Question

two blocks of masses 1kg and 2kg are connected by a metal wire going over a smooth pulley . the breaking stress of the metal is 2 x 10^9 Nm-^2 .what should be the minimum radius of wire used if it is not to break?

Answer 1

m1 a = T - m1 g     where T is the tension in the wire

m2 a = m2 g - T       assuming m2 > m1

(m1 + m2) a = (m2 - m1) g    adding equations

a = (m2 - m1) g / (m1 + m2) = g / 3     with m2 = 2 and m1 = 1

T / A = stress on wire

T = (m1 a + m1 g  = g / 3 +  g = 4 m1  g / 3   = 4 g / 3   from the first equation

S(tress) =T / A = T / (pi * r^2)     and r^2 = T / (pi * S) = 4 g / (3 * pi * S)

r^2 = 4 * 9.8 / (2 * 10E9 * 3 * pi) = 2.08 * 10E-9

r = 4.56 * 10E-5 m = .0456 mm