Answered

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Simple Harmonic Motion

How much force is needed to stretch a spring 1.2 m if the spring constant is 8.5 N/m?

A. 7.1 N
B. 7.3 N
C. 9.7 N
D. 10.2 N


Sagot :

To determine the force needed to stretch a spring, we use Hooke's Law. Hooke's Law states that the force [tex]\( F \)[/tex] required to stretch or compress a spring by a distance [tex]\( x \)[/tex] (displacement) is directly proportional to that distance.

The formula for Hooke's Law is:

[tex]\[ F = k \cdot x \][/tex]

where:
- [tex]\( F \)[/tex] is the force applied,
- [tex]\( k \)[/tex] is the spring constant, and
- [tex]\( x \)[/tex] is the displacement of the spring.

In this problem:

- The spring constant [tex]\( k \)[/tex] is given as [tex]\( 8.5 \, \text{N/m} \)[/tex].
- The displacement [tex]\( x \)[/tex] is given as [tex]\( 1.2 \, \text{m} \)[/tex].

Using the formula, we can substitute the given values:

[tex]\[ F = 8.5 \, \text{N/m} \times 1.2 \, \text{m} \][/tex]

After performing the multiplication:

[tex]\[ F = 10.2 \, \text{N} \][/tex]

Therefore, the force needed to stretch the spring 1.2 meters is [tex]\( 10.2 \, \text{N} \)[/tex]. The correct answer is:

[tex]\[ \boxed{10.2 \, \text{N}} \][/tex]
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