A section of a cable car system, showing three cars. They are being pulled by drag cables at 35 degrees above the horizontal. Each car weighs 2800 kg. The are all being accelerated at the same rate of 0.81 m/s/s. The problem asks for the difference between the tensions in the two cables that connect to the middle car.
The Attempt at a Solution
I started by writing the force equations in X and Y:
Fy = ma sin 35 = T sin 35 - mg
Fx = ma cos 35 = T2 cos 35 - T1 cos 35
Obviously, I don't need the Fy equation at all, since the cos 35 drops out and I have:
ma = T2- T1
Then I thought to try solving it by having the X axis along the 35 degree line of the cables. This gives me:
Fx = ma = T1 - mg sin 35 - T2
with T1 - T2 = m(a + g sin 35)
They both give very different results, and both seem reasonable to me. I have no idea which one is correct or why. If someone could help me out, I would appreciate it.