Question

A spring extends by a distance of 5 cm when subjected to a 10 N force.


Q: What is the amount of elastic potential energy contained in this spring when extended by 10 cm?
Give your answer in Joules and as a positive value.

Answer 1

Answer on Question #49060 – Engineering – Other

1. A spring extends by a distance of $5\mathrm{cm}$ when subjected to a $10\mathrm{N}$ force.

Q: What is the amount of elastic potential energy contained in this spring when extended by $10\mathrm{cm}$?

Give your answer in Joules and as a positive value.

where a spring constant $k$ is the proportionality factor.

Thus, the spring constant is $k = \frac{F}{\Delta x_1}$.

Elastic potential energy contained in this spring when extended by $\Delta x_{2}$ is

$$E = \frac{k \cdot \Delta x_{2}^{2}}{2} = \frac{F}{\Delta x_{1}} \cdot \frac{\Delta x_{2}^{2}}{2}, \quad \boxed{E = \frac{F \Delta x_{2}^{2}}{2 \Delta x_{1}}}.$$

Let check the dimension: $[E] = \frac{N \cdot m^2}{m} = N \cdot m = J$.

Let evaluate the quantities: $E = \frac{10 \cdot 0.1^2}{0.5} = 0.2(J)$.

Answer: 0.2 Joules.

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