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How heavy is 6.70 tons?

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It's about three-and-a-half times as heavy as a Car.
In other words, 6.70 tons is 3.6790 times the weight of a Car, and the weight of a Car is 0.27180 times that amount.
(for 2009 Ford Taurus; automatic transmission; curb weight)
A 2009 Ford Taurus weighs 1.8210 tons. The first mass-produced car, the Curved Dash Oldsmobile — introduced in 1901 — weighed just 0.42550 tons.
It's about nine times as heavy as a Cow.
In other words, 6.70 tons is 8.90 times the weight of a Cow, and the weight of a Cow is 0.110 times that amount.
(for Holstein, a.k.a. Holstein Friesian, a.k.a. Friesian, Bos primigenius) (adult, heifer)
A mature Holstein cow (the well-known black-and-white, spotted breed of cow) typically weighs 0.750 tons. President William Howard Taft (1909 - 1913) kept a Holstein cow named Pauline Wayne on the White House grounds — a gift from a Wisconsin senator and the source of the First Family's milk.
It's about one-tenth as heavy as The Space Shuttle.
In other words, the weight of The Space Shuttle is 12 times 6.70 tons.
(for Endeavour, a.k.a. OV-105, a.k.a. Orbiter Vehicle-105) (empty weight, excluding main engines)
When empty, the space shuttle Endeavour weighs 78 tons. The shuttle's spacious cargo bay carried the Chandra X-ray Observatory into orbit in 1999 — a payload that weighed 22 tons.
It's about eleven-and-a-half times as heavy as a Grizzly Bear.
In other words, the weight of a Grizzly Bear is 0.0855 times 6.70 tons.
(a.k.a. brown bear, a.k.a. silver bear, Ursus arctos horribilis) (Adult, male, coastal area population average)
An adult, male grizzly bear from a coastal area (where food is plentiful) can weigh up to 0.5740 tons. In spite of their tremendous size, grizzly bears can run at speeds of up to 55 kph (34 mph).
It's about twelve times as heavy as a Polar Bear.
In other words, 6.70 tons is 11.80 times the weight of a Polar Bear, and the weight of a Polar Bear is 0.0847 times that amount.
(Ursus maritimus) (adult, male)
An adult, male polar bear weighs between 0.5690 tons. Polar bears are so heavily insulated by their 9.9 cm (3.9 in) layer of blubber that they are often difficult to detect using infrared photography sensors.
It's about fourteen times as heavy as a Grand Piano.
In other words, the weight of a Grand Piano is 0.071 times 6.70 tons.
(for Steinway & Sons, Model D Concert Grand Piano)
A Grand Piano, of the kind used for concert performances in large music halls, weighs 0.50 tons. Well-made pianos such as this may last 75 to 100 years.
It's about fourteen times as heavy as a Horse.
In other words, the weight of a Horse is 0.071 times 6.70 tons.
(Equus ferus caballus) (Arabian, adult)
n Arabian riding horse (or similar breed) weighs between 0.460 tons. During races, horses must carry jockeys and their equipment, which in the Kentucky Derby, for example, can weigh up to 0.06 tons.