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

a)

`F = (1152)/(l)`

b) l=19.2 units

Explanation:

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

Then inverse variation relation is:

`F\propto \: (1)/(l)`

When we introduce the variation constant, we get:

`F = \: (k)/(l)`

From the question when F=96, l=12

`96= \: (k)/(12)`

`k = 1152`

The equation is

`F = \: (1152)/(l)`

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

`60 = (1152)/(l)`

`\implies \: l = (1152)/(60)`

`l = 19.2`

Hence the length of the wrench must be 19.2 units