If the 36.1 N force continues, the box accelerates at 0.71 m/s^2. What is the coefficient of kinetic friction? What is the coefficient of static friction between the box and the floor? If the 36.1 N force continues, the box accelerates at 0.71 m/s^2. What is the coefficient of kinetic friction?
To find the coefficient of kinetic friction, we first need to understand the relationship between force, mass, acceleration, and friction.
The force acting on the box is given as 36.1 N, and the acceleration is given as 0.71 m/s^2. We can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, we need to find the mass of the box. We can use the formula:
Force = mass x acceleration
Rearranging the formula, we have:
mass = force / acceleration
mass = 36.1 N / 0.71 m/s^2
mass ≈ 50.92 kg (rounded to two decimal places)
Now that we have the mass of the box, we can move on to finding the coefficient of kinetic friction.
The formula to calculate the force of kinetic friction is:
Force of kinetic friction = coefficient of kinetic friction x normal force
The normal force in this case is equal to the weight of the box since it is resting on a flat horizontal surface. The weight (W) can be calculated as:
Weight = mass x gravitational acceleration
Using a typical value for the gravitational acceleration of 9.8 m/s^2, we have:
Weight = 50.92 kg x 9.8 m/s^2
Weight ≈ 499.38 N (rounded to two decimal places)
Now, we can substitute the values into the equation for force of kinetic friction:
36.1 N = coefficient of kinetic friction x 499.38 N
Simplifying the equation, we get:
coefficient of kinetic friction = 36.1 N / 499.38 N
coefficient of kinetic friction ≈ 0.0723 (rounded to four decimal places)
Therefore, the coefficient of kinetic friction is approximately 0.0723.
To find the coefficient of static friction between the box and the floor, we need to know the maximum force of static friction that can prevent the box from moving when the applied force is at the verge of overcoming static friction.
The formula to calculate the maximum force of static friction is:
Maximum force of static friction = coefficient of static friction x normal force
Since the box is already moving with an acceleration of 0.71 m/s^2, the force of static friction has already been overcome. Therefore, the coefficient of static friction is not applicable in this scenario.
So, the coefficient of static friction between the box and the floor cannot be determined from the given information.
In summary:
Coefficient of kinetic friction ≈ 0.0723
Coefficient of static friction - not determined from the given information