A 73.0 kg box slides down a 30.0� ramp with
an acceleration of 3.60 m/s2.
Find ìk between the box and the ramp.
The acceleration of gravity is 9.81 m/s2 .
To find the coefficient of kinetic friction (μk) between the box and the ramp, we can use the following equation:
μk = tan(θ) - (a/g)
Where:
θ is the angle of the ramp,
a is the acceleration of the box, and
g is the acceleration due to gravity.
Given:
The weight of the box (mg) = 73.0 kg * 9.81 m/s^2 = 715.13 N
The acceleration of the box (a) = 3.60 m/s^2
The angle of the ramp (θ) = 30.0 degrees
The acceleration due to gravity (g) = 9.81 m/s^2
To find the coefficient of kinetic friction (μk), we need to calculate the tangent of the angle of the ramp (θ):
tan(θ) = tan(30.0 degrees) = 0.5774
Next, we substitute the known values into the equation:
μk = 0.5774 - (3.60 m/s^2 / 9.81 m/s^2)
Now, we can solve for μk:
μk = 0.5774 - 0.3669
μk = 0.2105
Therefore, the coefficient of kinetic friction (μk) between the box and the ramp is 0.2105.