The electric fan shown has the following specifications: -The entire unit weighs

Question

The electric fan shown has the following specifications:

-The entire unit weighs W = 15 lb with the center of gravity shown.

-The fan produces a maximum thrust of T = 6 lb.

-The height h can be adjusted by the user between 24 and 48 in.

-The fan can be rotated to any horizontal position desired by the user.

Specify the dimension b for a base having three equally spaced legs. In your work,

assume that the weight of the legs is already included in the 15 lb weight of the unit.

Your design should consider a reasonable degree of safety against overturning. Also

make at least two suggestions for how the stability of the fan can be improved without

increasing the weight W or increasing the dimension b.

Explanation / Answer

Normal Force exerted on fan from Ground = 15 lb.
When h = 48 in , then the moment of the thrust force will be maximum. This is the condition which gives required value of b.

So for toppling condition, we can assume the normal force to be acting at the extreme end of any 1 base leg .

So balancing Moments 15( b ) = 6 ( 48 )
so b = 19.2

Suggestion for Stability :
1) Use the fan at h < 48 . This will ensure stability as the Moment of the Thrust force will decrease.
2) Rotate the fan such that the resultant Thrust Force acts at an angle of 30 with respect to 2 of the base legs.

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