A Rod with mass m and length L can rotate freely about one of its ends. A pointmass with the same mass as the rod (m) can move freely along the length of the rod(ignore friction). The point mass is attached to a spring with a spring constant Kand a negligible initial length. Gravity acts. Use Newton's Second Law (thisincludes the torque equation if you need it) and derive the Equation(s) of motionfor this system.LmuKmm

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Answered: A Rod with mass m and length L can…

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

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Cam mechanisms are used in many machines. For example, cams open and close the valves in your car engine to admit gasoline vapor to each cylinder and to allow the escape of exhaust. The principle is illustrated in the figure below, showing a follower rod (also called a pushrod) of mass m resting on a wedge of mass M. The sliding wedge duplicates the function of a rotating eccentric disk on a camshaft in your car. Assume that there is no friction between the wedge and the base, between the pushrod and the wedge, or between the rod and the guide through which it slides. When the wedge is pushed to the left by the force F, the rod moves upward and does something such as opening a valve. By varying the shape of the wedge, the motion of the follower rod could be made quite complex, but assume that the wedge makes a constant angle of 0 = 19.0⁰. Suppose you want the wedge and the rod to start from rest and move with constant acceleration, with the rod moving upward 1.00 mm in 8.00 ms. Take m…
A 25.5 kg mass (m) is suspended by the cable assembly as shown in the figure. The cables have no mass of their own. The cable to the left (T) ) of the mass makes an angle of 0.00 with the horizontal, and the cable to the right (T;) makes an angle (02) of 40.6. If the mass is at rest, what is the tension in each of the cables, T and T; ? The acceleration due to gravity is g = 9.81 m/s?. T T = 123.52 N 123.52 TOOLS x10
A solid bar of mass m and length L stands vertically on a frictionless table and is then released to fall down. The moment of inertia about the center of mass is Ic = mL²/12. At the moment when the top end B just reaches the ground (0-0), (a) what are the angular velocity and angular acceleration? (b) what is the center-of-mass acceleration? (c) what is the normal force of the ground to end D? Hint: It may be helpful to find out the instant rotation axis. В m. L D
1. A force of 64 pounds stretches a spring 2 feet. A mass of 16 pounds is attached to the end of the spring and is initially released from the equilibrium position with a downward velocity of 3 feet per second. Find the equation of motion.
A block of mass m₁ is suspended from the ceiling with a spring k and damper b. Attached to the block is a massless rod of length L. Affixed to the end of the rod is a point-mass of mass m₂. Gravity is acting in the direction indicated in the figure. Use the energy method to set up the energy expression you would use to calculate the equations of motion for the system. Hint: be sure to decompose the velocity of the pendulum into horizontal and vertical components. DO NOT CALCULATE THE EQUATIONS OF MOTION, only setup the energy expression. x(t) b 7 m₁ e(t) (m₂
Figure 13 shows a simple model of a machine part, with an applied moment applied clockwise to the disc. The disc rotates without translation. Assume that the mass is on a frictionless surface and also that the disc rotates around the shaft with no friction effects. (a) Determine the kinetic and potential energy of the system. (b) Determine the equation of motion of the system using Lagrange’s equation.
5. A 25.0-g mass is attached to a vertical spring and it stretches 15.0 cm. It is then stretched an additional 10.0 cm and then released. What is the maximum velocity of the mass? What is its maximum acceleration? Vmax = Dmax =
what is the tension T1 in a cord attaching a baby to a scale? what is the tension T2 in the cord attaching the baby to the ceiling? The mass of a rocket sled is 2100KG and the force of friction opposing the motion is 640N. The thrust for the sled is 25900N. What is the acceleration in Metres per second second? A 1140 KG artillery shell is fired from a battleship,.W,hile it is in the barrel of the gun, it experiences an acceleration of 2.2 x 10^4 m/s^2. what net force is exerted on the artillery shell before it leaves the barrel of the gun in Newtons. What is the magnitude of the force exerted on the ship by the artillery shell in Newtons?
3.32). As shown in Figure 3, a yo-yo toy is formed by wrapping a massless cord around adisk of radius R= 0.2 m and mass M=3 kg. The cord is vertical and its top end is fixed and the disk isinitially stationary. The cord remains vertical for the entire motion and does not slide on the disk.When the disk is released from rest, it falls down by a distance H=0.8 m, The moment of inertia ofthe disk around its center is I disk=1/2mdiskR^2a . Find the angular acceleration of the disk when it is lowered by a distance H.b . Find the angular velocity of the disk when it is lowered by a distance H.
A block of mass 40 kg slides to the right due to the application of the force T. Neglect the mass of the pulleys. 30° 40 kg T = 100 N Hy = 0.50 Hp = 0.40 A Figure Q6 (a) Set up the global reference axes system and draw the free body, kinematic and kinetic diagrams of the block.
0.5 m, k = 500 N/m, and k = 40 N.m/rad, In the system shown, m = 10 kg, r = 0.3 m, Ko where ko is the radius of gyration of the pulley about point 0. There is no slippage between the cord and the pulley. Replace the system with an equivalent { a) torsional spring and mass moment of inertia at point 0, and b) translational mass and spring at point A. т, Ко kt А k m ww
For this problem, take a look at Figure 2 below. A disk with uniformly distributed mass m, radius R, and center of mass at point O is connected to a combination of springs at point P, which are then connected to a fixed wall. The disk rolls without slipping at point Q along an inclined plane that is at an angle a from the horizontal. Gravity acts in the vertical direction (towards the bottom of the page). ₁ is the linear coordinate of the point O along the inclined plane. The positive direction of ₁ is as shown. When the springs are undeflected, *₁ = 0. An angle , about the instant center of rotation, is shown. You may assume that the motion (and therefore angle ) is small. puny m Massless structure between springs R Figure 2: System schematic. Your tasks: A Draw the FBD for the disk. Don't forget the forces at point Q B Derive the equation of motion with as the dynamic variable. Be sure to put it in input-output standard form (inputs and constant forces on the right, things related to…

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