Question

A steel wire of 1 m long and 1 mm sqaure in area of cross section . If it takes 200 N to stretch the wire by 1mm how much force will be required to stretch the wire of same area and same material and having lenght of 10 m to 1002 cm ?

Answer 1

A steel wire of 1 m long and 1 mm square in area of cross section. If it takes 200 N to stretch the wire by 1 mm how much force will be required to stretch the wire of same area and same material and having length of 10 m to 1002 cm?

Hooke's law:

$$F = k \Delta l$$

where $k = \frac{ES}{l}$ - a constant factor characteristic of the spring, E - modulus of elasticity of steel, S - cross section, l - length.

In first case:

$$F_1 = \frac{ES}{l_1} \Delta l_1$$

Similarly, for second:

$$F_2 = \frac{ES}{l_2} \Delta l_2$$

Therefore:

$$\frac{F_2}{F_1} = \frac{\Delta l_2}{l_2} \frac{l_1}{\Delta l_1}$$ $$F_2 = \frac{\Delta l_2}{l_2} \frac{l_1}{\Delta l_1} F_1 = \frac{1002 \, \text{cm} - 10 \, \text{m}}{10 \, \text{m}} \cdot \left(\frac{1 \, \text{m}}{1 \, \text{mm}}\right) 200 \, \text{N} = \frac{0.02 \, \text{m}}{10 \, \text{m}} \cdot \frac{1 \, \text{m}}{0.001 \, \text{m}} \cdot 200 \, \text{N} = 400 \, \text{N}$$

Answer: 400 N