Question

The car rests on four scales, and in this position, the scale readings of both the front and rear tires are shown by FA and FB. When the rear wheels are elevated to a height of 3 ft above the front scales, the new readings of the front wheels are also recorded. Use this data to compute the center of gravity G of the car. The tires each have a diameter of 1.98 ft. a. The center of gravity G cannot be determined from the given data. b. The center of gravity G is at the midpoint between the front and rear axles. c. The center of gravity G is closer to the front wheels than the rear wheels. d. The center of gravity G is closer to the rear wheels than the front wheels.

Answer 1

The shift in scale readings during the elevation of the rear wheels indicates a redistribution of weight towards the front, suggesting that the center of gravity is located closer to the front wheels.

c. The center of gravity G is closer to the front wheels than the rear wheels.

Step-by-step explanation:

The center of gravity (G) can be determined by analyzing the changes in the scale readings when the car is in different positions. When the rear wheels are elevated, the front scale readings change, indicating a shift in weight distribution. Since the front scale readings increase when the rear wheels are lifted, it suggests that the center of gravity is closer to the front wheels.

To understand this, consider the basic principle that the center of gravity is the point where the entire weight of an object can be concentrated. When the rear wheels are lifted, more weight is transferred to the front wheels, leading to an increase in the front scale readings. This implies that the center of gravity must be situated closer to the front wheels.

The tire diameters are mentioned, and assuming a symmetrical design, we can further deduce that the midpoint between the front and rear axles is not the center of gravity. The change in scale readings directly correlates with the redistribution of weight, supporting the conclusion that the center of gravity is closer to the front wheels than the rear wheels.

Answer 2

The statement " The center of gravity G is closer to the front wheels than the rear wheels" is correct. (option C)

Why is this correct?

Given the scenario where a car rests on four scales, indicating front and rear tire readings
`\( F_A \)` and
`\( F_B \)` respectively, the situation shifts when the rear wheels are raised 3 ft above the front scales. The new recorded readings on the front tires lead to determining the center of gravity (COG) of the car.

To approach this, let's designate:

`\( W \)` as the total weight of car.

`\( L \)` as distance between the front and rear axles.

`\( x \)` as distance from the front axle to the COG.

Initially, with the car resting on all wheels, the sum of the front and rear tire readings equals the total weight
`\( W \)`:

`\[ F_A + F_B = W \]` (Equation 1)

When the rear wheels are raised, altering the distribution of weight without changing the total weight of the car, the new front tire reading
`\( F_A' \)` is recorded while the rear tire reading remains constant at
`\( F_B \)`:

`\[ FA' + FB = W \]` (Equation 2)

Comparing Equation 1 and Equation 2 reveals that
`\( F_A \)` changes to
`\( F_A' \)` while
`\( F_B \)` remains unchanged. The shift in front tire readings signifies a shift in the center of gravity towards the front wheels when the rear wheels were elevated.

Hence, based on the data provided and the change observed in the front tire readings when the rear wheels were raised, it can be concluded that c. The center of gravity
`\( G \)` is closer to the front wheels than the rear wheels.

See missing part of the question below.