A road research organisation recently claimed that the damage to road surfaceswas proportional to the fourth power of the axle load. The axle load of a 44-tonne HGV is about 15 times that of a car. Calculate the ratio of the damage to road surfaces made by a 44-tonne HGV and a car.
Answers
Given : damage to road surfaces was proportional to the fourth power of the axle load.
The axle load of a 44-tonne HGV is about 15 times that of a car
To Find : Calculate the ratio of the damage to road surfaces made by a 44-tonne HGV and a car.
Solution:
damage to road surfaces was proportional to the fourth power of the axle load.
D = Damage to Road
A = Axle load
=> D ∝ A⁴
=> D = kA⁴
The axle load of a 44-tonne HGV is about 15 times that of a car
Axle load of HGV = 44 tonne
Axle load of car = 44/15 tonne
Damage by 44-tonne HGV = k (44)⁴
Damage by Car = k (44/15)⁴
ratio of the damage to road surfaces made by a 44-tonne HGV and a car.
= k (44)⁴ : k (44/15)⁴
= 15⁴ : 1
= 50,625 : 1
ratio of the damage to road surfaces made by a 44-tonne HGV and a car. = 50,625 : 1
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