An open cart of mass \(M\) moves to the right at a constant velocity \(v_0\) along a horizontal track where friction between the track and the wheels is negligible. Sand from a stationary overhead hopper drops vertically into the cart at a constant mass flow rate \(R = \dfrac{\Delta m}{\Delta t}\). A constant horizontal force \(F\) is applied to the cart so that the cart continues to move at the constant velocity \(v_0\). In terms of \(R\) and \(v_0\), what is the magnitude of the applied force \(F\), and what is the magnitude of the horizontal force that the sand exerts on the cart?