At from the floor a mass is dropped on a inclined plane which form an angle with the horizontal. If the base of the inclined plane is long, and the coefficient of friction of the mass with the inclined plane is , what is the absolute value of the work (in Joules) done by the friction force untill the mass get to the floor?
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At drawing an FBD with x axis parallel to the surface where is falling the object we can realize that there is a normal force, gravity force and friction force; with N = c o s ( θ ) m g and therefore f = μ ⋅ c o s ( θ ) m g . We are given all these values, except θ , but we can see that the inclined plane is a right triangle, so the hypotenuse equals 1 0 [ m ] and then c o s ( θ ) = 1 0 8 = 0 , 8 , so replacing the values and using the fact that friction force opposes to the movement, we have: f = − 0 , 6 ⋅ 0 , 8 ⋅ 5 0 [ N ] = − 2 4 ⇒ W f = f ⋅ r = − 2 4 ⋅ 1 0 [ J ] = − 2 4 0 [ J ]