Solving Dynamics Questions on Two Uniform Thin Discs

[billybomb]

Ok, I'm doing Mechanical Engineering so my assumption was to post in here?

I'm doing a dynamics module and revising for an up and coming exam. One of the 'revision' questions doesn't have the answer to work through, and typically I am finding it very difficult to get my head around it.

The question:

The two uniform thin discs shown in the figure below rest on a horizontal plane
and are connected through frictionless pin-joints at A and B by a rigid rod AB of
negligible mass which remains horizontal. The mass of disc A is 15 kg and that of
disc B is 25 kg. The static coefficients of friction between the plane and disc A and
B are 0.2 and 0.55, respectively, and the dynamic coefficients of friction are 0.15
and 0.45, respectively. At the instant shown, a counter-clockwise moment
T = 125 Nm. is applied to disc B. You are required to
Marks
(a) identify the type of ensuing motion of the discs,
(b) draw the free-body, kinematic and kinetic diagrams of the discs,
(c) write down the appropriate kinetic and kinematic relationships with
respect to a global reference axes system, indicating any assumption
made and
(d) determine the magnitudes and senses of the angular accelerations of
the discs and force developed, if any, in the rod AB.
(e) If slipping is anticipated, indicate with supporting arguments, whether
one of the discs will first slip or both will slip at the same time.
You must clearly show details of the analysis you have carried out using
equations in part (c) above to arrive at the results in part (d) in a reasonably
logical way.

a) I am assuming its Rotational? But it moves position, so maybe circular motion?

b) Do i break down each component and do the FBD etc on each bit? Or do it as one big chunk? This is as far as i am...

 

[Stevo_McMax]

looking at notes i have from uni i would say that its either curvinlinear motion or general plane motion

 

[billybomb]

oo i didn't expect a reply so i haven't been checking this!

Yes, I've made some progress and i agree, i think its General Plane Motion. I've made my FBD, Kinetic and Kinematic diagrams. ill upload them later and see if anyone can point me in the right direction!

Cheers

 

[billybomb]

Is there a reaction force on both discs in the Y direction where the bar connects to the disc? Or is it just in the x direction?

 

[DeeNos]

Thank you for reaching out for help with this dynamics problem. I would approach this question by first identifying the key information and variables given, and then organizing them into a clear and logical format. This could involve creating diagrams, writing out equations, and making assumptions where necessary.

To answer your first question, yes, this problem involves rotational motion as the discs are connected by a rod and are experiencing a moment. However, the motion may also involve circular or translational components, which we will need to investigate further.

To begin, I would start by drawing a free-body diagram for each disc, showing all the forces acting on them. This will help us identify the forces that are causing the motion and the direction of those forces. Next, we can draw a kinematic diagram to show the motion of each disc, including any rotational or translational components.

In part (c), we are asked to write down the appropriate kinetic and kinematic relationships with respect to a global reference axes system. This means we need to consider the equations of motion for rotational and translational motion, as well as any assumptions that we may need to make. For example, we may assume that the discs are in contact with the ground and that friction is the only external force acting on them.

Using these equations, we can then determine the angular accelerations of the discs and the force developed in the rod AB. This will involve using the given information, such as the mass and coefficients of friction, and applying them to the appropriate equations. It is important to show all the steps and calculations used to arrive at the final results.

Finally, part (e) asks us to determine if slipping is anticipated and which disc will slip first. This will require us to consider the frictional forces acting on each disc and compare them to the maximum frictional force that each disc can withstand before slipping. Based on this comparison, we can determine if one or both discs will slip at the given moment.

In conclusion, solving dynamics questions on two uniform thin discs requires a thorough understanding of rotational and translational motion, as well as the ability to organize and analyze information in a logical manner. By following these steps and considering all the given information, we can arrive at the correct answers and provide a clear and detailed explanation of our analysis. Good luck with your exam!