Consider a system consisting of a smooth pulley with two masses suspended from e

Question

Consider a system consisting of a smooth pulley with two masses suspended from each end. Find a and b.

Problem 1: Consider a system consisting of a smooth pulley with two masses (m and m2, withm > m2) suspended from a light string at each end. (See Fig. 1 below.) Find: (a) an expression for the acceleration of mass 1; (b) an expression for the acceleration of mass 2; and (c) an expression for the magnitude of the tension Fr of the string. All forces to be considered are shown in the figure. +Z F. m.2 g2

Explanation / Answer

let the acceleration of m1 is 'a1' (to down) and acceleration of m2 is 'a2' (to up).

then equation of m1

Fg1 - Ft = m1a1

m1g - Ft = m1a1

a1 = g - Ft/m1 ...   (1)

now equation for m2

Ft - Fg2 = m2a2

Ft - m2g = m2a2

a2 = (Ft/m2) - g

both acceleration should be equal

g - Ft/m1 = (Ft/m2) - g

2g = Ft/m1 + Ft/m2

2g = Ft*(m1 + m2)/m1*m2

Ft = 2g*m1*m2/(m1 + m2)

now a1 = g - Ft/m1 = g - 2g*m2/(m1 + m2) = g*(m1 - m2)/(m1 + m2)

a2 = (Ft/m2) - g = 2g*m1/(m1 + m2) - g = g*(m1 - m2)/(m1 + m2)

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