Mechanical principles rotating systems

[Mitch1]

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.

(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

 

[SteamKing]

Sorry, the attached figure doesn't appear in your post.

If you have an attempted solution to the problem, please post it.

 

[Mitch1]

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

 

[SteamKing]

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.

 

[Mitch1]

Sorry yes there you go

 

[SteamKing]

This is a better view:

​

Along with your calculations:

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

 

[Mitch1]

No problem, do u think that is on the right lines or way off?

 

[SteamKing]

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.

 

[Mitch1]

No problem cheers