Problem $3$

A person is applying a horizontal pushing force on a train such that the whole train has a constant acceleration $0\mathrm{.}20\frac{m}{s^{{?}^{{?}^{?}}}}2$ to the right. The train is composed of two carts connected by a solid bar. The masses of cart A is $150kg$ and cart B is $100kg,$ and the mass of the connecting bar is $60kg.$ Assume that the friction forces are negligible.

$(1)$ Determine the force that the person is applying on cart A

$(2)$ Determine the force that the bar exerts on cart B

$(3)$ Determine the force that cart A exerts on the bar