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## 24 February 2009

### Rainwater in a cart – why does the cart slow down?

A multiple choice question on, I think, the 1998 AP B exam, asks about rainwater falling into a moving cart. If the rain falls vertically, does the cart speed up, slow down, or maintain constant speed? And is that because of conservation of momentum or energy? (Note that we're not considering a donkey-pulled cart, just a freely-rolling cart.)

The answer is that the cart slows down due to conservation of momentum. Mechanical energy is not conserved in this situation because much of the kinetic energy of the water dissipates as thermal energy upon splashing in the cart. And since momentum is conserved, the additional mass added by the rainwater causes the cart’s speed to drop in order to maintain the overall mass×velocity.

My students often miss the question on first pass. They’re not really sure what’s conserved and why. “Conservation of energy” is so ingrained in their consciousness – both from a physics and an environmental standpoint – that they nearly automatically choose an answer with the magic phrase.

I asked this question on my first trimester exam back in November. Anyone who missed the question had to write a test correction. Problem was, a lot of folks still made poor arguments. Some thought that energy was conserved. Some thought the cart would speed up because of the water’s initial speed – they didn’t separate vertical from horizontal momentum. I knew many of these folks were ripe for making the same mistake again.

I’m not averse to hammering an idea over and over. That’s the main idea of the “Less is More” teaching philosophy – you don’t have to assign that much work, but you must hold students thoroughly accountable for understanding everything that is assigned. So, I told the class to expect a quiz based on this question. Below is the quiz I assigned...

1. An open cart on a level surface is rolling without frictional loss through a vertical downpour of rain. As the cart rolls, an appreciable amount of rainwater accumulates in the cart. Thus, the cart and water can be treated as if they are colliding.

(a) Which of the following is conserved in this collision? Circle all that apply.

Kinetic energy
momentum
velocity
acceleration

(b) What is the horizontal velocity of the rainwater before it lands in the cart?

(c) What will happen to the speed of the cart? Explain in one or two sentences.

GCJ

(Top photo from donchesnut.com.)

#### 1 comment:

1. I know this problem well and understand it well. What I have a very hard time picturing is if the water is then horizontally removed from the cart. Does the conservation of momentum require that the velocity of the cart would increase? I just can't picture this...