Question

A combination 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 grip it between your thumb and forefinger with a force of 4.0 N as you twist your wrist. Suppose the coefficient of static friction between the knob and your fingers is  0.75.

A)What is the most torque you can exert on the knob without having it slip between your fingers?

Answer 1

Given data is

• A combination 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 grip it between your thumb and forefinger with a force of 4.0 N as you twist your wrist.
• Suppose the coefficient of static friction between the knob and your fingers is  0.75

What is the most torque you can exert on the knob without having it slip between your fingers?

Solution::--

Torque = Force * radius
T = F*r

F = Normal Force * coefficiant of friction
F = N * u

F = 4.0 N * 0.75 = 3 N

If you are pinching the knob you are applying the force to two points on the knob. So you need to use the force in two places.

T_thumb = 3 N * 0.65 cm = 1.95 N-cm
T_forefinger = 3 N * 0.65 cm = 1.95 N-cm

Total T = T_thumb + T_forefinger
Total T = 1.95 N-cm + 1.95 N-cm
Total T = 3.9 N-cm

If you want it more common units of N-m then just divde by 100.

Max T= 0.039 N-m = 39*10^-3 N-m