A 6 kg mass is resting on a horizontal surface it is determined that a force of 20 N will start the object skidding and keep it sliding with an acceleration of 0.83 m/s what are the coefficient of static and kinetic friction between the mass and the surface ?
Static problem:
F = mu m g
static mu = F / m g = 20 /(6 * 9.81)
Dynamic problem
F - mu m g = 0.83 m
mu m g = F- 0.83 m
dynamic mu = (20 - 0.83*6) / ( 6 * 9.81)
To determine the coefficient of static friction (μs), we can use the equation:
μs = Fs/ (mg)
where Fs is the force of static friction, m is the mass, and g is the acceleration due to gravity.
Given that the force required to start the object skidding is 20 N and the mass is 6 kg, we can calculate Fs:
Fs = 20 N
Next, we can calculate the force of gravity:
mg = 6 kg * 9.8 m/s^2 = 58.8 N
Now, we can calculate the coefficient of static friction:
μs = Fs / (mg) = 20 N / 58.8 N = 0.34
So, the coefficient of static friction (μs) is 0.34.
To determine the coefficient of kinetic friction (μk), we can use the equation:
μk = Fk / (mg)
where Fk is the force of kinetic friction.
Given that the acceleration of the object is 0.83 m/s^2, we can calculate Fk:
Fk = m * a = 6 kg * 0.83 m/s^2 = 4.98 N
Now, we can calculate the coefficient of kinetic friction:
μk = Fk / (mg) = 4.98 N / 58.8 N ≈ 0.085
So, the coefficient of kinetic friction (μk) is approximately 0.085.
To determine the coefficients of static and kinetic friction between the mass and the surface, we can make use of Newton's second law of motion.
1. Let's start by finding the force of friction acting on the object. The force of friction can be calculated using the equation:
Force of friction = mass * acceleration
Plugging in the given values, we have:
Force of friction = 6 kg * 0.83 m/s^2 = 4.98 N
2. The force of friction can also be calculated using the equation:
Force of friction = coefficient of friction * normal force
A normal force is equal to the weight of the object, which can be calculated using the equation:
Weight = mass * gravity
Given that the mass is 6 kg and gravity is approximately 9.8 m/s^2:
Weight = 6 kg * 9.8 m/s^2 = 58.8 N
Therefore, the normal force acting on the object is 58.8 N.
Now, we can substitute the force of friction (4.98 N) and the normal force (58.8 N) into the equation:
4.98 N = coefficient of static friction * 58.8 N
Solving for the coefficient of static friction:
coefficient of static friction = 4.98 N / 58.8 N = 0.085
Hence, the coefficient of static friction between the mass and the surface is 0.085.
3. Once the object starts skidding, the force of friction changes from static to kinetic. The coefficient of kinetic friction can be determined by using the equation:
coefficient of kinetic friction = Force of kinetic friction / normal force
Given that the force of kinetic friction (which is equivalent to the force of friction) is 4.98 N and the normal force is 58.8 N:
coefficient of kinetic friction = 4.98 N / 58.8 N = 0.085
Therefore, the coefficient of kinetic friction between the mass and the surface is also 0.085.
In conclusion, both the coefficient of static and kinetic friction between the 6 kg mass and the horizontal surface are 0.085.