Question

The amount of force one exerts on a wrench handle to loosen a bolt is inversely
proportional to the length of the wrench handle. With a wrench 12 inches long
it takes 96 pounds of force to loosen the bolt.
(a) Write the variation function for the force in this situation.
(b) If a person can only exert 60 pounds of force on a wrench, what length
wrench must be used in this situation?

Answer 1

Answer:

a)

$F = \frac{1152}{l}$

b) l=19.2 units

Step-by-step explanation:

a)Let F represent the force and l represents the length of the wrench handle.

Then inverse variation relation is:

$F\propto \: \frac{1}{l}$

When we introduce the variation constant, we get:

$F = \: \frac{k}{l}$

From the question when F=96, l=12

$96= \: \frac{k}{12}$

$k = 1152$

The equation is

$F = \: \frac{1152}{l}$

b) If a person can only exert 60 pounds of force on a wrench,then

$60 = \frac{1152}{l}$

$\implies \: l = \frac{1152}{60}$

$l = 19.2$

Hence the length of the wrench must be 19.2 units