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What is the restoring force of a spring with a spring constant of [tex]$4a$[/tex] and a stretched displacement of [tex]$3b$[/tex]?

A. [tex]-7ab[/tex]
B. [tex]-7\frac{a}{b}[/tex]
C. [tex]-12ab[/tex]
D. [tex]-12\frac{a}{b}[/tex]

Sagot :

GinnyAnsweridn
To find the restoring force of a spring, we can use Hooke's Law, which states that the force [tex]\( F \)[/tex] exerted by a spring is proportional to the displacement [tex]\( x \)[/tex] and is given by the formula:

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

where:
- [tex]\( k \)[/tex] is the spring constant,
- [tex]\( x \)[/tex] is the displacement,
- The negative sign indicates that the force exerted by the spring is in the direction opposite to the displacement.

Given in the problem:
- The spring constant [tex]\( k = 4a \)[/tex],
- The displacement [tex]\( x = 3b \)[/tex].

We plug these values into Hooke's Law:

[tex]\[ F = - (4a) (3b) \][/tex]

Multiplying these values together:

[tex]\[ F = -12ab \][/tex]

Hence, the correct answer is:

C. [tex]\(-12ab\)[/tex]
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