Estimate the velocity and angular velocity of an empty pipe

[Calum Mulryan]

Hi, I need to resit some exams and I'v been having difficulty trying to solve this problem.

Estimate the velocity and angular velocity of an empty pipe of mass (m)=1000kg, Diameter (d)=10mm, shell thickness (h)=1mm at the bottom of a slope of angle $$\theta$$=45$$^{}o$$ and path length L=5000mm on the planet uranus (g=8.9 m/s$$^{}-2$$)

thanks

Calum

 

[mshinavar]

firstly, i have no interest in doing the problem for you (don't think you'll learn - i had to learn that the hard way); however, i have a high interest that you do well in your exam.

perhaps this may help:

use an energy balance: all potential energy is converted into kinetic energy

use trig knowing the hypotenuse is 5000m, and theta is 45*. easy to find the height.
you know the mass, and g. PE=mgh

shell thickness is to account for moment of inertia losses. unfortunately I am at a loss (in the 1 minute while i type this, and i don't have a dynamics book at my desk). something like I*(ang vel)^2, though

that equals 1/2 m Vfinal^2

so we have PE - MoI losses = KE
the MoI losses will act like a friction loss for the most part where they are summed along the length of the path (i.e. retarding force* distance it acts along)

from Vfinal, knowing diameter, you can find omega without too much difficulty

sorry i can't help too much on the MoI stuff, my book is 60 miles away. perhaps tomorrow if you are still stuck, i'll come back. or another member can contribute

or tell your professor that Uranus is gaseous, and therefore has no surface in which to support the ramp, so for practical purposes the problem does not require a solution