A cable attached to a block of mass 8 kg pulls the block along a horizontal floor at a constant velocity. If the tension in the cable is 5.3 N, what is the coefficient of kinetic friction between the block and the floor?
ma=0=T-F(fr) = T-μ•mg .
μ = T/mg = 5.3/8•9.8=0.068
To find the coefficient of kinetic friction between the block and the floor, we need to use Newton's second law of motion along with the concept of friction.
1. Identify the forces acting on the block:
- Tension force along the cable
- Weight force (mg) due to gravity
- Kinetic friction force (fk)
2. Write down the equation for Newton's second law of motion:
∑F = ma
3. Resolve the forces along the horizontal direction:
Tension force (T) and friction force (fk) act in opposite directions.
So, the equation becomes:
T - fk = ma
4. Calculate the acceleration (a) of the block:
Since the block is moving at a constant velocity, the acceleration is zero.
Therefore, we have:
T - fk = 0
5. Substitute the given values into the equation:
T - fk = 0
5.3 N - fk = 0
6. Solve for the friction force (fk):
fk = 5.3 N
7. Calculate the normal force (N):
The normal force (N) is equal in magnitude and opposite in direction to the weight force (mg).
N = mg
N = 8 kg * 9.8 m/s^2
N = 78.4 N
8. Calculate the coefficient of kinetic friction (μk):
The coefficient of kinetic friction can be found using the formula:
fk = μk * N
Substitute the known values:
5.3 N = μk * 78.4 N
Solve for μk:
μk = 5.3 N / 78.4 N
9. Calculate the coefficient of kinetic friction:
μk = 0.0676 (rounded to four decimal places)
Therefore, the coefficient of kinetic friction between the block and the floor is approximately 0.0676.