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Homework Statement
A dump truck loaded with rock has a coefficient of static friction of 0.4, and a coefficient of kinetic friction of 0.2 between the rock and steel tray. If the truck tilts its bed to 25°, calculate the coefficient of static friction on the load. Hence calculate the angle at which the load begins to slide. The mass of the rock in the truck is 77110kg.
Homework Equations
Ff = mgsinθ
FN = mgcosθ
Ff = μFN
The Attempt at a Solution
Ff = μFN
so
mgsinθ = μmgcosθ
Cancelling mg from both sides gives
sinθ = μcosθ
μ = (sinθ)/(cosθ)
μ = tanθ
μ = tan 25°
μ = 0.466
How can this be? How can μ on an inclined plane be greater than μ between the two flat surfaces? Is this saying that the coefficient of friction on the inclined plane is 0.466 x μ given in the question? Which would give a value of μ=0.1864 for the load on the inclined plane?
Taking this value for μ as 0.466 and using it to determine the angle at which the load begins to slide gives us:
The load will begin to slide when tanθ > 0.466
But this gives θ > 25°
So the load will begin to slide when the tray is tilted to more than 25°?
I have been through every method I can think of and every time I keep coming back to μ = 0.466 and θ > 25° but I am sure that these values are incorrect.