Final answer:
The distribution of a car's weight between its axles influences its center of gravity, which can be calculated using equilibrium equations and understanding of forces acting on the car in terms of torques balanced around the center of gravity.
Step-by-step explanation:
The question pertains to the distribution of weight in a vehicle and how it affects the location of the center of gravity (CM). Specifically, it is about calculating the position of the CM in a car with a given distribution of weight between its front and rear axles.
A passenger car with a 2.5-m wheelbase—where d equals 2.5 m—has 52% of its weight on the front wheels. To find the position of the CM, we must use the balance of torques due to the weight distributed on the front and rear axles.
If 52% of the car's total weight (0.52w) is on the front wheels, and the remainder (0.48w) is on the rear, we can infer that the CM lies closer to the front axle.
When the vehicle is in equilibrium, these forces must balance around the CM. Looking at the free-body diagram of the car, we can assign the reference frame with the axis of rotation at the CM, and use equilibrium equations to locate the CM precisely at a distance x from the rear axle.
The concept of CM is vital for understanding a vehicle's stability. If the center of gravity is within the area of support, a vehicle is more stable and less likely to tip over, as compared to when the CM is outside the support area as shown in the demonstrations with the truck and box images presented.