Acombination lock has a 1.3-cm-diameter knob that is part of the dial you turn to unlock the lock. to turn that knob, you twist your wrist as you grip it between your thumb and forefinger with a force of 5.0 n . suppose the coefficient of static friction between the knob and your fingers is 0.65.
what is the most torque that you can exert on the knob without having it slip between your fingers?

0.04225 Nm

Explanation:

N = Force applied = 5 N

= Coefficient of static friction = 0.65

d = Diameter of knob = 1.3 cm

r = Radius of knob =

Force is given by

When we multiply force and radius we get torque

Torque on thumb

Torque on forefinger

The total torque is given by

The most torque that exerted on the knob is 0.04225 Nm

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .