Dynamic movement in polar coordinates, Mechanical Engineering

Assignment Help:

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.


Related Discussions:- Dynamic movement in polar coordinates

Study and design of pattern, TO Study And Design Of Pattern A pattern i...

TO Study And Design Of Pattern A pattern is an element used for making cavities in the mould, into which molten metal is poured to produce a casting. It is not an exact replica

Determine maximum fibre stress - beam, Determine Maximum fibre stress: ...

Determine Maximum fibre stress: A beam of rectangular section of 80 mm to 120 mm carries a uniformly distributed load of 40 kN/m over a span of 2 m an axial compressive force

Calculation of total energy - thermodynamics, T ota l Energy: Total ...

T ota l Energy: Total energy possessed by system is the sum of all types of stored energy. Thus it will be given by E total  = PE + KE + U = mgh + 1/2mv 2  + U It is ex

Drawing, for drawing large size circles diameter greter than 150mm what is...

for drawing large size circles diameter greter than 150mm what is attached to compass? \

Define cases in which automation is done, Define Cases in which Automation ...

Define Cases in which Automation is Done Automation is done in following cases:- a) Loading and unloading of parts. b) Automatic production lines. c) Automatic tool ch

Manufacturing, #draw a net sketch of the geometry of a single point tool.

#draw a net sketch of the geometry of a single point tool.

Counterclockwise direction, Figure presents a gearbox that you are going to...

Figure presents a gearbox that you are going to design. The input shaft rotates at n1= 1500 rpm in a counterclockwise direction. The gearbox is needed to be designed sothat the out

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd