I set up an equal proportion [tex]\frac{100}{0.25} = \frac{80}{x}[/tex]
cross multiply to get 80 * 0.25 = 100x
20 = 100x; divide both sides by 100
0.2 = x so the answer is choice B
Answer:
B. 0.2 meters.
Step-by-step explanation:
Let x represent meters of spring stretched by 80 newtons.
We have been given that a force of 100 newtons will stretch a spring 0.25 meters.
We will use Hooke's law, which states that the force needed to compress or extend a spring is directly proportional to the distance we stretch it.[tex]N=kx[/tex], where,
N = Force in Newtons,
k = The spring constant,
x = Amount of extension in meters.
Let us find spring constant by substituting [tex]N=100[/tex] and [tex]x=0.25[/tex].
[tex]100=k*0.25[/tex]
[tex]\frac{100}{0.25}=\frac{k*0.25}{0.25}[/tex]
[tex]400=k[/tex]
So, our equation would be [tex]N=400x[/tex].
Now, we will substitute [tex]N=80[/tex] in our equation to find x.
[tex]80=400x[/tex]
Upon dividing both sides of our equation by 400 we will get,
[tex]\frac{80}{400}=\frac{400x}{400}[/tex]
[tex]\frac{1}{5}=x[/tex]
[tex]0.2=x[/tex]
Therefore, the force of 80 newtons will stretch the spring 0.2 meters and option B is the correct choice.
