Final answer:
The minimum coefficient of friction between the block and the ground is 0.243 for all cases.
Step-by-step explanation:
To find the minimum coefficient of friction between the block and the ground, we need to consider the forces acting on the block. In this case, the only force acting against the motion of the block is the frictional force. We can use the equation F_friction = μ * F_normal, where F_friction is the frictional force, μ is the coefficient of friction, and F_normal is the normal force.
Since we are given the frictional force, we can rearrange the equation to solve for the coefficient of friction: μ = F_friction / F_normal. The normal force can be calculated using the equation F_normal = m * g, where m is the mass of the block and g is the acceleration due to gravity.
Let's calculate the minimum coefficient of friction for each case:
a. 2 m/s: F_normal = 2 kg * 10 m/s^2 = 20 N, μ = 4.86 N / 20 N = 0.243
b. 4 m/s: F_normal = 2 kg * 10 m/s^2 = 20 N, μ = 4.86 N / 20 N = 0.243
c. 6 m/s: F_normal = 2 kg * 10 m/s^2 = 20 N, μ = 4.86 N / 20 N = 0.243
d. 8 m/s: F_normal = 2 kg * 10 m/s^2 = 20 N, μ = 4.86 N / 20 N = 0.243