A student pulls horizontally on a 12 kg box, which then moves horizontally with an acceleration of 2 m/s^2. If the student uses a force of 15 N, what is the coefficient of kinetic friction of the floor?
To find the coefficient of kinetic friction of the floor, we need to use Newton's second law of motion and the formula for kinetic friction. Here are the steps to find the coefficient:
1. Write down the given information:
- Mass of the box (m): 12 kg
- Acceleration of the box (a): 2 m/s^2
- Applied force by the student (F): 15 N
2. Use Newton's second law of motion:
The force applied by the student is equal to the product of mass and acceleration.
F = m * a
Substitute the values:
15 N = 12 kg * 2 m/s^2
3. Solve for force applied by the student:
15 N = 24 kg⋅m/s^2
4. Determine the frictional force:
The force applied by the student (F) is equal to the sum of the frictional force (Ff) and the force due to acceleration (Fnet).
F = Ff + Fnet
Since the box is moving horizontally, the force due to acceleration (Fnet) is zero.
F = Ff
5. Substitute the values:
15 N = Ff
6. Use the formula for kinetic friction:
The frictional force (Ff) can be calculated using the formula:
Ff = μ * N
where μ is the coefficient of kinetic friction and N is the normal force acting on the box.
7. Determine the normal force:
The normal force (N) is the force exerted by a surface perpendicular to the surface.
In this case, the box is moving horizontally, so the normal force is equal to the weight of the box.
N = m * g
where g is the acceleration due to gravity, approximately 9.8 m/s^2.
8. Substitute the values:
N = 12 kg * 9.8 m/s^2
9. Solve for the normal force:
N = 117.6 N
10. Substitute the values:
15 N = μ * 117.6 N
11. Solve for the coefficient of kinetic friction:
Dividing both sides by 117.6 N:
μ = 15 N / 117.6 N
12. Perform the calculation:
μ ≈ 0.1275
Therefore, the coefficient of kinetic friction of the floor is approximately 0.1275.