A 25 kg chair initially at rest on a horizontal floor requires 393 N horizontal force to set it in motion. Once the chair is in motion, a 301 N horizontal force keeps it moving at a constant velocity.
a) Find the coefficient of static friction between the chair and the floor.
b) Find the the coefficient of kinetic friction between the chair and the floor.
Use the definitions to answer the questions:
(a) coeficient of static friction =
(force required to start motion)/weight
(b) coefficient of kinetic friction =
(force required to maintain constant velocity)/weight
(Make sure you use weight = M*g)
To find the coefficients of static and kinetic friction, we can use the equations that relate the frictional force to the normal force and the coefficients of friction.
a)
The force required to set the chair in motion is equal to the maximum static friction force. The formula is given by:
\(F_{\text{{max}}} = \mu_{\text{{s}}} \cdot N\)
Where:
\(F_{\text{{max}}}\) is the maximum static friction force
\(\mu_{\text{{s}}}\) is the coefficient of static friction
\(N\) is the normal force acting on the chair
The normal force on the chair is equal to its weight since it is on a horizontal floor. The formula is:
\(N = m \cdot g\)
Where:
\(m\) is the mass of the chair
\(g\) is the acceleration due to gravity
Given that the mass of the chair is 25 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the normal force:
\(N = 25 \, \text{{kg}} \cdot 9.8 \, \text{{m/s}}^2 = 245 \, \text{{N}}\)
Substituting the values into the equation for maximum static friction force:
\(393 \, \text{{N}} = \mu_{\text{{s}}} \cdot 245 \, \text{{N}}\)
Solving for \(\mu_{\text{{s}}}\):
\(\mu_{\text{{s}}} = \frac{{393 \, \text{{N}}}}{{245 \, \text{{N}}}} = 1.60408 \, \text{{(approximately)}}\)
Therefore, the coefficient of static friction between the chair and the floor is approximately 1.604.
b) Once the chair is in motion and moving at a constant velocity, the frictional force acting on it is kinetic friction. The formula is:
\(F_{\text{{kinetic}}} = \mu_{\text{{k}}} \cdot N\)
Where:
\(F_{\text{{kinetic}}}\) is the kinetic friction force
\(\mu_{\text{{k}}}\) is the coefficient of kinetic friction
\(N\) is the normal force
Using the same normal force value of 245 N, we can find the coefficient of kinetic friction by:
\(301 \, \text{{N}} = \mu_{\text{{k}}} \cdot 245 \, \text{{N}}\)
Solving for \(\mu_{\text{{k}}}\):
\(\mu_{\text{{k}}} = \frac{{301 \, \text{{N}}}}{{245 \, \text{{N}}}} = 1.228 \, \text{{(approximately)}}\)
Thus, the coefficient of kinetic friction between the chair and the floor is approximately 1.228.
To find the coefficients of static and kinetic friction, we can use the equations relating force and friction.
a) To find the coefficient of static friction, we can use the equation:
fs = μs * N
where fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.
The normal force, N, is equal to the weight of the chair, which can be calculated using the equation:
N = m * g
where m is the mass of the chair and g is the acceleration due to gravity.
Given:
m = 25 kg
g = 9.8 m/s^2
Substituting these values into the equation, we have:
N = 25 kg * 9.8 m/s^2
N = 245 N
Now, we can use the fact that the static friction force is equal to the applied force that sets the chair in motion, which is 393 N:
fs = 393 N
Substituting this value, we have:
393 N = μs * 245 N
Now, we can solve for the coefficient of static friction:
μs = 393 N / 245 N
μs ≈ 1.60
Therefore, the coefficient of static friction between the chair and the floor is approximately 1.60.
b) To find the coefficient of kinetic friction, we can use the equation:
fk = μk * N
where fk is the force of kinetic friction, μk is the coefficient of kinetic friction, and N is the normal force.
Using the same value for N as before (245 N), we can now use the force of kinetic friction, which is 301 N:
fk = 301 N
Substituting these values into the equation, we have:
301 N = μk * 245 N
Now, we can solve for the coefficient of kinetic friction:
μk = 301 N / 245 N
μk ≈ 1.23
Therefore, the coefficient of kinetic friction between the chair and the floor is approximately 1.23.