment if the bar of Figure 3 has a mass…

Q: A bar is attached to the spring at the point C. The left end of the bar is pin supported and can…

Q: What is the length of the wire? Express your answer with the appropriate units. HẢ ? Iwire =Value…

Q: The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is…

Q: PROBLEM 3 3. Mechanical system consists of solid body 1 of mass mm which is connected by non-elastic…

A: Given:The mass of the solid body 1, The mass of the disk 2, The radius of the disk The coefficient…

Q: The swinging frame of a balancing machine is shown in figure 1. The lever ACB has a mass of 6 kg and…

A: Given:To find:Frequency of vibration

Q: A beam, uniform in mass, M = 47.6 kg and length L = 10.2 m, hangs by a cable supported at point B,…

Q: The body and bucket of a skid steer loader has a weight of 1990 lb, and its center of gravity is…

A: The weight of the body and bucket is P=1990 lb. The weight of each wheel is W=95 lb. The radius of…

Q: PROBLEM 3 Mechanical system consists of solid body 1 of mass mm which is connected by non-clastic…

A: Given:The mass of the solid body 1, The mass of the disk 2, The radius of the disk The coefficient…

Q: Problem 05: The circular disk of 200 mm radius has a ma centroidal radius of gyration k-175 mm. The…

A: The kinetic diagram for the system is as follows,Consider no slipping condtion.

Q: A bar is attached to the spring at the point C. The left end of the bar is pin supported and can…

Q: The 6.0-1b bar is pinned at its center O and connected to a torsional spring. The spring has a…

A: In this problem first the moment about O is taken and the acceleration is integrated to get the…

Q: A car is pushing a barrel to the right. The pushing force P is applied by the front bumper which is…

A: (1) Draw the free-body diagram of barrel when no slipping occur.

Q: A bar is attached to the spring at the point C. The left end of the bar is pin supported and can…

Q: A stationary bicycle wheel of radius 0.7 m is mounted in the vertical plane (see figure below). The…

Q: A bar is attached to the spring at the point C. The left end of the bar is pin supported and can…

Q: The body and bucket of a skid steer loader has a weight of 2060 lb, and its center of gravity is…

A: The speed of the loader. Given: The weight of the body and bucket is P=2060 lb. The weight of each…

Q: A beam of length L and mass M rests on two pivots. The first pivot is at the left end, taken as the…

Q: A bar is attached to the spring at the point C. The left end of the bar is pin supported and can…

Q: 3. A slender, rigid bar of mass 20 kg and length 4 m is rotating about its pin joint at Point A as…

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

The figure shows a mass-pulley system. It consists of a pulley which is connected to the inertial
frame through a frictionless revolute joint. The pulley has two sheaves, one with radius r=50 mm and
the other with radius R=100mm. The sheaves are rigidly coupled together. The moment of inertia of
the pulley is 1=0.03 kg m². A mass M-8 kg is suspended from the smaller sheave the pulley. A damper
with damping coefficient C is connected between the mass and the inertial frame. A spring with
stiffness k links the larger sheave to the inertial frame.
The undamped natural frequency of the system is w₁ = 50 rad/s and the damping ratio is = 0.6.
k
www.
1.
R
M
Focos (nt)
Figure: Mass pulley system
Calculate the stiffness, k, of the spring and the damping coefficient, C.

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: Free body digram

Step 2: for K

Step 3: for C

Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

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

The position of the head and neck and the forces acting on the head are shown in the figure. The center of gravity of the head of mass m=9 kg is located at point C. The joint reaction force of F J = 150 N, which makes an angle of α = 30° with the vertical from the point B, is acting on the skull by the neck extensor muscles. The center of the atlantooccipital joint is located at point B. For this flexion position of the head, the neck muscle force FM, which makes an angle of γ with the horizontal from the point A , is effective . (Take the gravitational acceleration g as 9.81 m/s 2. ) Accordingly; a) Calculate the angle γ of the muscle force F M with the horizontal. b) Calculate the muscle strength F M. (Write your result in N units.)
A student sits on a freely rotating stool holding two dumbbells, each of mass 2.97 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 1.09 m from the axis of rotation and the student rotates with an angular speed of 0.749 rad/s. The moment of inertia of the student plus stool is 2.57 kg. m² and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.305 m from the rotation axis (Figure b). Wf Wi a 30€ 30€ = b (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward. K before J J after
The mass of the gear is 48 kg and it has a radius of gyration of ko = 125 mm. The mass of the gear rack is 22 kg. Assume that the contact surface between the gear rack and the horizontal plane is smooth. (Figure 1) Figure 150 mm- 75 mm vira 1 of 1 P = 150 N Part A If the cord is subjected to a horizontal force of P = 150 N, and gear is supported by a fixed pin at O, determine the angular velocity of the gear in 1 s, starting from rest. Express your answer to three significant figures and include the appropriate units. Enter positive value if the angular velocity is counterclockwise and negative value if the angular velocity is clockwise. Submit Part B V = μÀ Value Submit Request Answer Provide Feedback Determine the velocity of the gear rack in 1 s, starting from rest. Express your answer to three significant figures and include the appropriate units. Enter positive value if the velocity is rightward and negative value if the velocity is leftward. Value μA Units Request Answer www…
A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following. (4) the work done by the reaction force of the pin.____________ (J)
A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following. (2) ) the work done by the couple moment. __________(J) (two decimal places)
A Pin spanner as shown in Figure, requires moment of 80 Nm to turn the 200 mm diameter shaft about its center O under the action of the applied force P. determine the contact reaction force on the smooth surface at the point A. Engagement of the pin at B may be considered to occur at the periphery of the collar OPTIONS:(MULTI CORRECT(MAY BE)): 1.Reaction at Point A is around 1047 N 2.Value of force P is around 102 N 3.Value of force P is around 133 N 4.Reaction at Point A is around 720 N 5.Reaction at Point A is around 1321 N 6.Value of force P is around 200 N 7.Value of force P is around 213 N 8.Reaction at Point A is around 970 N
The assembly shown in the figure below consists of a thin rod of length { = 22.4 cm and mass m = 1.20 kg with a solid sphere of diameter d = 10.0 cm and mass M = 2.00 kg attached to its top. The assembly is free to pivot about a frictionless axle through the bottom of the rod. The assembly is initially vertical and at rest when it starts to rotate clockwise. (a) After the combination rotates through 90 degrees, what is its rotational kinetic energy (in J)? (b) What is the angular speed (in rad/s) of the rod and sphere? rad/s (c) What is the linear speed (in m/s) of the center of mass of the sphere? m/s (d) How does it compare with the speed had the sphere fallen freely through the same distance of 27.4 cm? (Express your answer as a percentage.) %. is ---Select--- V swing v Vall by