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Zorluk: OrtaLoad Distribution and Balancing

Four different vehicles each have a total loaded weight of 6,0006,000 pounds. Arrange the following vehicles in order based on the amount of weight supported by their REAR axle, from greatest weight to least weight.

  1. 1A delivery van with a 1515-foot wheelbase, and its center of gravity located 1010 feet behind the front axle.
  2. 2A pickup truck with a 1212-foot wheelbase, and its center of gravity located 55 feet forward of the rear axle.
  3. 3A flatbed truck with a 1414-foot wheelbase, and its center of gravity located 77 feet behind the front axle.
  4. 4A box truck with a 1616-foot wheelbase, and its center of gravity located 1212 feet forward of the rear axle.

Cevap

The correct order from greatest to least rear axle load is: Delivery van (4,0004,000 lbs), Pickup truck (3,5003,500 lbs), Flatbed truck (3,0003,000 lbs), and Box truck (1,5001,500 lbs).
To find the load on the rear axle, the vehicle is treated as a beam where the front axle acts as the pivot (fulcrum). The rear axle load is found by taking the proportion of the center of gravity's distance from the front axle relative to the entire wheelbase, and multiplying by the total weight. The delivery van has the highest proportion (1015=66.7%\frac{10}{15} = 66.7\%), followed by the pickup truck (712=58.3%\frac{7}{12} = 58.3\%), flatbed truck (714=50%\frac{7}{14} = 50\%), and box truck (416=25%\frac{4}{16} = 25\%).

Adım Adım Çözüm

1
Determine the formula for load distribution on the rear axle.
Rear Axle Load = Total Weight×(Distance from Front AxleWheelbase)\text{Total Weight} \times (\frac{\text{Distance from Front Axle}}{\text{Wheelbase}})
The vehicle acts as a beam supported at both ends (the axles). The load on the rear support is directly proportional to how far the center of gravity is from the front support.
2
Calculate the rear axle load for the delivery van.
6,000 lbs×(10 ft15 ft)=6,000×23=4,000 lbs6,000\text{ lbs} \times (\frac{10\text{ ft}}{15\text{ ft}}) = 6,000 \times \frac{2}{3} = 4,000\text{ lbs}.
The center of gravity is explicitly given as 1010 feet behind the front axle.
3
Calculate the rear axle load for the pickup truck.
Distance from front = 12 ft−5 ft=7 ft12\text{ ft} - 5\text{ ft} = 7\text{ ft}. Load = 6,000 lbs×(7 ft12 ft)=3,500 lbs6,000\text{ lbs} \times (\frac{7\text{ ft}}{12\text{ ft}}) = 3,500\text{ lbs}.
The center of gravity is 55 feet forward of the rear axle, meaning it is 77 feet behind the front axle.
4
Calculate the rear axle load for the flatbed truck.
6,000 lbs×(7 ft14 ft)=6,000×12=3,000 lbs6,000\text{ lbs} \times (\frac{7\text{ ft}}{14\text{ ft}}) = 6,000 \times \frac{1}{2} = 3,000\text{ lbs}.
The center of gravity is 77 feet behind the front axle, exactly in the middle of the 1414-foot wheelbase.
5
Calculate the rear axle load for the box truck.
Distance from front = 16 ft−12 ft=4 ft16\text{ ft} - 12\text{ ft} = 4\text{ ft}. Load = 6,000 lbs×(4 ft16 ft)=1,500 lbs6,000\text{ lbs} \times (\frac{4\text{ ft}}{16\text{ ft}}) = 1,500\text{ lbs}.
The center of gravity is 1212 feet forward of the rear axle, meaning it is 44 feet behind the front axle.
6
Arrange the vehicles based on the calculated loads.
Delivery van (4,0004,000 lbs) > Pickup truck (3,5003,500 lbs) > Flatbed truck (3,0003,000 lbs) > Box truck (1,5001,500 lbs).
The question asks for the order from greatest weight to least weight supported by the rear axle.

Anahtar Kavram

Load distribution on a beam with two supports (axles) is inversely proportional to the distance from the center of gravity to each support.

Alternatif Yöntem

You can calculate the weight on the front axle first by using the distance to the rear axle divided by the total wheelbase, then subtract that front axle load from the 6,0006,000 lbs total weight to find the rear axle load.
Tahmini Süre:1m 30s
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