A pully has two weights either side one 40kg and m kg.The 40 kg is heavier.Find m and tension in terms a and g

Question

g= gravity 9.8m/s^2

Please show workings.

Answer 1

The net force on the system is the weight of the bigger weight minus the smaller: 40g - mg, which is equal to the total mass times the acceleration: (40 + m)a

40g - mg = 40a + ma

40g - 40a = ma + mg

40(g-a) = m(a+g)

m= 40(g-a)/(a+g)

Consider only the larger block.  The two forces acting on it are the weight downward and the tension upward.  Since it is accelerating down, 40g - T = ma

T = 40g - ma

T = 40g - 40a(g-a)/(a+g)

T = 40(g - a(g-a)/(a+g))