Understanding the Concepts

* Static Friction: The force that prevents an object from moving when a force is applied to it.

* Coefficient of Static Friction (μs): A dimensionless quantity that represents the ratio of the maximum static friction force to the normal force.

Formula

The maximum static friction force (Fs) is calculated using the following formula:

Fs = μs * N

Where:

* Fs = Maximum static friction force

* μs = Coefficient of static friction

* N = Normal force (equal to the weight of the object in this case)

Calculations

1. Calculate the Normal Force (N):

* The normal force is equal to the weight of the sofa, which is mass (m) times gravitational acceleration (g):

* N = m * g = 105 kg * 9.8 m/s² = 1029 N

2. Determine the Maximum Static Friction Force:

* The maximum static friction force is the force required to start the sofa moving, which is given as 102 N.

3. Calculate the Coefficient of Static Friction:

* Using the formula Fs = μs * N, solve for μs:

* μs = Fs / N = 102 N / 1029 N ≈ 0.099

Answer:

The coefficient of static friction between the sofa and the carpet is approximately 0.099.