Afreight car of mass m contains a mass of sand m. at t = 0 a constant horizontal force f is applied in the direction of rolling and at the same time a port in the bottom is opened to let the sand flow out at constant rate dm/dt. find the speed of the freight car when all the sand is gone. assume the freight car is at rest at t = 0.

Amount of linear movement

Explanation:

Our system is defined by the rate of change in mass that

leaves the car , this happens during a time interval

, in addition to freight car and sand at time t.

In this way we need to define the two states:

State 1,

consider and V.

State 2,

consider

In this state is the mass of sand output, which

is composed of

In this way we define the Linear movement in x, like this:

In this way we proceed to obtain the Force

Since the mass of the second term becomes 0, the same term is eliminated, thus,

the force on the thing and the distance the force moves the thing