The strength of a cable is proportional to the square of its diameter. If a 2-cm cable will support 800kg, how much will a 3-cm cable support?
"The strength of a cable is proportional to the square of its diameter."
A 2-cm cable has a diameter of 2 cm, and a 3-cm cable has a diameter of 3 cm.
If a 2-cm cable supports 800kg, so a 3-cm cable supports:
800*(3/2)²
=?
To find out how much a 3-cm cable will support, we need to set up a proportion based on the relationship between the cable diameter and its strength.
According to the given information, the strength of a cable is proportional to the square of its diameter. Let's represent the strength of the cable as S and the diameter as D.
Since the strength is proportional to the square of the diameter, we can say that:
S ∝ D²
Now, let's use the given information:
For a 2-cm cable, the strength is known to be 800 kg. So, we have:
S = 800 kg and D = 2 cm
To find out how much a 3-cm cable will support, we can set up a proportion using the ratio of strengths based on the squared diameter:
S₁ / S₂ = (D₁)² / (D₂)²
Let's plug in the values we know:
800 / S₂ = (2)² / (3)²
Now, let's solve for S₂, which represents the strength of the 3-cm cable.
To do this, we can cross multiply:
800 * (3)² = (2)² * S₂
Now, let's calculate:
800 * 9 = 4 * S₂
7200 = 4 * S₂
Dividing both sides by 4, we get:
S₂ = 1800 kg
Therefore, a 3-cm cable will support 1800 kg of weight.