Dynamic movement in polar coordinates, Mechanical Engineering

You are required to investigate the dynamic movement of a mass m sliding along a rod as shown in the diagram below. The rod is rotating at a constant angular velocity θ. The mass m is able to slide along the rod from position 1 (given by r = r1 to position 2 given by r = r2). At position 2 there is a stop as shown on the figure .Initially, at time t = 0, the mass m is tied by a string to the centre of rotation O which is then suddenly cut and frees the mass. At time t = 0, the angular position of the rod is θ = 0 rad. You are to neglect friction and the mass of the rod.

995_Dynamic Movement in Polar Coordinates.png

Notes:
Your own values of , r1, r2 and m are given in your Data Sheet

This investigation is to be carried out with your own specific data provided on a separate Data Sheet. No written material such as paragraphs or parts of text should be copied from any other source including your fellow students. All written text should be your own work.

Your tasks and corresponding marking scheme are as follows:

A. Draw the free body diagram of the forces on mass m at a position r between r1 and r2 and deduce the expressions for ar and aθ.

B. Determine the values of radial and tangential accelerations at position 1 just after cut-off of the string.

C. Determine the expressions for radial and tangential velocities for the mass m at any position r between r1 and r2.

D. Deduce the speed of the mass m when reaching position 2 and calculate the corresponding force involved when it stops at 2.

E. At t = 0.01 s, determine the angular and radial position of the mass as well as all the components of radial and tangential velocities and accelerations.

F. Explain why there is no such a thing as a centrifugal force.

G. If friction had been taken into account, what would be the relevant equations of motion. (do not solve them).

H. Report structure & presentation.

Posted Date: 4/1/2013 6:28:45 AM | Location : United States







Related Discussions:- Dynamic movement in polar coordinates, Assignment Help, Ask Question on Dynamic movement in polar coordinates, Get Answer, Expert's Help, Dynamic movement in polar coordinates Discussions

Write discussion on Dynamic movement in polar coordinates
Your posts are moderated
Related Questions
Superheate d Steam: When the dry saturated steam is heated further at constant pressure, the temperature of it rises up above the saturation temperature. This rise in tempera

Describe the following terms:- a) Shear force and bending moment b) Concentrated load, Uniformly varying load and Uniformly distributed load c) Beam & Types of beam. d)

(a) Mention the needs to be satisfied by power transmission system of vehicles. (b) What is an overdrive? Explain its principle of operation and advantages.

CLOSED CIOL HELICAL ,WIRE DAI 10MM AND COMLITE10 TURNS WITH MEAN RADIOUS AND AXIAL LOAD 200N ,C=80KN/MM2.FIND DIFLECTION OF SPRING?

Working, specification construction of Lancashire boiler

Find out load carried and compressive stress: The concrete column 300mm x 300mm in section can be reinforced by 10 longitudinal 20mm diameter round steel bars. The column car


Cylinder Head De-carburising and Valve Lapping: Cylinder head mounts on the top of the engine cylinder, the inner side of the cylinder head is always in direct contact of combusti

COMMON RULES CONCERNING CORRESPONDING OPTION:     Let us consider the DATA DIVISION entries as shown below. Now, let us see which data items will be moved if

Tensile strength: What will be its ultimate tensile strength? Solution The condition for necking is = n = 0.3077 Hence using this value of , the true stress at ne