Questions: The maximum force exerted onto a 22.8 kg chair at rest is 57.0 N due to static friction. What is the coefficient of static friction? μ=[?]

Solution Steps

We are given:

• The mass of the chair, \( m = 22.8 \) kg
• The maximum force of static friction, \( F_{\text{max}} = 57.0 \) N

The maximum static friction force can be calculated using the formula: \[ F_{\text{max}} = \mu_s \cdot F_N \] where \( \mu_s \) is the coefficient of static friction and \( F_N \) is the normal force.

The normal force \( F_N \) for an object at rest on a horizontal surface is equal to the gravitational force acting on it: \[ F_N = m \cdot g \] where \( g \) is the acceleration due to gravity, approximately \( 9.81 \, \text{m/s}^2 \).

Substituting the given values: \[ F_N = 22.8 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 223.668 \, \text{N} \]

Rearrange the static friction formula to solve for \( \mu_s \): \[ \mu_s = \frac{F_{\text{max}}}{F_N} \]

Substitute the known values: \[ \mu_s = \frac{57.0 \, \text{N}}{223.668 \, \text{N}} = 0.2549 \]

Final Answer