A 6 kg mass is resting on a horizontal surface. It is determined that, a force of 20 N will start the object sliding and keep it sliding with an acceleration of 0.83 m/s². What are the coefficients of static and kinetic friction between the mass and the surface?
To determine the coefficients of static and kinetic friction, we need to use the following equation:
F_net = m * a
where F_net is the net force acting on the object, m is the mass of the object, and a is the acceleration.
Given:
m = 6 kg
a = 0.83 m/s²
Therefore,
F_net = 6 kg * 0.83 m/s²
F_net = 4.98 N
The force required to start the object sliding is the force of static friction, while the force required to keep it sliding is the force of kinetic friction. Let's denote the force of static friction as F_s and the force of kinetic friction as F_k.
According to the question,
F_s = 20 N
F_k = 4.98 N
The force of static friction can be expressed as:
F_s = μ_s * N
where μ_s is the coefficient of static friction and N is the normal force.
The normal force can be calculated as:
N = m * g
where g is the acceleration due to gravity, approximately equal to 9.8 m/s².
N = 6 kg * 9.8 m/s²
N = 58.8 N
Substituting the values back into the equation for F_s, we have:
20 N = μ_s * 58.8 N
Solving for μ_s, we get:
μ_s = 20 N / 58.8 N
μ_s ≈ 0.34
So, the coefficient of static friction between the mass and the surface is approximately 0.34.
Similarly, we can calculate the coefficient of kinetic friction using the equation:
F_k = μ_k * N
Substituting the known values, we have:
4.98 N = μ_k * 58.8 N
Solving for μ_k, we get:
μ_k = 4.98 N / 58.8 N
μ_k ≈ 0.085
Therefore, the coefficient of kinetic friction between the mass and the surface is approximately 0.085.