Physics kinetics circular motion

Question

Assume a 80kg student (A) holds onto a frictionless rope spun over a frictionless pulley with a 60kg student (B) holding the other end. If the students are allowed to move, the acceleration of student A would be what?

Answer 1

This is an application of Atwood"s machine. Let m₁ =80 kg and m₂ =60 kg and T is the tension in the rope. The equations of motion are m₁ a= m₁ g -T and T- m₂ g =m₂ a where a is the acceleration of the two masses. Add the equations to eliminate T and get m₁ g -m₂ g = (m₁ +m₂)a and solve for a to get a= g(m₁ -m₂)/(m₁ + m₂) and a= 9.8• 20/80 = 9.8/4 and a = 2.45 m/sec².