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?
T=constant*dia^2
800=k*2^2
T3=k*9
divide one equation by the other
T/800= 9/4
solve for T
To find out how much a 3-cm cable will support, we can use the concept that the strength of a cable is proportional to the square of its diameter.
Let's find the proportionality constant first. We know that a 2-cm cable can support 800 kg. So, we can set up the following equation:
(2 cm)^2 * constant = 800 kg
Simplifying the equation, we have:
4 cm^2 * constant = 800 kg
Now, let's solve for the constant:
constant = 800 kg / (4 cm^2)
constant = 200 kg/cm^2
Now, we have the proportionality constant.
To determine how much a 3-cm cable will support, we can use the formula:
Strength of cable = (diameter)^2 * constant
Plugging in the values, we get:
Strength of 3-cm cable = (3 cm)^2 * 200 kg/cm^2
Strength of 3-cm cable = 9 cm^2 * 200 kg/cm^2
Strength of 3-cm cable = 1800 kg/cm^2
Therefore, a 3-cm cable will support 1800 kg.