The coefficient of static friction between a block and a horizontal floor is 0.414, while the coefficient of kinetic friction is 0.107. The mass of the block is 4.03 kg. A horizontal force is applied to the block and slowly increased. What is the value of the applied horizontal force at the instant that the block starts to slide?
What is the net force on the block after it starts to slide?
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.
To find the value of the applied horizontal force at the instant the block starts to slide, we need to consider the concept of static friction.
When an object is in equilibrium and at rest, the force of static friction acts in the opposite direction to the applied force, preventing the object from moving. The maximum value of static friction is given by the coefficient of static friction (μs) multiplied by the normal force (Fn), which is equal to the weight (mass x gravity).
In this case, the coefficient of static friction is given as 0.414, and the mass of the block is given as 4.03 kg. Assuming the acceleration due to gravity is 9.8 m/s^2, we can calculate the normal force (Fn):
Fn = mass x gravity = 4.03 kg x 9.8 m/s^2 = 39.494 N
The value of the maximum static friction force (Fs_max) is then:
Fs_max = μs x Fn = 0.414 x 39.494 N = 16.342 N
Therefore, the applied horizontal force needs to reach a value of 16.342 N for the block to start sliding.
After the block starts to slide, we transition from static friction to kinetic friction. The force of kinetic friction (Fk) is given by the coefficient of kinetic friction (μk) multiplied by the normal force (Fn).
In this case, the coefficient of kinetic friction is given as 0.107. We can calculate the force of kinetic friction (Fk):
Fk = μk x Fn = 0.107 x 39.494 N = 4.227 N
The net force (Fnet) on the block after it starts to slide is equal to the applied horizontal force (Fa) minus the force of kinetic friction (Fk):
Fnet = Fa - Fk
Note: The direction of the net force is the same as the direction of the applied force.