Question

Two masses 8kg and 4kg are connected by a string over a frictionless pulley.Then the acceleration if the system is

Answer 1

Equation for mass m1:

(1)  m1 g - T = m1 a             ( where T stays for a tension in the string )

For mass m2:

(2)  T - m2 g = m2 a

Adding those two equations:

m1 g - m2 g = m1 a + m2 a

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

a = ( m1 - m2 ) g / ( m1 + m2 ) = ( 8 kg - 4 kg ) g / ( 8 kg + 4 kg ) = 4 g / 12 = g / 3

a = 3.27 m/s²

T - 4 g = 4 g / 3  ( from the second equation )

T = 16 g / 3 = 16 · 9.8 / 3 = 52.27 N

Answer: The acceleration is 3.27 m/s² and tension in the string is 52.27 N.