The coefficient of static friction between a block and a horizontal floor is 0.35, while the coefficient of kinetic friction is 0.12. The mass of the block is 4.5 kg. A horizontal force is applied to the block and slowly increased.
(a) What is the value of the applied horizontal force at the instant that the block starts to slide?
(b) What is the net force on the block after it starts to slide?
wryae
To find the value of the applied horizontal force at the instant the block starts to slide, we can calculate the maximum possible static friction force.
(a)
The maximum static friction force (F_max_s) can be calculated using the equation: F_max_s = μ_s * N
where μ_s is the coefficient of static friction and N is the normal force.
The normal force (N) is equal to the weight of the block, which can be calculated as: N = m * g
where m is the mass of the block and g is the acceleration due to gravity.
In this case, the mass of the block is given as 4.5 kg.
The acceleration due to gravity, g, is approximately equal to 9.8 m/s^2.
Therefore, N = 4.5 kg * 9.8 m/s^2 = 44.1 N.
Now, we can calculate F_max_s as follows:
F_max_s = μ_s * N = 0.35 * 44.1 N = 15.435 N.
So, the applied horizontal force at the instant the block starts to slide is approximately 15.435 N.
(b)
Once the block starts to slide, we are dealing with kinetic friction. The force of kinetic friction (F_k) can be calculated using the equation: F_k = μ_k * N
where μ_k is the coefficient of kinetic friction and N is the normal force.
The coefficient of kinetic friction μ_k is given as 0.12.
Using the value of N calculated earlier (44.1 N), we can calculate F_k as follows:
F_k = μ_k * N = 0.12 * 44.1 N = 5.292 N.
The net force on the block after it starts to slide is equal to the applied force minus the force of kinetic friction:
Net force = Applied force - Force of kinetic friction = Applied force - 5.292 N.
Please note that the net force will vary depending on the magnitude of the applied force.