Question

A factory has a machine which bends wire at a rate of 2 unit(s) of curvature per second. How long does it take to bend a straight wire into a circle of radius 7

Answer 1

Answer:

21.994 seconds

Explanation:

l = length of the wire

r = radius of bend = 7

Perimeter of the bend = perimeter of a circle = 2πr

Perimeter = dl = 2 * π * 7 = 14π

dl = 14π ...............(1)

Rate of bend = dl/dt =2 units/sec

dl = 2 dt...............(2)

Equate (1) and (2)

2 dt = 14π

dt = 14π/2

dt = 7π seconds

dt = 21.994 seconds

Answer 2

Answer:

$\Delta t = 3.5\,s$

Explanation:

Time require per unit is directly proportional to need radio of curvature. In other words:

$\Delta t \propto \rho$

The time requiered to bend the straight wire into a circule of radius 7 is estimated by simple rule of three:

$\Delta t = \frac{7\,u}{2\,u}\cdot (1\,s)$

$\Delta t = 3.5\,s$