A force of 300 N is sufficient to keep a 100 kg crate moving at a constant speed across a wooden floor. What is the coefficient of sliding floor?
The vertical force on the floor is M*g = 980 N
Uk*980 = 300 (since there is no acceleration)
Uk = 300/980 = 0.306
is the kinetic friction coefficient
thank you!
To find the coefficient of sliding friction between the crate and the wooden floor, we can use the equation:
\( \text{Friction force} = \text{Coefficient of sliding friction} \times \text{Normal force} \)
Since the crate is moving at a constant speed, we know that the applied force is equal to the friction force.
Given:
Force applied (F) = 300 N
Mass of the crate (m) = 100 kg
Normal force (N) = mass × gravity
Gravity (g) = 9.8 m/s^2
First, we calculate the normal force:
N = m × g
N = 100 kg × 9.8 m/s^2
N = 980 N
Now, we can substitute the values into the equation:
300 N = coefficient of sliding friction × 980 N
Simplifying the equation:
\( \text{coefficient of sliding friction} = \frac{{300 \, \text{N}}}{{980 \, \text{N}}} \)
Calculating the coefficient of sliding friction:
\( \text{coefficient of sliding friction} \approx 0.31 \)
Therefore, the coefficient of sliding friction between the crate and the wooden floor is approximately 0.31.
To find the coefficient of sliding friction, we need to use the formula:
frictional force = coefficient of sliding friction * normal force
In this scenario, the force of 300 N acts as the frictional force. The normal force can be calculated by multiplying the mass (100 kg) by the acceleration due to gravity (9.8 m/s²):
normal force = mass * acceleration due to gravity
normal force = 100 kg * 9.8 m/s² = 980 N
Now, to find the coefficient of sliding friction, we rearrange the formula:
coefficient of sliding friction = frictional force / normal force
coefficient of sliding friction = 300 N / 980 N
coefficient of sliding friction ≈ 0.306
Therefore, the coefficient of sliding friction for the wooden floor is approximately 0.306.