A 23 kg chair initially at rest on a horizontal

floor requires a 370 N horizontal force to set
it in motion. Once the chair is in motion, a
332 N horizontal force keeps it moving at a
constant velocity.
The acceleration of gravity is 9.81 m/s
2
.
a) What is the coefficient of static friction
between the chair and the floor?

F=F(fr)

370=μ(s)•m•g
μ(s)=370/mg,

μ(k)=332/mg,

To find the coefficient of static friction between the chair and the floor, we need to use the concept of Newton's laws of motion.

First, let's determine the force of static friction that needs to be overcome in order to set the chair in motion.

We know that the force required to set the chair in motion is 370 N. This force is equal to the maximum force of static friction (F_s), which can be calculated using the formula:

F_s = μ_s * N

Where:
- F_s is the force of static friction
- μ_s is the coefficient of static friction
- N is the normal force, which is equal to the weight of the chair (mass * acceleration due to gravity)

Given that the mass of the chair is 23 kg and the acceleration due to gravity is 9.81 m/s^2, we can calculate the normal force:

N = mass * acceleration due to gravity
N = 23 kg * 9.81 m/s^2
N = 225.63 N

Now, we can substitute the values of F_s and N into the equation to find the coefficient of static friction:

370 N = μ_s * 225.63 N

Solving for μ_s:

μ_s = 370 N / 225.63 N
μ_s ≈ 1.64

Therefore, the coefficient of static friction between the chair and the floor is approximately 1.64.