Problem 1 SpherulleyA solid sphere of mass 3m and radius 2R has a rope tied aroundit. The free end is wrapped around a pulley with mass mand radius R which in turn suspends a block of mass m'. (a)What is the moment of inertia for the sphere and for the pul-ley/disk?(b) Draw an extended free-body diagram for the sphere and then findthe tension in the rope pulling the sphere in terms of the linear acce-leartion of the rope and mass m. (c) Draw a simple free-body diagramof the hanging mass and solve for the tension in the other part of the rope in terms of the linear acceler-ation and the mass m'.(d) Now, draw an extended free-body diagram of the pulley and solve for the linear acceleration of therope. Your answer should now only depend on the given masses. (e) Does your answer make sense if thepulley and sphere have no mass?

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

Answered: m A solid sphere of mass 3m and radius…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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4. A student followed strictly correct procedure in the lab during the experiment of moment of inertia. He measured the mass and diameter of plastic cylinder with value of m = 0.36 kg and D = 0.1 m. The period of system without plastic cylinder is To = 0.667 s. The period of system with plastic cylinder T₁ = 0.92 s. Find: The spring constant K of the system. If a metallic cylinder and a plastic cylinder have same diameter and same thickness, which one has larger moment of inertia? Explain.
A long, thin, wire of uniform cross-section has Young's Modulus Y and mass density D. When laid horizontally on a bench its unstretched length is L. One end is attached to a fixed point and the rest of the wire is allowed to hang freely and vertically in the earth's gravitational field. Find the extension of the lowest end of the wire (i.e., the wire's length additional to L) due to gravitational force. The acceleration due to gravity is g.
A\a = 60" B= ??/ B Figure (d): (D) is a homogeneous disk of mass 300 g and of center o. Calculate the tension in the strings AE and BC and the value of ß. We can use an axis of rotation passing through C. E (D)
A uniform aluminum beam 9.00 m long, weighing 300 N,rests symmetrically on two supports 5.00 m apart (Fig. ). A boyweighing 600 N starts at point A and walks toward the right. (a) In thesame diagram construct two graphs showing the upward forces FA andFB exerted on the beam at points A and B, as functions of the coordinatex of the boy. Let 1 cm = 100 N vertically and 1 cm = 1.00 m horizontally.(b) From your diagram, how far beyond point B can the boy walkbefore the beam tips? (c) How far from the right end of the beam shouldsupport B be placed so that the boy can walk just to the end of the beamwithout causing it to tip?
L W (1) (25pts) Find the description of the linear acceleration vector of the mass center of the segment (B) as functions of the distance (r), angular displacement (0), angular velocity (0), and angular acceleration (a). (2) (bonus: 5pts) Find the mass moment of inertia of the lower leg about the knee joint. Assume that the lower leg can be modeled as a cylinder. The length of the lower leg L is 30cm, and the diameter D is 4cm. The mass of the lower leg segment is 2kg. * This is a bonus problem - you learned how to calculate the mass moment of inertia in physics.
please define the system and provide the free-body diagram with x-y-axis Please answer these two questions together cause there is a follow-up question.
- 2a 2a o' 2a -2a Figure P4.17 4.17. Find the product inertia Iyy for the beam section shown in Figure P4.17. Notice that the centroid must be at O by symmetry.
For each mechanism, determine the mobility and the number and type of each kinematic pair: Q3 # of Turning Pairs: # of Sliding Pairs: # of Rolling Pairs: # of 2 Deg. of Freedom Pairs: No Slip. (a) (b) (c)
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
5. Car doors are easy to slam shut but difficult to press shut by hand force. The door lock as two latches, the first easily engaged, and the second requiring the rubber seal around the door to be quite compressed before it can engage. The rubber seal gives a spring constant of 50,000N/m at the lock position for the door, and the mass moment of inertia for the door around its hinges is 2.5kg- m². The distance between the lock and the hinges is Im. Calculate what force is needed to press the car door shut at the lock if a speed of 0.8m/s at the lock slams it shut.
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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