A 20kg block is initially at rest on a rough, horizontal surface. A horizontal force of 75N is required to set the block in motion. After it is in motion, a horizontal force of 60N is required to keep the block moving with constant speed.
Find the coefficient of static and kinetic friction from this information.
weight = m g
friction force = mu m g
so
static mus
75 = mus (20)(9.81)
and
kinetic muk
60 = muk (20)(9.81)
To find the coefficient of static friction, we need to use the formula:
Coefficient of static friction (μs) = Force required to overcome static friction (Fs) / Normal force (N)
From the information given, we know that a horizontal force of 75N is required to set the block in motion. This force is equal to the force required to overcome static friction. Therefore, we can say:
Fs = 75N
The normal force (N) is equal to the weight of the block, which can be calculated by multiplying the mass (m) by the acceleration due to gravity (g).
N = m * g
Given that the mass of the block is 20kg and the acceleration due to gravity is approximately 9.8 m/s^2, we have:
N = 20kg * 9.8 m/s^2
N = 196N
Now we can substitute the values into the formula to find the coefficient of static friction:
μs = Fs / N
μs = 75N / 196N
μs ≈ 0.3827
Therefore, the coefficient of static friction is approximately 0.3827.
To find the coefficient of kinetic friction, we use a similar formula:
Coefficient of kinetic friction (μk) = Force required to maintain constant speed (Fk) / Normal force (N)
From the information given, we know that a horizontal force of 60N is required to keep the block moving with constant speed. This force is equal to the force required to maintain constant speed (Fk). Therefore, we can say:
Fk = 60N
Using the same normal force as before (N = 196N), we can substitute the values into the formula to find the coefficient of kinetic friction:
μk = Fk / N
μk = 60N / 196N
μk ≈ 0.3061
Therefore, the coefficient of kinetic friction is approximately 0.3061.
In summary, the coefficient of static friction is approximately 0.3827, and the coefficient of kinetic friction is approximately 0.3061.