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

Answer:

#"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