A box slides downwards at a constant velocity on an inclined surface that has a coefficient of friction uK = .58 The angle of the incline, in degrees, is most nearly:
well, constant velocity, so weight going down = friction force
mg*sinTheta=mu*mgcosTheta
tantheta=mu
[ ì k = tan èk ]
45
To find the angle of the incline, we need to first understand the relationship between the coefficient of friction and the angle. The coefficient of kinetic friction is given by the formula:
μK = tan(θ)
where θ is the angle of the incline.
To find the angle θ, we can rearrange the formula:
θ = arctan(μK)
Now, we can substitute the given value of the coefficient of friction (μK = 0.58) into the formula:
θ = arctan(0.58)
To find the value of θ, we can use a scientific calculator or an online trigonometric calculator that has an inverse tangent function (arctan). Entering the value 0.58 into the inverse tangent function will give us the angle in radians.
Converting the radians to degrees, we get the angle of the incline:
θ ≈ 32.73 degrees
Therefore, the angle of the incline is most nearly 32.73 degrees.