A 23 kg chair initially at rest on a horizontal
floor requires a 371 N horizontal force to set
it in motion. Once the chair is in motion, a
345 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?
The force required to make it move is
F = (mu_s)*W = (mu_s)*M*g
M is the chair's mass. Solve for mu_s
For question (a), you don't need the force needed to keep it oving.
To find the coefficient of static friction between the chair and the floor, we need to use Newton's second law of motion and the concept of static friction.
The force required to set the chair in motion is equal to the product of the coefficient of static friction and the normal force (the force exerted by the floor on the chair). Therefore, we can write:
Force to set chair in motion = Coefficient of static friction × Normal force
Given that the force required to set the chair in motion is 371 N, we need to find the normal force. The normal force is equal to the weight of the chair, which is the mass of the chair multiplied by the acceleration due to gravity. Therefore, we can write:
Normal force = mass of chair × acceleration due to gravity
Substituting the given values, we have:
Normal force = 23 kg × 9.81 m/s^2 = 225.63 N
Now, we can substitute the values for the force to set the chair in motion and the normal force into our previous equation to find the coefficient of static friction:
371 N = Coefficient of static friction × 225.63 N
Solving for the coefficient of static friction:
Coefficient of static friction = 371 N / 225.63 N
Coefficient of static friction = 1.643
Therefore, the coefficient of static friction between the chair and the floor is approximately 1.643.