Solve "Moments of Force" with Uniform Meter Rule & Pulley

[look416]

Homework Statement

A uniform metre rule of mass 100 g is supported by a knife-edge at the 40 cm mark and a string at the 100 cm mark. The string passes round a frictionless pulley and carries a mass of 20 g as shown in the diagram.

At which mark on the rule must a 50 g mass be suspended so that the rule balances?

Homework Equations

The Attempt at a Solution

using the \sum F=0
therefore, R at the knife-edge + T at the 100 cm = W
R = 0.8
then take the moment at the c.g, which is at 0.5
therefore R(z)=T(50)
in the end,what i got is z=0.3125
where T=0.5N
wrong again...

 

[tiny-tim]

Hi look416!

(have a sigma: ∑ )

I don't understand what you've done …

there should be moments of three forces …

and where does T = 0.5N come from?

(btw, no need to convert to N … they're all weights, so just use the masses )

 

[look416]

lolz
maybe I am not good in explaining XD
anyway
if i take the head of the ruler as the moment
which means
RX + 50(100) = 50(100)
which results in RX = 0
=.=
T = 0.5N is because the question demand for the X cm when the load is 50g
for 50g x 10 x 10^-3 = 0.5N

 

[tiny-tim]

RX + 50(100) = 50(100)

uhh? where's the 40cm? where's the 20g? and what's R?

 

[look416]

=.=
so, i have to find the value of R by taking moments as the head of the ruler
if so,
R(40)+20(100)=50(100)
R=75g
then??

 

[tiny-tim]

=.=
so, i have to find the value of R by taking moments as the head of the ruler

Is R the reaction force at the knife-edge?

If so, you don't find it by taking moments, you find it by adding the vertical components of force to zero …

which I thought you'd already done, and found it was 80g (weight) ??

R(40)+20(100)=50(100)

You haven't included the 50 g mass in this moments equation.

(btw, if you take moments about the knife-edge you won't need to find R anyway)

 

[look416]

but there said at which mark on the rule must a 50 g mass be suspended so that the rule balances?
so shouldn't i have to included the knife edge in my calculation?
not taking it as the moments ...

 

[tiny-tim]

but there said at which mark on the rule must a 50 g mass be suspended so that the rule balances?
so shouldn't i have to included the knife edge in my calculation?
not taking it as the moments ...

(i wish you wouldn't say "taking it as the moments" … you take moments of forces about a point )

Yes, the 50g mass, and its unknown position, must be included (unless you take moments about that position).

You can take moments about any point …

it can be either end of the ruler, or the knife-edge, or the point where the 50g is, or indeed anywhere else, either on or off the ruler.

But in this case it's easier to use the knife-edge, since that avoids working out the reaction force, R.