Freight Car

Goal:

Be able to solve K&K  3.10 :

An empty freight car of mass M starts from rest under an applied force F. At the same time, sand begins to run into the car at steady rate b from a hopper at rest along the track.

Find the speed when a mass of sand, m, has been transferred. (Hint: There is a way to do this problem in one or two lines.)

- K&K pg. 148

Basic Premise of simulation:

We have a cart that is at rest and empty at time t = 0. Also at time t = 0, Domo-kun begins pushing the cart with a constant force, and a magical sand cloud decides to hinder Domo-kun's progress by allowing sand to fall into the cart at a constant rate. The magical sand cloud always hovers directly above the cart, no matter what speed the rapidly filling cart is moving. Once sand hits the cart, it moves with the cart.

Because this is a problem in the text, it has a textbook solution that we can find by solving Newton's second law. But also, our simulation solves the equation of motion to find v(t) by a numerical algorithm. On the graph of v(t), you will see the textbook solution as a solid blue curve, and the numerical solution as a set of discrete black points. Hopefully the points lie on the curve!