By Sam Wopperer

I saw this video
a few months ago, and it made me think back to when I played these carnival
side games, though I was never as successful as this guy.

http://www.cbsnews.com/8301-18563_162-57500152/detroit-mans-life-is-stuffed-with-carnival-game-prizes-thanks-to-talent/

If you’ve ever
been to a carnival or amusement park, you’ve probably noticed hundreds of these
side games along the paths. For me, they use to be huge sinkholes for my time
and money. Well, not anymore. Armed with the physics we’ve learned so far, you
can figure out how to beat the odds, win the big prizes, and impress your
friends (and understanding the different physics concepts behind each game is
good review for the final). So, step right up, and give it a shot.

***Note: There
are few actual calculations here. I mainly just used physics equations and the
theory behind them to model how to most effectively play these games. When you
next go to an amusement park, you probably won’t calculate the exact velocity
or trajectory needed to throw a ball or ring in order to win the game, but I
think as long as you can understand the physics behind the games, you’ll
greatly increase your chances of winning. Also, you should never cheat, but in
the name of winning big, fluffy stuffed animals, it’s okay to bend the rules a
little bit here.

Game 1: Basket
toss

Objective: Throw
the ball into the basket

Sounds pretty
easy right? Well, if you’ve tried this one before, you’ll know it’s not quite
that simple, so here’s the trick. Toss the ball along the sides of the basket.

The physics
behind it: When I was thinking about this, I thought of conservation of momentum
and conservation of energy. When you toss the ball, it has a momentum equal to
p (p=mv=Ft). When the ball hits the backboard, the basket really doesn’t move,
so the only way momentum can be conserved is if the balls retains its initial
velocity, but in the opposite direction. (This isn’t exactly the case due to
air resistance, but the work of this is extremely small and doesn’t change the
final velocity that drastically.) By retaining its initial velocity in the
x-direction, the ball will go into the basket, hit the back wall, and then come
out of the basket at the same speed, so you can’t just toss the ball into the
basket. So, when you throw your ball, aim along the inside edges of the basket.
Upon hitting the inside edge, the y-component of the velocity will be converted
into an inward component (see diagram below). This will help direct the ball
towards a more angled collision with the back wall as opposed to the head on
collision it would have experienced if the ball had just been tossed straight
in. Additionally, the increased contact between the ball and the basket
increases the work friction does on the ball and acts to reduce its velocity.
This will reduce the final velocity of the ball and help it stay in the basket.

You can draw
tangent lines along the curvature of the basket, which illustrate the new
direction the ball travels in as each infinitesimally small collision between
the ball and basket take place.

Game 2: Test
your strength

Objective: Hit
the detector with enough force to ring the bell

Well, this game
isn’t so difficult if you hang out at the gym all day. But even if you don’t do
that, you’re in luck. There’s a secret to this game too. If you increase the
velocity with which you spin the hammer, make sure you hit the detector exactly
head on, and hold the hammer at the very end, you’ll be ringing the bell and
winning prizes in no time.

The physics
behind it: When I was thinking about this game, I thought of how can I maximize
the force being imparted onto the detector, and I thought of three ways to do
this. First off, use what we know about torque (t=Frsin(theta)) to get the most
out of your swing. Hold onto the hammer at the very end. This will increase the
radius term in the torque equation. Additionally, the angle that you must hit
the detector must be as close to 180 as possible. This will allow all of your force
to be imparted unto the detector and will prevent any component of the force
being applied to something else (see diagram below). You can also increase the
momentum of your hammer by increasing the velocity with which you move the hammer.
v_{final}=sqrt(2ad) (from kinematics where v_{initial}=0), and
by increasing the distance term by moving the hammer outward and then over your
head, you generate a larger arc than you would have otherwise by just lifting
the hammer straight over your head and then straight down onto the target.

Game 3: Ring
toss

Objective: Toss
a ring on the bottle

This is probably
the most difficult of the three games I’ve analyzed. From what I can think of,
you must toss the ring along a row of bottles with more x-velocity than
y-velocity, so the ring sort of skims over the row of bottles. Additionally,
you must toss the ring in a way so that it is slightly angled away from the
tops of the bottles (see diagrams below).

The physics
behind it: When you first toss the ring, the force of gravity will act to pull
the ring down onto a bottle. However, if you can toss the ring horizontally,
its chance of landing on a bottle in the row is increased because if it misses
one bottle, it may hit any of the ones after it in line. Tossing the ring just
straight up in the air reduces the odds of landing it on a bottle because the
area of the ring can only encircle one bottle top (see diagram below).
Additionally, if the ring is tossed at an angle slightly away from the bottle
top, when it finally does fall onto a bottle, the ring will lasso the bottle
top and stick on the bottle top. This is more easily seen in the diagram below.