A giant snowboard, represented by a rigid and slender rod with mass m and length L, slides on the undersized cylindrical half-pipe of radius r without friction at its ends A and B. The motion of the snowboard within the half-pipe occurs only within the vertical plane shown. Using the generalized coordinate 0, derive the equations of motion for this system using Lagrange's Equations. Note: The moment of inertia of a slender rod about its center of mass I=1/12*m*L2

A giant snowboard, represented by a rigid and slender rod with mass m and length L, slides on the undersized cylindrical half-pipe of radius r without friction at its ends A and B. The motion of the snowboard within the half-pipe occurs only within the vertical plane shown. Using the generalized coordinate 0, derive the equations of motion for this system using Lagrange's Equations. Note: The moment of inertia of a slender rod about its center of mass I=1/12mL2

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: The figure shows a trolley of mass 10 kg that can move freely along a smooth fixed horizontal rail…

A: Given: The mass of trolley, M = 10 kg The mass of link AB, m = 2 kg The length of AB, L = 1.5 m The…

Q: Derive the equations of motion of the block of mass m1 in terms of its displacement x. Surface…

A: Given, a block of mass m1, Mass of the cylinder is m2, Radius of the cylinder is R, Distance between…

Q: 1 A thin 5m long uniform rod is free to rotate in the plane of the page about a fixed axis at Point…

Q: NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to…

Q: (5) The uniform slender rod (mass m and length L) is pinned to the center of the uniform disk (mass…

Q: 2 An object is made of two identical uniform 3m long rods connected as shown. The total mass of the…

Q: Please don't provide handwritten solution ...

A: Proper solution with step by step is provided below:Explanation:Step 1: Given dataThe radius of the…

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: The pendulum shown in the image below can rotate about the axis perpendicular to page and pass…

Q: A uniform hemisphere of mass m = 5 kg. and radius r = 0.5m. is released from rest on a horizontal…

A: Given:Mass,m=5 kgRadius,r=0.5 mI0=(2/5)mr2To determine:Free body diagram, Kinematic and Kinetic…

Q: A flywheel with a radius of gyration 0.5 m is fitted to a multi cylinder engine, which runs at a…

A: Given k=0.5 mN=360rpmCs=0.02−(−0.04)=0.06ΔE=45kN⋅mTo FindMoment of inertia of the flywheelMass of…

Q: You are tossing the baton up into the air while it is turning, resulting in a motion that is…

A: Given:

Q: Problem 2: The drum shown weighs 80lb and has a mass moment of inertia about O of 0.8 lb.ft?.…

Q: Given: The gear shown moves on a fixed horizontal rack. The gear has mass m and a radius of gyration…

A: Given: Mass of the gear=mgear Radius of gyration of the gear=R Mass of the rod=mrod Length of the…

Q: (a) At this instant, what is the speed of the center of the apparatus? U = Part 2 0.708548386 (b) At…

Concept explainers

Power Transmission Elements

It is defined as the energy transfer from one location to another location. The energy will start moving from the energy generation source to the energy applied position to obtain the work output. From this method, a large amount of electric energy moves from the power station to various electrical substations.

Question

A giant snowboard, represented by a rigid and slender rod with mass m
and length L, slides on the undersized cylindrical half-pipe of radius r
without friction at its ends A and B. The motion of the snowboard within the
half-pipe occurs only within the vertical plane shown. Using the generalized
coordinate 0, derive the equations of motion for this system using
Lagrange's Equations.
Note: The moment of inertia of a slender rod about its center of mass
IG=1/12*m*L2
A
C

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Design of Power Transmission Elements and Power Transmission Systems

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

An elliptical hoop of negligible thickness with a vertical orientated semi-major axis a and a horizontal orientated semi-minor axis b, which has a mass per unit length of p, is mounted on a circular peg to which is attached a Carte- sian xy coordinate system in a vertical orienta- tion as shown in the accompanying sketch (the gravity g ellipse and peg are not rigidly joined to each other and are simply in kinematic contact with each other with negligible friction), such that the physical system lies within a flat ry plane. The ellipse is then allowed to freely oscillate in a to-and-fro rocking motion by a small angle 0, such that the gravitational acceleration g acts in a downwards direction that is parallel to the ellipse semi-major axis. 1.3 a 1.4 b Considering the above system determine the following information clearly showing all steps and appropriate reasoning: Y Utilizing the previously derived equation of motion determine the corresponding natural angular frequency wn for the…
4. In order to determine the mass moment of inertia of a 4-foot diameter flywheel, the flywheel is tested\twice with different deadweight. In the first test a weight of 20 lb is attached by cord and observed to fall 10 ft in 4.6 seconds. In the second test a weight of 40 lb falls 10 ft in 3.1 seconds. Assuming that the torque due to bearing friction is constant, determine mass moment of inertia of the flywheel. Your solution must include W supporting FBDS.
Edit question Calculate the radius of gyration for the system of two tubes and a seat that form a swing with respect to the axis A shown in the figure. The dimensions of this system are shown in the figure below.The tubes have a mass of 19 kg/m. This means that each meter of tube has a mass of 19. Tubes can be thought of as slender rods.The seat has a mass of 23 kg and can be considered as a thin plate. Note that several views of the swing are offered so that you can better understand which is the reference axis A and the necessary dimensions. As you solve the problem, take into account that you are going to fill a table with the following format. It must be filled with the corresponding units.
Problem 4. A thin, semi-circular ring of mass m and radius R is pinned to ground at point O. The bar is released from rest in the position shown. Note that a = 2R, IG = mR² - ma² (a) Find the mass moment of inertia of the body about point O (b) Find the angular acceleration of the ring when released (c) Find the reaction forces on the ring at point O Ans: (b) a=0.5(g/R); (c) Ox = (mga)/(2R), Oy = mg/2 6.0 g G a -R-