Calculating Potential Performance How to use math and physics to inform your mousetrap car design.

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Presentation transcript:

Calculating Potential Performance How to use math and physics to inform your mousetrap car design

Engineering Calculations Math and Physics are the backbone of mechanical engineering Doing calculations before hand can; Inform design decisions Help to optimize parameters Save time and money during prototyping

Alignment Short-distance Speed Car 1. tan(θ) = 5m / 5m 2. θ = arctan (5/5) 3. θ = arctan(1) 4. θ = 45 ° Long-Distance Endurance Car 1. tan(θ) = 5m / 100m 2. θ = arctan (5/100) 3. θ = arctan(0.05) 4. θ = 2.86 ° θ θ

String Length String for a Car w/ Goal of 5m 1. Pulling Distance = Length of String x r wheel / r axle 2. 5m = Length of String x 0.025m / m 3. 5m = Length of String x /5 = Length of String 5. 1m = Length of String String for a Car w/ Goal of 100m 1. Pulling Distance = Length of String x r wheel / r axle m = Length of String x 0.025m / 0.005m m = Length of String x /5 = Length of String 5. 20m = Length of String 1.Pulling Distance = Number of Turns x 2Πr wheel 2.Number of Turns = Length of String / 2Πr axle 3.Pulling Distance = Length of String x r wheel / r axle Note If you increase the wheel size to 10 cm (0.1m); 1.Pulling Distance = Length of String x r wheel / r axle 2.100m = Length of String x 0.1m / 0.005m 3.100m = Length of String x /20 = Length of String 5.5m = Length of String So, the larger the wheels, the shorter the string required!

Wheel Radius 1. x f = x o + v o t + ½ at m = ½ a (2) = 2 a 4. 5/2 = a = a 1. a = αr wheel 2. a / r wheel = α So, angular acceleration can be increased or decreased according to the size of your wheel; a / Large r wheel = Small α a / Small r wheel = Large α Note Think about it second by second; 0  2.5 m/s  5 m/s 0  1.25 m  5 m

Potential and Kinetic Energy 1. U = ½ k θ 2 2. U = ½ (3.5) (Π) 2 3. U = 17.3 J The amount of Kinetic Energy (K) that an object is capable of exerting is the same as the amount of Potential Energy (U) stored in that object. So if all of the mousetrap’s U is converted into K, K = 17.3 J

Inertia K = ½ I ω J x 2 = I ω = I ω / I = ω 2 √(34.6 / I) = ω So, the lower your wheel’s inertia, the higher its angular velocity. √(34.6 / Low I) = High ω √(34.6 / High I) = Low ω