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?

1 Answer
Jul 31, 2016

"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 BTony 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