Two workers are sliding 450 kg crate across the floor. One worker pushes forward on the crate with a force of 380 N while the other pulls in the same direction with a force of 380 N using a rope connected to the crate. Both forces are horizontal, and the crate slides with a constant speed. What is the crate's coefficient of kinetic friction on the floor?
To find the coefficient of kinetic friction, we can use the concept of equilibrium. When the crate is moving at a constant speed, the net force acting on it is zero.
Let's analyze the forces acting on the crate:
1. The force applied by the worker pushing forward on the crate with a force of 380 N (F1 = 380 N).
2. The force applied by the worker pulling the crate with a force of 380 N (F2 = 380 N).
3. The force of kinetic friction opposing the crate's motion (fk).
Since the crate is moving at a constant speed, the net force (Fnet) is zero:
Fnet = F1 + F2 - fk = 0
Rearranging the equation:
fk = F1 + F2
fk = 380 N + 380 N
fk = 760 N
Now, we can use the equation for the force of kinetic friction:
fk = μk * N
where μk is the coefficient of kinetic friction and N is the normal force.
Since the crate is on a horizontal floor and not accelerating vertically, the normal force (N) is equal to the weight of the crate (mg):
N = mg
Given that the mass of the crate (m) is 450 kg and the acceleration due to gravity (g) is approximately 9.8 m/s^2, we can calculate the normal force:
N = 450 kg * 9.8 m/s^2
N = 4410 N
Now, we can substitute the values of fk and N into the equation for the force of kinetic friction:
760 N = μk * 4410 N
Solving for μk:
μk = 760 N / 4410 N
μk ≈ 0.172
Therefore, the coefficient of kinetic friction for the crate on the floor is approximately 0.172.
To find the crate's coefficient of kinetic friction on the floor, we can use the following steps:
Step 1: Find the net force acting on the crate.
Since the crate is sliding with a constant speed, we know that the net force on the crate must be zero. This means that the force due to friction must be equal in magnitude and opposite in direction to the sum of the pushing and pulling forces.
Net force = Force due to friction + Pushing force + Pulling force
Since the pushing force and the pulling force are equal in magnitude and opposite in direction, their sum is zero.
Net force = Force due to friction + 0
Therefore, the net force is equal to the force due to friction.
Step 2: Calculate the force due to friction.
The force due to friction can be calculated using the formula:
Force due to friction = coefficient of friction × normal force
In this case, the normal force is equal to the weight of the crate, which can be calculated using the formula:
Weight = mass × gravity
Given that the mass of the crate is 450 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:
Weight = 450 kg × 9.8 m/s^2
Step 3: Equate the net force and force due to friction.
Since the net force is equal to the force due to friction, we can equate the two:
Net force = Force due to friction
But we already found that the net force is zero (due to the constant speed), so we have:
0 = Force due to friction
Therefore, the force due to friction is also zero.
Step 4: Calculate the coefficient of kinetic friction.
Now that we know the force due to friction is zero, we can calculate the coefficient of kinetic friction using the formula:
Coefficient of kinetic friction = Force due to friction / Normal force
Since the force due to friction is zero, the coefficient of kinetic friction is also zero.
Therefore, the crate's coefficient of kinetic friction on the floor is zero.
normal force = 450*9.81 = 4414. N
friction force = 4415 mu
so
380 + 380 = 4415 mu