A balanced lever has two weights on it, the first with mass 16kg and the second with mass 14kg. If the first weight is 2m from the fulcrum, how far is the second weight from the fulcrum?

1 Answer
Jul 31, 2016

The second weight =217metres from the fulcrum as an exact value

The second weight 2.143metres from the fulcrum to 3 decimal places

Explanation:

Tony B
Assumption 1
The beam ends at the points of loading. It is not stated as such

Assumption 2
The weight of the beam is discounted. No uniformly distributed load given.
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For the beam to be in equilibrium (balanced and not moving)

All forces and moments cancel out.

Taking moments about point B

Let clockwise moments be positive
Let anticlockwise moments be negative

A moment is force × length of moment arm

The force of the 'Reaction' has moment arm length of 0. So this cancels itself out giving only:

So for the system to be in equilibrium (not moving)

(clockwise moment) + (anticlockwise moment)=0

We have chosen that anticlockwise rotation is negative

(16×2)+(14×x)=0

32=+14x

x=3214167metres 217metres as an exact value

x2.143metres to 3 decimal places