The system starts at rest. A mass of 20kg (m1) is connected to a pulley of uniform mass m=5kg and radius 10cm and a mass of 30kg (m2) hangs on the other side of the pulley hanging 2m above the ledge
Find the tension of the strings
I tried to find the acceleration by finding the sum of the forces on both blocks and the sum of the torque:
F1 = T1 - m1*g = m1*a
so T1 = m1a + m1g
F2 = m2*g - T2 = m2*a
so T2 = m2*a - m2*g
sum torque = r*T2 - r*T1 = I*A^2 [because T2>T1? and A is angular acceleration]
I = 1/2*m*r^2 and A = a/r
all the values of r cancel,
T2 - T1 = 1/2*m*a
m2*a - m2*g - m1*a - m1*g = 1.2*m*a
solving for a gives
a = (m2*g - m1*g)/(1/2*m + m2 - m1)
I got 7.84 m/s^2 with the given values, and substituting into equations for T1 and T2
T1 = m1*a + m1*g
= 20*7.84 + 20*9.8
= 353N
T2 = m2*g - m2*a
= 30*9.8 - 30*7.84
= 58.8
But this makes no sense because T2 should be greater than T1? Can you please tell me where i went wrong
0 answers