The length [tex]$L$[/tex] of a spring is given by

[tex]\[ L = \frac{2}{3} F + 12 \][/tex]

where [tex]$F$[/tex] is the applied force. What force [tex]$F$[/tex] will produce a length of 14?

[tex]\[ F = \boxed{\square} \][/tex]



Answer :

To find the force [tex]\( F \)[/tex] that will produce a length of 14 units for the spring, we start with the given equation:

[tex]\[ L = \frac{2}{3} F + 12 \][/tex]

We are given that the length [tex]\( L \)[/tex] is 14, so we can substitute 14 for [tex]\( L \)[/tex] in the equation:

[tex]\[ 14 = \frac{2}{3} F + 12 \][/tex]

Next, we need to isolate [tex]\( F \)[/tex] on one side of the equation. First, subtract 12 from both sides:

[tex]\[ 14 - 12 = \frac{2}{3} F \][/tex]

This simplifies to:

[tex]\[ 2 = \frac{2}{3} F \][/tex]

Now, to solve for [tex]\( F \)[/tex], we multiply both sides by the reciprocal of [tex]\( \frac{2}{3} \)[/tex], which is [tex]\( \frac{3}{2} \)[/tex]:

[tex]\[ F = 2 \times \frac{3}{2} \][/tex]

This simplifies to:

[tex]\[ F = 3 \][/tex]

Therefore, the force [tex]\( F \)[/tex] that will produce a length of 14 units is:

[tex]\[ F = 3.0 \][/tex]