Question

What is the maximum force that can be applied to a 1.5 cm-diameter combination lock knob without it slipping, given a coefficient of static friction of 0.20 between the knob and fingers, and a gripping force of 0.80 N?

Answer 1

To solve this problem, we need to determine the maximum force that can be applied to the combination lock knob without it slipping, based on the coefficient of static friction and the gripping force.

1. **Identify the parameters:**
- Diameter of the knob \( d = 1.5 \, \text{cm} = 0.015 \, \text{m} \)
- Radius of the knob \( r = \frac{d}{2} = \frac{0.015}{2} = 0.0075 \, \text{m} \)
- Coefficient of static friction \( \mu_s = 0.20 \)
- Gripping force \( F_n = 0.80 \, \text{N} \)

2. **Calculate the maximum static friction force \( F_f \):**
The maximum static friction force can be calculated using the formula:
\[
F_f = \mu_s F_n
\]
Substituting the known values:
\[
F_f = 0.20 \times 0.80 = 0.16 \, \text{N}
\]

3. **Determine the maximum tangential force \( F_{\text{max}} \):**
The maximum force \( F_{\text{max}} \) that can be applied tangentially to the knob without slipping is equal to the maximum friction force:
\[
F_{\text{max}} = F_f = 0.16 \, \text{N}
\]

This means that the maximum force that can be applied to the knob without it slipping is **0.16 N**.