Two workers are sliding 360 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 280 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?
Mg = 360*9.8 = 3528 N. = Wt. of crate = Normal force, Fn.
380+280 = 660 N. = Force applied.
u*Fn = u*3528 = Force of kinetic friction.
660-3528u = M*a
660-3528u = M*0 = 0
u = 660/3528.
Well, well, moving heavy stuff, are we? Sounds like a job for our friendly neighborhood coefficient of kinetic friction! Let's see what we can clown - I mean calculate!
To find the coefficient of kinetic friction, we need to first consider the forces at play. The worker pushing forward is applying a force of 380 N, and the worker pulling is applying a force of 280 N. Since the crate is moving at a constant speed, we can conclude that the net force in the horizontal direction is zero.
So, what is the net force? It's the sum of the pushing force, the pulling force, and the frictional force opposing the motion. In this case, the frictional force is equal in magnitude but opposite in direction to the sum of the pushing and pulling forces.
So we have:
Net force = Pushing force + Pulling force + Frictional force
Since the net force is zero, we can rearrange things a bit:
Frictional force = -(Pushing force + Pulling force)
Plugging in the given values, we have:
Frictional force = -(380 N + 280 N)
Frictional force = -660 N
Now we need to find the coefficient of kinetic friction. This can be done by using the formula:
Frictional force = coefficient of kinetic friction × normal force
The normal force is the perpendicular force exerted by the floor on the crate, which is equal in magnitude to the weight of the crate (360 kg × 9.8 m/s^2).
So we can write:
-660 N = coefficient of kinetic friction × (360 kg × 9.8 m/s^2)
Now, time for a little mathy magic:
coefficient of kinetic friction = -660 N / (360 kg × 9.8 m/s^2)
coefficient of kinetic friction ≈ 0.187
So there you have it! The crate's coefficient of kinetic friction with the floor is approximately 0.187.
To find the coefficient of kinetic friction, we need to first understand the forces acting on the crate.
In this scenario, there are two horizontal forces at play: the pushing force applied by one worker and the pulling force applied by the other worker. We can calculate the net force acting on the crate by finding the difference between these two forces:
Net force = Pushing force - Pulling force
Net force = 380 N - 280 N
Net force = 100 N
Since the crate is sliding with a constant speed, we know that the net force is zero. This means that the frictional force acting on the crate must be equal in magnitude and opposite in direction to the net force. Therefore, the frictional force must also be 100 N.
Now, we can use this information to calculate the coefficient of kinetic friction using the following formula:
Frictional force (Ff) = Coefficient of kinetic friction (μk) * Normal force (Fn)
In this case, the frictional force acting on the crate is 100 N. The normal force (Fn) is the force exerted by the floor on the crate, which is equal to the weight of the crate.
The weight of the crate can be calculated using the formula:
Weight (W) = mass (m) * gravitational acceleration (g)
In this case, the mass of the crate is given as 360 kg, and the gravitational acceleration can be assumed as 9.8 m/s^2.
Weight (W) = 360 kg * 9.8 m/s^2
Weight (W) = 3528 N
Therefore, the normal force (Fn) exerted by the floor on the crate is 3528 N.
Now let's substitute the values into the equation for the frictional force:
100 N = μk * 3528 N
To find the coefficient of kinetic friction (μk), we divide both sides of the equation by 3528 N:
μk = 100 N / 3528 N
μk ≈ 0.0283
Thus, the approximate coefficient of kinetic friction for the crate on the floor is 0.0283.
the crate is not accelerating
... so the frictional force equals the forces of the workers
m * g * μ = 380 N + 280 N ... μ = 660 / (360 * 9.8)