Final answer:
To calculate the position of the center of mass (CM) or Center of Balance for a vehicle, use the principle of moments around the pivot point, which in this case is the rear axle.
Step-by-step explanation:
To solve for the Center of Balance (CB) or the center of mass (CM) of a vehicle with two axles, particularly when choosing the pivot at the location of the rear axle as in Check Your Understanding 12.1, we need to apply the principle of moments which states that for a system to be in equilibrium, the sum of clockwise moments about any point must be equal to the sum of anticlockwise moments about that same point.
In the scenario provided, we are given that 52% of the weight of the car is on the front wheels, the weight being distributed over a wheelbase of 2.5m. If we denote the total weight of the car by 'w', we can say that the force at the front wheels (FF) is 0.52w and the force at the rear wheels (FR) is 0.48w. Setting up our equation with the rear axle as the pivot, we have:
FR × 0m = FF × d
where 'd' is the distance from the rear axle to the center of mass. Since there is no moment force on the rear axle itself (as the distance is 0), we solve for 'd' to find the CM:
d = (FR / FF) × 2.5m
By substituting the given values, we get:
d = (0.48w / 0.52w) × 2.5m
which simplifies to:
d = (0.48 / 0.52) × 2.5m
This equation will provide the position of the CM with respect to the rear axle.