Homework Help: Mechanical principles rotating systems

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1. May 13, 2015

Mitch1

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
F=mrω^2

up forces must equal down to be in equilibrium

3. 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 cant seem to get the correct answer

2. May 13, 2015

SteamKing

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

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

3. May 13, 2015

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

4. May 13, 2015

SteamKing

Staff Emeritus
Any word on the figure missing from the OP? That would be a big help to anyone trying to guide you.

5. May 13, 2015

Mitch1

Sorry yes there you go

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6. May 13, 2015

SteamKing

Staff Emeritus
This is a better view:

7. May 13, 2015

Mitch1

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

8. May 13, 2015

SteamKing

Staff Emeritus
I haven't had a chance to look at it. If someone else has any suggestions, please feel free to dive in.

9. May 13, 2015

Mitch1

No problem cheers