Mechanical principles rotating systems

In summary, the problem involves balancing a rotating shaft by placing a mass at a certain position and size. In the first part, a single mass is used to balance the shaft, with the reactions at the bearings being zero. In the second part, two masses are used on radius arms to balance the shaft. Calculations and equations are used to determine the size and position of the masses.
  • #1
Mitch1
55
1

Homework Statement


A shaft 2 m long rotates at 1500 revs min–1 between bearings as
shown in FIGURE 2. The bearings experience forces of 5 kN and
3 kN acting in the same plane as shown. A single mass is to be used
to balance the shaft, so that the reactions are zero. The mass is to be
placed at a radius of 200 mm from the shaft centre, 180° from the
direction of the bearing reactions. Determine the size and position (a
and b) of the mass to be used.

HNCPic1.jpg


(b) The shaft in part (a) is to be balanced using two masses (m1 and m2)
placed 0.5 m and 1.5 m from end A and 180° from the direction of
the bearing reactions, each on radius arms 100 mm long. Calculate
the sizes of m1 and m2.

Homework Equations


F=mrω^2

up forces must equal down to be in equilibrium

The Attempt at a Solution


It is B) that I am confused about

Do you need to use some sort of simultaneous equation to work out any of the two masses ? I have tried using the balancing equating but I can't seem to get the correct answer
 
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  • #2
Sorry, the attached figure doesn't appear in your post. :frown:

If you have an attempted solution to the problem, please post it.
 
  • #3
5000N x 2m - ((m1 x .1m x157^2)x1.5) - ((m2 x .1m x 157^2)x0.5m) =0
10,000 - (m1 x 3697.35) + (m2x1232.45)=0
10000/(3697.35+1232.45)=m1+m2
2.028= m1+m2

Pretty sure this is wrong to be honest but not sure where to go from here or what approach I should be making

Thanks
 
  • #4
Mitch1 said:
5000N x 2m - ((m1 x .1m x157^2)x1.5) - ((m2 x .1m x 157^2)x0.5m) =0
10,000 - (m1 x 3697.35) + (m2x1232.45)=0
10000/(3697.35+1232.45)=m1+m2
2.028= m1+m2

Pretty sure this is wrong to be honest but not sure where to go from here or what approach I should be making

Thanks
Any word on the figure missing from the OP? That would be a big help to anyone trying to guide you.
 
  • #5
Sorry yes there you go
 

Attachments

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  • #6
This is a better view:

image-shaft.jpg

​
Along with your calculations:
Mitch1 said:
5000N x 2m - ((m1 x .1m x157^2)x1.5) - ((m2 x .1m x 157^2)x0.5m) =0
10,000 - (m1 x 3697.35) + (m2x1232.45)=0
10000/(3697.35+1232.45)=m1+m2
2.028= m1+m2

Pretty sure this is wrong to be honest but not sure where to go from here or what approach I should be making

Thanks
 
  • #7
No problem, do u think that is on the right lines or way off?
 
  • #8
Mitch1 said:
No problem, do u think that is on the right lines or way off?
I haven't had a chance to look at it. If someone else has any suggestions, please feel free to dive in. :smile:
 
  • #9
No problem cheers
 

FAQ: Mechanical principles rotating systems

What are mechanical principles?

Mechanical principles refer to the fundamental laws and theories that govern the behavior of physical systems and their components. These principles are used to understand and predict the motion, forces, and energy involved in mechanical systems.

What are rotating systems?

Rotating systems are mechanical systems that involve motion around a central axis. These systems can range from simple objects, such as a spinning top, to complex systems like engines or turbines.

What are the main types of rotating systems?

The three main types of rotating systems are rotational motion, rolling motion, and angular motion. Rotational motion involves objects rotating around a fixed axis, rolling motion involves objects moving while also rotating, and angular motion involves objects changing their angle of rotation.

What is the importance of understanding mechanical principles in rotating systems?

Understanding mechanical principles in rotating systems is crucial for designing, analyzing, and troubleshooting various mechanical systems. It allows engineers and scientists to predict and control the motion, forces, and energy involved in these systems.

What are some practical applications of mechanical principles in rotating systems?

Mechanical principles in rotating systems are used in various fields, such as engineering, physics, and technology. Some examples of practical applications include designing car engines, wind turbines, and amusement park rides, as well as studying planetary motion and the dynamics of celestial bodies.

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