A 25 kg chair initially at rest on a horizontal floor requires 360 N horizontal force to set it in motion. Once the chair is in motion, a 316 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.
a) Well, well, looks like this chair is quite the diva! Let's talk static friction, shall we? Since the chair is initially at rest, we need to find the coefficient of static friction between the chair and the floor.
The force required to set it in motion is 360 N. That's the maximum static friction, my friend! Now, we know that the normal force is equal to the weight of the chair, which is 25 kg multiplied by the acceleration due to gravity (which is approximately 9.8 m/s^2). So, the normal force equals 25 kg multiplied by 9.8 m/s^2.
To find the coefficient of static friction, we can use the formula: coefficient of static friction = maximum static friction force / normal force.
Therefore, the coefficient of static friction between the chair and the floor is 360 N divided by (25 kg * 9.8 m/s^2).
b) Now that the chair is in motion, we need to find the coefficient of kinetic friction. The force required to keep the chair moving at a constant velocity is 316 N.
The coefficient of kinetic friction, my friend, is given by the formula: coefficient of kinetic friction = kinetic friction force / normal force.
Therefore, the coefficient of kinetic friction between the chair and the floor is 316 N divided by (25 kg * 9.8 m/s^2).
So, there you have it! You now have the coefficients of static and kinetic friction between the chair and the floor.
To find the coefficients of static and kinetic friction, we need to analyze the forces acting on the chair and use the equations of motion.
a) Finding the coefficient of static friction:
The static frictional force can be calculated using the equation F_friction = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force acting on the chair.
In this case, the normal force N is equal to the weight of the chair, which can be calculated as N = m * g, where m is the mass of the chair and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given:
Mass of the chair (m) = 25 kg
a1) Calculate the normal force N:
N = m * g = 25 kg * 9.8 m/s^2 = 245 N
The horizontal force required to set the chair in motion is 360 N, which is equal to the maximum static frictional force (F_friction_max) acting on the chair before it starts moving.
a2) Calculate the coefficient of static friction μ_s:
F_friction_max = μ_s * N
360 N = μ_s * 245 N
μ_s = 360 N / 245 N
μ_s = 1.47 (rounded to two decimal places)
Therefore, the coefficient of static friction between the chair and the floor is approximately 1.47.
b) Finding the coefficient of kinetic friction:
Once the chair is in motion, it experiences a kinetic frictional force. The magnitude of this force is given by F_friction = μ_k * N, where μ_k is the coefficient of kinetic friction.
The kinetic frictional force is equal to the applied horizontal force (316 N) that keeps the chair moving at a constant velocity.
b1) Calculate the coefficient of kinetic friction μ_k:
F_friction = μ_k * N
316 N = μ_k * 245 N
μ_k = 316 N / 245 N
μ_k = 1.29 (rounded to two decimal places)
Therefore, the coefficient of kinetic friction between the chair and the floor is approximately 1.29.