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.
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. vfinal=sqrt(2ad) (from kinematics where vinitial=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.