Question

A steel wire of diameter 2mm has a breaking strength of 400000n. What is the breaking force of similar steel wire of diameter 1.5 mm

Answer 1

Breaking strength of the wire is 225988.7 N.

Breaking force is directly proportional to the area of the wire

F∝area∝d²

Here, d is diameter of the wire

Now for Wire 1 and wire 2

$\frac{F_1}{F_2}$=$\frac{d_1^{2} }{d_2^{2} }$

Plugging the values in the above equation

$\frac{400000}{F_2}$=$\frac{2^2}{1.5^2}$

F_2=225988.7 N

Therefore the breaking force of the 1.5 wire is 225988.7 N.

Answer 2

Explanation:

Breaking strength of the wire is 225988.7 N.

Breaking force is directly proportional to the area of the wire

F∝area∝d²

Here, d is diameter of the wire

Now for Wire 1 and wire 2

\frac{F_1}{F_2}F2F1 =\frac{d_1^{2} }{d_2^{2} }d22d12

Plugging the values in the above equation

\frac{400000}{F_2}F2400000 =\frac{2^2}{1.5^2}1.5222

F_2=225988.7 N

Therefore the breaking force of the 1.5 wire is 225988.7 N.