Final answer:
To calculate the coefficient of static friction, the inclined angle at which the box begins to slip can be used to set up an equation equating the gravitational force component down the slope and the maximum static friction force. By inserting 40° into the equation μs = tan θ, we find the coefficient of static friction to be approximately 0.84.
Step-by-step explanation:
To find the coefficient of static friction, we can use the scenario where the box starts to slip at the inclination angle of 40°. At the point of slipping, the component of the box's weight down the ramp (mg sin θ) is equal to the maximum static frictional force (fs(max) = μs N). The normal force (N) at this angle is the component of the weight perpendicular to the ramp (mg cos θ).
Therefore, the static frictional force can be expressed as fs(max) = μs mg cos θ. Since fs(max) = mg sin θ, we can equate the two expressions and solve for μs. By substituting θ = 40° and using g = 9.8 m/s² (acceleration due to gravity), the equation simplifies to μs = tan θ, and so the coefficient of static friction is equal to tan(40°).
Performing the calculation yields the coefficient of static friction to be approximately 0.84, if we ignore complicating factors such as air resistance and assume that the start of the box's movement represents the transition from static to kinetic friction.