Final answer:
To determine the minimum value of the coefficient of static friction needed for the block to remain motionless, we need to analyze the forces acting on the block. the minimum value of the coefficient of static friction can be calculated to be B. 0.24.
Step-by-step explanation:
To determine the minimum value of the coefficient of static friction needed for the block to remain motionless, we need to analyze the forces acting on the block. The force of static friction is what prevents the block from moving. We can use the equation Fs = μs Fn, where Fs is the force of static friction, μs is the coefficient of static friction, and Fn is the normal force. Since the block is on an incline, the normal force can be found using the equation Fn = mg cosθ, where m is the mass of the block, g is the acceleration due to gravity, and θ is the angle of the incline.
Given that the frictional force is 4.86 N and the mass of the block is 2 kg, we can solve for the coefficient of friction using the equation Ff = μ Fn, where Ff is the frictional force and μ is the coefficient of friction. Rearranging the equation, we get μ = Ff / Fn.
To find the incline at which the box will slide at a constant velocity, we need to determine the angle at which the force of friction is equal to the force pulling the block down the incline. This occurs when the frictional force is equal to μk Fn, where μk is the coefficient of kinetic friction.