A 28 kg chair intially at rest on a horizontal floor requires a 360 N horizontal force to set it in motion. Once the chair is in motion, a 329 N horizontail force keeps moving it at a constant velocity. The acceleration of gravity is 9.81 m/s^2. What is the coefficient of static friction between the chair and floor?
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The static friction coefficient is the force reuired to start it moving, divided by M g.
The kinetic friction coefficient is the force required to keep it moving at constant speed, divided by M g.
M g in this case is 28 x 9.81 Newtons
To find the coefficient of static friction between the chair and the floor, we need to use the given information and apply the concepts of static friction and Newton's laws of motion.
First, let's break down the problem:
The mass of the chair (m) = 28 kg
Initial force required to set the chair in motion (F1) = 360 N
Force applied to keep the chair moving at a constant velocity (F2) = 329 N
Acceleration due to gravity (g) = 9.81 m/s^2
Now, let's analyze the situation using Newton's laws of motion:
1. Initially at rest:
When the chair is at rest, the force of static friction (Fs) opposes the applied force (F1) until it reaches the maximum static friction force (Fstatic_max). This relationship can be written as:
Fs = Fstatic_max
2. In motion at constant velocity:
When the chair is moving at constant velocity, the force of kinetic friction (Fk) is equal to the applied force (F2) that keeps the chair moving. This can be written as:
Fk = F2
To find the coefficient of static friction (μs), we need to find the maximum static friction force (Fstatic_max).
Using Newton's second law of motion:
Fstatic_max = μs * N
where N represents the normal force acting on the chair. In this case, the normal force (N) is equal to the weight of the chair (mg):
N = m * g
Substituting the value of N, we have:
Fstatic_max = μs * m * g
Now, let's solve the problem step by step:
1. Calculate the maximum static friction force (Fstatic_max):
Fstatic_max = μs * m * g
2. Calculate the normal force (N):
N = m * g
3. Substitute the value of N in the equation for Fstatic_max:
Fstatic_max = μs * m * g
4. Substitute the given values:
Fstatic_max = μs * 28 kg * 9.81 m/s^2
5. Calculate Fstatic_max:
Fstatic_max = 274.536 μs N
Now, we know that Fstatic_max is equal to the initial force required to set the chair in motion (F1). Hence:
F1 = 274.536 μs N
Substituting the given value of F1, we can solve for the coefficient of static friction (μs):
360 N = 274.536 μs N
Divide both sides by N:
360 N / 274.536 N = μs
μs ≈ 1.31
Therefore, the coefficient of static friction between the chair and the floor is approximately 1.31.