Incline angel of both the inclines =
= 36.87 o
Let tension in cord connected to mass 300 lb be T 1 and tnbsion in cord connected to 400 lb be T 2
As pulleys are massless therefore by Newtons second law on left pulley
2T 2 - T 1 = 0
So T 1 = 2T 2
Let acceleleration in block A be a A and acceleration in block B be a B .
We assume block B is going down and block A is going up.
Friction force on block A
F fA = m A g Cos
= 0.2 X 300 X 32.2 X Cos 36.87 = 1545.6 lbs
Applying Netons second law on block A
T 1 - m A g Sin - F fA = m A a A
So 2T 2 - 300 X 32.2 X Sin 36.87 - 1545.6 = 300 a A
So 2T 2 - 7341.6 = 300 a A
So T 2 - 150 a A = 3670.8 ----------------------(1)
Friction force on block B
F fB = m A g Cos
= 0.2 X 400 X 32.2 X Cos 36.87 = 2060.8 lbs
Applying Netons second law on block B
T 2 - m B g Sin + F fA = m B a B
So T 2 - 400 X 32.2 X Sin 36.87 + 2060.8 = 400 a B
So T 2 - 5667.2 = 400 a B
So T 2 - 400 a B = 5667.2 ----------------------(2)
Also as cord connected with block B will move double the distance as moved by block A
a B = 2 a A
Putting value of a B is equation (2)
T 2 - 800 a A = 5667.2 -------------------(1)
Sustracting equation (3) from (2)
650 a A = -1996,4
So a A = -3.1 ft /s 2
a B = 2a A = - 6.2 ft /s 2
Minus sign indicates that block B will move upward.
So acceleration of block B = 6.2 ft /s 2 (upward )
Putting vale of a B in equation (2)
T 2 - 400 X (-6.2) = 5667.2
So T 2 = 3187.2 lb
So acceleration of block B = 6.2 ft /s 2 (upward )
Tension is cord attached to B , T 2 = 3187.2 lb