1) The elongation is 5.2 cm for the 1st spring and 10.4 cm for the 2nd spring
2) At the limit of proportionality, the elongation is 8.0 cm for the 1st spring and 18.0 cm for the 2nd spring
3) At the elastic limit, the elongation is 9.0 cm for the 1st spring and 19.0 cm for the 2nd spring
Explanation:
1)
When 2 N of force are applied to the two springs, they react in a different way.
In fact, we observe that:
- For the 1st spring (lower curve), the elongation is 5.2 cm
- For the 2nd spring (upper curve), the elongation is 10.4 cm
Using these data, we can calculate the spring constant of each spring. In fact, using Hooke's law:
[tex]F=kx[/tex]
where F is the force, k the spring constant, and x the elongation, we find:
For spring 1,
[tex]k_1 = \frac{F}{x_1}=\frac{2}{5.2 cm}=0.384 N/cm[/tex]
For spring 2,
[tex]k_2 = \frac{F}{x_2}=\frac{2}{10.4}=0.192 N/cm[/tex]
So, the spring constant of the 1st spring is twice the spring constant of the 2nd spring.
2)
The limit of proportionality of a spring (or any other elastic object) is the the point above which Hooke's law is no longer valid, and the elongation of the spring is no longer proportional to the force applied.
By looking at the graph, we can identify the limit of proportionality as the point where the curves deviate from a straight-line relationship: this is marked as point C.
By looking at the graph, we notice that this occurs when:
- For the 1st spring (lower curve), it occurs when the force applied is 3.0 N; after this point, the graph is no longer a straight line, and the elongation is 8.0 cm
- For the 2nd spring (upper curve), it occurs when the force applied is 3.8 N, and the elongation is 18 cm
3)
The elastic limit of a spring (or any other elastic object) is the point above which the object is no longer elastic, i.e. the material becomes permanently deformed, and it is no longer able to return to its original length after the force has been removed.
This point is marked in the graph as point D. We observe that:
- For the 1st spring (lower curve), this occurs when the force applied is 5.0 N, and the elongation of the spring is 9.0 cm
- For the 2nd spring (upper curve), this occurs when the force applied is 5.0 N, and the elongation is 19.0 cm
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