Moments Question: Bike Equilibrium Conditions

[Boogeyman]

Homework Statement

A bicycle of a mass 15kg resting in a vertical position, with the front and back wheels touching the horizontal ground at points P and Q respectively, where PQ=1m. The centre of gravity of the bike is vertically above O, a point on PQ where PO=30cm.

Given that the normal reactions of the ground on the front and rear where are R₁ and R₂, write 2 equations in R₁ and R₂ which satisfy the conditions of equilibrium.

The Attempt at a Solution

So I know you have to use the principle of moments to give the equations. I am just unsure where the pivot is. Is it at the line of center of gravity of the bicycle?

 

[Saladsamurai]

The pivot can be at any point that you choose. Since it asks for the equation in R1 and R2, then yes take them about O. If you draw it out, you know the horizontal distances d1 and d2 from O to R1 and R2.

 

[Boogeyman]

Ok, taking O as the pivot I get:

Eqn 1:
sum of CM=sum of ACM
0.3R₁=0.7R₂

Eqn 2:
sum of upward forces=sum of downward forces
R₁ + R₂=150

I'm assuming that's the answer?