The equation µ = tan θ is derived from the balance of forces acting on a block placed on an inclined wooden plank. When the plank is lifted, the frictional force (Ff) equals the component of the gravitational force acting parallel to the incline, expressed as Ff = -mgsinθ. This leads to the conclusion that the static friction coefficient (µ) is equal to the tangent of the angle of inclination (θ), as shown in the equation µ = (-mgsinθ) / (-mgcosθ). The block remains stationary, indicating that the frictional force counteracts the gravitational component along the incline.
PREREQUISITESStudents studying physics, particularly those focusing on mechanics and friction, as well as educators seeking to clarify concepts related to forces on inclined planes.
Yes, the block is assumed not to move, and so the frictional force must balance the component of the weight of the block parallel to the plank.1010 said:Where i am confused is why Ff = -mgsinθ. Is it because the block has an acceleration of zero when falling down the plank?