Math Problem Statement

The maximum force exerted onto a 34.5 kg box at rest is 28.9 N due to static friction. What is the coefficient of static friction?

Solution

To calculate the coefficient of static friction (μs\mu_s), we use the following formula:

Ffriction=μsFnormalF_{\text{friction}} = \mu_s \cdot F_{\text{normal}}

Where:

  • FfrictionF_{\text{friction}} is the maximum static friction force (28.9 N),
  • FnormalF_{\text{normal}} is the normal force, which is equal to the weight of the box (mass m=34.5kgm = 34.5 \, \text{kg}) times the acceleration due to gravity (g=9.81m/s2g = 9.81 \, \text{m/s}^2).

First, we calculate the normal force:

Fnormal=mg=34.5kg×9.81m/s2F_{\text{normal}} = m \cdot g = 34.5 \, \text{kg} \times 9.81 \, \text{m/s}^2

Now let's solve for ( F_{\text{normal

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Math Problem Analysis

Mathematical Concepts

Physics
Statics
Friction

Formulas

F_friction = mu_s * F_normal
F_normal = m * g

Theorems

Newton's Laws of Motion

Suitable Grade Level

High School Physics