Question

Figure 3 shows a bicycle of mass 15 kg resting in a vertical position, with the front and back
wheels touching the horizontal ground at points P and Q respectively, where PQ = 1 m.
The centre of gravity of the bicycle is vertically above O, a point on PQ where PO = 30 cm.
k
c.g. along this line
Figure 3
Given that the normal reactions of the ground on the front and rear wheels are R and R.
respectively, write TWO equations, in R and R,, which satisfy the conditions of equilibrium.​

Answer 1

Explanation:

There are three forces on the bicycle:

Reaction force Rp pushing up at P,

Reaction force Rq pushing up at Q,

Weight force mg pulling down at O.

There are four equations you can write: sum of the forces in the y direction, sum of the moments at P, sum of the moments at Q, and sum of the moments at O.

Sum of the forces in the y direction:

Rp + Rq − (15)(9.8) = 0

Rp + Rq − 147 = 0

Sum of the moments at P:

(15)(9.8)(0.30) − Rq(1) = 0

44.1 − Rq = 0

Sum of the moments at Q:

Rp(1) − (15)(9.8)(0.70) = 0

Rp − 102.9 = 0

Sum of the moments at O:

Rp(0.30) − Rq(0.70) = 0

0.3 Rp − 0.7 Rq = 0

Any combination of these equations will work.