To find the value of the applied horizontal force at the instant the block starts to slide, we can use the equation:
Fapplied = μs * Normal force
Where:
Fapplied is the applied horizontal force
μs is the coefficient of static friction
Normal force is the force perpendicular to the surface of contact (equal to the weight of the block, mg)
Given:
μs = 0.414
m = 4.03 kg
g = 9.8 m/s² (acceleration due to gravity)
Using the equation, we can calculate the normal force:
Normal force = mg = (4.03 kg)(9.8 m/s²) = 39.44 N
Now, substitute the values back into the equation to find the applied horizontal force:
Fapplied = (0.414)(39.44 N) = 16.31 N
Therefore, the value of the applied horizontal force at the instant the block starts to slide is 16.31 N.
After the block starts to slide, the coefficient of kinetic friction comes into play. The kinetic friction force can be calculated using the equation:
Fkinetic = μk * Normal force
Where:
Fkinetic is the kinetic friction force
μk is the coefficient of kinetic friction
Given:
μk = 0.107
Normal force = 39.44 N (from earlier calculation)
Now, substitute the values into the equation to calculate the kinetic friction force:
Fkinetic = (0.107)(39.44 N) = 4.22 N
Since the block is sliding, the applied force has to overcome the kinetic friction force, so the net force on the block is equal to the applied force:
Net force = Fapplied = 16.31 N
Therefore, the net force on the block after it starts to slide is 16.31 N.