MAT136H1 Lecture Notes - Lecture 2: Density, Equilibrium Point

• School: UTSG
• Department: Mathematics
• Course: MAT136H1
• Professor: Paul Milgram

Document Summary

Find centre of mass of a bar of non-uniform density, (x), for x [a, b] o a b x x = ?cm. Note: if density were uniform, ie. (x) = then mass = density * distance. [kg] [kg/m] * [m] and centre of mass c. m. : a+(b-a)/2 x = (b- a)/n m1 x. Assume constant density of (xk) for kth slice, such that mk (xk) x . What are we trying to do? m. For first 2 slices (treat as point mass) d1 d2 m1 x1 m2 x2 x1. Using (archimedes) law of levers equilibrium point x = x12 (c. m. for m1, m2) define for m1d1 = m2d2 m1(x12 - x1) = m2(x2 - x12) m1x12 - m1x1 = m2x2 - m2x12 x12= m1 x1+m2 x2 m1+m2. Now find equilibrium point for first 3 masses: Treat m1 + m2 as one mass m12 = m1 + m2 at mk xk.