Question

A spring is subjected to a force of 40 Newtons at a rest position. When an additional load of 3 N is exerted the spring has moved by 20 cm. Calculate the spring constant k of this spring.

Answer 1

Answer on Question #49050 – Engineering – Other

A spring is subjected to a force of 40 Newtons at a rest position. When an additional load of 3 N is exerted the spring has moved by 20 cm. Calculate the spring constant k of this spring.

Solution:

$$F_1 = 40 \, \text{N} - \text{first force};$$ $$F_2 = 3 \, \text{N} - \text{second force};$$ $$\Delta x = 0.2 \, \text{m} - \text{change in length of the spring};$$

That linear dependence of displacement upon stretching force is called Hooke's law. Final position of the spring:

$$k = \frac{F_1 + F_2}{\Delta x_2} = \frac{40 \, \text{N} + 3 \, \text{N}}{0.2 \, \text{m}} = 215 \, \frac{\text{N}}{\text{m}}$$

Answer: spring constant is equal to $215 \, \frac{\text{N}}{\text{m}}$.

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