A horizontal plane with the coefficient of friction k supports two bodies: a bar and an electric motor with a battery on a block. A thread attached to the bar is wound on the shaft of the electric motor. The distance between the bar and the electric motor is equal to l. When the motor is switched on, the bar, whose mass is twice as great as that of the other body, starts moving with a constant acceleration `w`. How soon will the bodies collide?

Explanation

From the Newton's second law in projection from:
For the bar,
`T-2kmg=(2m)w` (1)
For the motor,
`T-kmg=mw^'` (2)
Now, from the equation of kinematics in the frame of bar or motor:
`l=1/2(w+w^')t^2` (3)
From (1), (2) and (3) we get on eliminating T and `w^'`
`t=sqrt(2l//(kg+3w))`