Question

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

Answer 1

`"The second weight "=2 1/7 metres` from the fulcrum as an exact value

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

Explanation:

Tony B
`color(red)("Assumption 1")`
The beam ends at the points of loading. It is not stated as such

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

All forces and moments cancel out.

`color(blue)("Taking moments about point B")`

Let clockwise moments be positive
Let anticlockwise moments be negative

A moment is `"force "xx" 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`
`" " color(brown)(uarr )`
`color(brown)("We have chosen that anticlockwise rotation is negative")`

`(16xx2)+(-14xx x)=0`

`32=+14x`

`x=32/14 -= 16/7 metres" " ->" " 2 1/7 metres` as an exact value

`x~~2.143 metres` to 3 decimal places