An applied force of 450N is needed to drag a 100kg crate at a constant speed across a horizontal rough floor. Calculate the coefficient of kinetic friction for the crate on the floor.
Wc = M*g = 100kg * 9.8N/kg = 980 N. = Normal(Fn).
Fap-Fk = M*a.
450-u*980 = M*0 = 0.
-980u = -450.
u = 0.459
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To calculate the coefficient of kinetic friction, we can use the formula:
Coefficient of kinetic friction = Applied force / Normal force
First, we need to find the normal force acting on the crate. Since the crate is on a horizontal surface and moving at a constant speed, the normal force is equal in magnitude and opposite in direction to the force of gravity acting on the crate.
The force of gravity can be calculated using the formula:
Force of gravity = mass * acceleration due to gravity
where
mass = 100 kg (given)
acceleration due to gravity = 9.8 m/s^2 (constant)
Force of gravity = 100 kg * 9.8 m/s^2 = 980 N
Since the crate is being dragged at a constant speed, the applied force of 450N must balance out the force of friction.
So, the normal force can be found by subtracting the force of gravity from the applied force:
Normal force = Applied force - Force of gravity
Normal force = 450 N - 980 N
Normal force = -530 N
Note: The negative sign indicates that the normal force acts in the opposite direction (upwards) to the force of gravity.
Now we can calculate the coefficient of kinetic friction using the formula mentioned earlier:
Coefficient of kinetic friction = Applied force / Normal force
Coefficient of kinetic friction = 450 N / (-530 N)
Finally, calculating the coefficient of kinetic friction:
Coefficient of kinetic friction = -0.85
Therefore, the coefficient of kinetic friction for the crate on the floor is -0.85. It is negative because the normal force is acting opposite to the applied force when the crate is moving at a constant speed.
To calculate the coefficient of kinetic friction, we need to use the formula:
Coefficient of kinetic friction (μ) = Force of friction (Ff) / Normal force (N)
In this case, we'll find the force of friction first.
The force of friction can be determined using the equation:
Force of friction (Ff) = Applied force (F) - Net force (Fn)
Since the crate is moving at a constant speed, the net force is zero. Therefore:
Force of friction (Ff) = Applied force (F)
Substituting the values into the equation:
Force of friction (Ff) = 450N
To find the normal force, we use the equation:
Normal force (N) = Mass (m) * Acceleration due to gravity (g)
Substituting the values into the equation:
Normal force (N) = 100kg * 9.81m/s²
Normal force (N) = 981N
Now we have both the force of friction (Ff) and the normal force (N). Plugging these values into the formula for the coefficient of kinetic friction:
Coefficient of kinetic friction (μ) = Force of friction (Ff) / Normal force (N)
Coefficient of kinetic friction (μ) = 450N / 981N
Coefficient of kinetic friction (μ) ≈ 0.459
Therefore, the coefficient of kinetic friction for the crate on the floor is approximately 0.459.