# The rolling cart problem

Here’s an interesting physics/unicycling problem discovered at our weekly
unicycle club meeting. A flat bed cart with 4 hard wheels was sitting out in the
gym we practice in. It immediately presented a challenge. Is it possible to ride
on top of the cart? Sounds easy at first, but it presents a good physics
problem. Think about it. Is it possible to mount the unicycle while on top of
the cart? The cart had very low friction wheels. I figured out how to mount on
the cart…can you?

Brett “Taking two physics classes now” Bymaster

PS Mounting on the ground and hoping on top of the cart is cheating!

Re: The rolling cart problem

>PS Mounting on the ground and hoping on top of the cart is cheating!

Would it really be cheating? Landing the jump without causing the cart to scoot
out from underneath you probably wouldn’t be the easiest way to mount up there.
Sounds like a good way to end up flat on your back.

john_childs

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Re: The Rolling Cart Problem

> Newton discovered F=ma many years ago which applies to the situation you
> describe. Since the masses of the objects are constants, the only
> variable you can manipulate is the “a” (acceleration) term to keep F

That’s exactly right. The problem is actually ver similar to riding a two
wheeled unicycle. You can model the rolling cart as frictionless for a first
order understanding. When you pedal forward, the cart will move backwards, while
you will stay stationary according to non-moving observer. If you pedal
backwards, the cart goes foward etc. So your natural unicycle reactions get all
screwed up.

> 1) Design of the casters and whether they all swiveled.
The front two swivel

> 2) Number and type of trials you attempted before achieving your goal.
Described by the following eqn: Attempts = lim 1/x x->0

> 3) What actions are required following a mount.
I couldn’t figure that out. I just hopped. With a sufficiently frictional
cart, it should be possible to propel the cart…hmm

> 4) Your thoughts on analysis.
I think I used “fuzzy” logic. For those of you who know me, that isn’t
surprising.

To mount on the cart, you have to get the cart rolling foward first. Once the
cart is rolling forward, you simply step on the cart and mount normally.
Assuming the cart has no friction, initially mounting feels perfectly normal
since you are in a non-accelerating inertial frame. When you jump forward to
free mount, the cart reacts with the opposite force, and stops rolling. If you
get the speed just right, the cart will come to a dead stop as soon as you
mount. Then you can hop or try to ride or whatever. And that’s the answer to the
problem (or at least that’s my answer).

Re: The rolling cart problem

Jump mount.

Brett Bymaster <bymaster@ecn.purdue.edu> wrote in message
news:200001271545.KAA03146@shay.ecn.purdue.edu
>
> Here’s an interesting physics/unicycling problem discovered at our weekly
> unicycle club meeting. A flat bed cart with 4 hard wheels was sitting out in
> the gym we practice in. It immediately presented a challenge. Is it possible
> to ride on top of the cart? Sounds easy at first, but it presents a good
> physics problem. Think about it. Is it possible to mount the unicycle while on
> top of the cart? The cart had very low friction wheels. I figured out how to
> mount on the cart…can you?
>
> Brett “Taking two physics classes now” Bymaster
>
> PS Mounting on the ground and hoping on top of the cart is cheating!

Re: The rolling cart problem

I would never do this - I have too much common sense. But if I were forced to
for some sadistic reason, I would certainly mount from the side - similar to
getting on a horse. That way center of gravity stays relatively stationary and
under control.

Just to note, however, that I was mounting a Coker in this manner last night
when I craterred the rim. Thankfully a very good friend was able to true the
wheel again. Thanks Steve. Sorry again AJ.

Bb Brian Berlin Austin One Wheelers

PS It must’ve not been a good night for me because following this, I got back on
my 24" and ended up losing controll and actually crashed (first time).
Somehow I ended up falling with the small of my back landing perpendicular on
my left (or right?) pedal. Ouch! Well I REALLY warped my rim and broke a
spoke. OK OK…I know when to quit for the night. Bb

Re: The rolling cart problem

I have balanced for short periods of time on top of flatbed carts. In order to
stay on top it is important to avoid drastic changes in the direction that the
wheel is moving (avoid every kind of of acceleration acceleration). Getting on
the unicycle is the most challenging part, I usually mount using a combination
of a free mount and a jump mount. Once I am on the unicycle, all I can do is hop
a few times; and then dismount before I fall down (in a drastic way).

Javier

Brett Bymaster wrote:

> Here’s an interesting physics/unicycling problem discovered at our weekly
> unicycle club meeting. A flat bed cart with 4 hard wheels was sitting out in
> the gym we practice in. It immediately presented a challenge. Is it possible
> to ride on top of the cart? Sounds easy at first, but it presents a good
> physics problem. Think about it. Is it possible to mount the unicycle while on
> top of the cart? The cart had very low friction wheels. I figured out how to
> mount on the cart…can you?
>
> Brett “Taking two physics classes now” Bymaster
>
> PS Mounting on the ground and hoping on top of the cart is cheating!
>

********************************************
Javier Ruiz, PE
javruiz@caribe.net

Re: The Rolling Cart Problem

Brett Bymaster wrote:
>
> To mount on the cart, you have to get the cart rolling foward first. Once the
> cart is rolling forward, you simply step on the cart and mount normally.
> Assuming the cart has no friction, initially mounting feels perfectly normal
> since you are in a non-accelerating inertial frame. When you jump forward to
> free mount, the cart reacts with the opposite force, and stops rolling. If you
> get the speed just right, the cart will come to a dead stop as soon as you
> mount. Then you can hop or try to ride or whatever. And that’s the answer to
> the problem (or at least that’s my answer).

Or, stand on the stationary cart with your unicycle in front of you and rest the
seat on your stomach (like the trick). Then hold the wheel with one hand and
lift your feet up onto the pedals. Next go into seat in front and then push the
seat in so you’re sitting on it. Now stillstand until you feel like falling.

## My way of doing it just doesn’t sound like it was as much fun as Brett’s.

``````    ___________ =========================================== ___ /_/ / / / /
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Re: The rolling cart problem

Brett,

``````    Newton discovered F=ma many years ago which applies to the situation you
describe. Since the masses of the objects are constants, the only
variable you can manipulate is the "a" (acceleration) term to keep F
(force) to a minimum. The F term would of course be responsible for
moving the cart in an undesirable way. One might guess a mounting style
and position relative to the cart reducing the potential for
acceleration in two directions would yield a successful cart mount. Your
description of the problem provides much less information than would
otherwise be available to a rider in visual and physical contact with
the problem variables. Perhaps you might share some additional
information like the following:
``````
1. Design of the casters and whether they all swiveled.
2. Number and type of trials you attempted before achieving your goal.
3. What actions are required following a mount.

We’re all looking forward to the answer. I certainly don’t have it!

“The Muniac”

Re: The rolling cart problem

How about flipping the cart on its back? How about immobilizing its wheels? How
about posting to the newsgroup that you’d done it–and that it was easy–when

Any of these solutions on the right track?

David Maxfield Bainbridge Island, WA

Re: The rolling cart problem

ask Kip. not me. it’s his question. BB Scott Bridgman wrote in message
<86s8qi\$phi\$1@nntp9.atl.mindspring.net>…
>Brett,
>
> Newton discovered F=ma many years ago which applies to the situation you
> describe. Since the masses of the objects are constants, the only variable you
> can manipulate is the “a” (acceleration) term to keep F (force) to a minimum.
> The F term would of course be responsible for moving the cart in an
> undesirable way. One might guess a mounting style and position relative to the
> cart reducing the potential for acceleration in two directions would yield a
> successful cart mount. Your description of the problem provides much less
> information than would otherwise be available to a rider in visual and
> physical contact with the problem variables. Perhaps you might share some
> additional information like the following:
>
>1) Design of the casters and whether they all swiveled.
>2) Number and type of trials you attempted before achieving your goal.
>3) What actions are required following a mount.