A cable attached to a block of mass 11 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?
Since there is no acceleration, the rope tension (5.3 N) equals the friction force, which is M g Uk
Solve for Uk, the kinetic friction coefficient
Well, since the block is moving at a constant velocity, it means the net force acting on it is zero. We can break down the forces involved here.
First, we have the tension in the cable pulling the block forward with a force of 5.3 N.
Next, we have the force of kinetic friction, which is opposing the motion. We can use the equation for kinetic friction:
frictional force = coefficient of kinetic friction * normal force
Since the block is on a horizontal floor, the normal force is just equal to the weight of the block, which is given by:
weight = mass * gravitational acceleration
Plugging in the values, we have:
weight = 11 kg * 9.8 m/s^2 = 107.8 N
Now we can use the given tension in the cable to find the coefficient of kinetic friction:
frictional force = coefficient of kinetic friction * 107.8 N
But we also know that the net force is zero, so:
5.3 N - frictional force = 0
Solving for the frictional force, we get:
frictional force = 5.3 N
Plugging it into the equation, we have:
5.3 N = coefficient of kinetic friction * 107.8 N
Simplifying, we find:
coefficient of kinetic friction = 5.3 N / 107.8 N ≈ 0.0492
So, the coefficient of kinetic friction between the block and the floor is approximately 0.0492. It seems like the block and the floor aren't getting along so well!
To find the coefficient of kinetic friction between the block and the floor, we can use the equation:
μk = (T - Fnet) / (mg)
Where:
- μk is the coefficient of kinetic friction
- T is the tension in the cable
- Fnet is the net force acting on the block
- m is the mass of the block
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
In this case, the block is moving at a constant velocity, so the net force acting on the block is zero. This means that the tension in the cable is equal to the force of kinetic friction:
T = Fk
Substituting this into the equation, we have:
μk = (T - Fnet) / (mg)
= (Fk - 0) / (mg)
= Fk / (mg)
Given that the mass of the block is 11 kg and the tension in the cable is 5.3 N, we can substitute these values into the equation to find the coefficient of kinetic friction:
μk = (5.3 N) / (11 kg * 9.8 m/s^2)
≈ 0.048
Therefore, the coefficient of kinetic friction between the block and the floor is approximately 0.048.