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Units, Constants and Useful Formulas

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Last modified: January 26, 2018

Inclined Plane -------------- Friction -------- Vertical force = mg Normal force, FN = mgcosθ Parallel to slope force = mgsinθ frictional force = Ff = μFN where μ is the coefficient of friction. mass will slide if mgsinθ > Ff with acceleration = gsinθ - Ff/m Ex: A box slides downwards at a constant velocity on an inclined surface that has a coefficient of friction μ = .58 The angle of the incline, in degrees, is calculated as follows: Ff = μmgcosθ mgsinθ ~ μmgcosθ μ = tanθ θ = 30 degrees With frictionless pulley: m2g - T = m2a2 T - m1gsinθ - μkm1gcosθ = m1a1 For simplicity consider μk = 0 Now a1 = a2 = a. Therefore, if we substitute for T we get: T = m2g - m2a Therefore, m2g - m2a - m1gsinθ = m1a Thus, a = (m2g - m1gsinθ)/(m1 + m2) Note: if θ = 0 the equation reduces to: a = m2g/(m1 + m2) Which the same as the table case. T m1 --->------- ------------ O //////////| | ^ T | m1 F1 = T = m1a1 - μkm1g = m1a1 F2 = m2g - T = m2a2 so, m2a2 = m2g - T = m2g - m1a1 For simplicity assume μk = 0 Now a1 = a2 = a. Therefore, a = m2g/(m1 + m2) and T = m1a = m1m2g/(m1 + m2)