To determine the maximum force acting on the cup due to static friction, we need to follow a series of steps, utilizing the concepts of mechanics and friction:
1. Determine the Mass of the Cup:
- The mass of the cup is given as [tex]\(0.382\)[/tex] kg.
2. Calculate the Weight (Normal Force):
- The weight of the cup, which acts as the normal force, can be calculated using the formula:
[tex]\[
F_{\text{normal}} = m \cdot g
\][/tex]
where:
- [tex]\(m\)[/tex] is the mass of the cup
- [tex]\(g\)[/tex] is the acceleration due to gravity (approximately [tex]\(9.81 \, \text{m/s}^2\)[/tex])
Plugging in the values:
[tex]\[
F_{\text{normal}} = 0.382 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 3.74742 \, \text{N}
\][/tex]
3. Static Friction Calculations:
- The maximum static friction force can be calculated using the formula:
[tex]\[
F_{\text{friction}} = \mu \cdot F_{\text{normal}}
\][/tex]
where:
- [tex]\(\mu\)[/tex] is the coefficient of static friction, given as [tex]\(0.125\)[/tex]
- [tex]\(F_{\text{normal}}\)[/tex] is the normal force we calculated previously
Plugging in the values:
[tex]\[
F_{\text{friction}} = 0.125 \times 3.74742 \, \text{N} = 0.4684275 \, \text{N}
\][/tex]
4. Conclusion:
- Therefore, the maximum force acting on the cup due to static friction is approximately [tex]\(0.4684 \, \text{N}\)[/tex].
