B ALLOON P OWERED C ARS Linear Equations/Scatter Plots/Unit Rates

B ALLOON C ARS : Video: Bugatti Veyron top speed (Nat Geo)(Nat Geo) Write down the numbers/metrics of the car’s run at it’s top speed and discuss. What are some of the items necessary to make the car go that fast?

B ALLOON C ARS : In your groups, you’ll have six (6) minutes to review your research homework on balloon powered cars and come up with your top three things that will make your balloon car successful. Be prepared to share your ideas at the end of the time period.

B ALLOON C ARS : What are some of the design considerations to make your car successful?

B ALLOON C ARS : Now, take 2 minutes in your same groups and come up with a list of items that your car will actually need to work. These will be items that will be necessary to make the car work properly.

B ALLOON C ARS : We’re going to form racing teams of 2 – 3 people. You’ll need to do the following once you’ve created your team: Team Name Team Color Number for your race car Pick a name for your car Write your team members’ name on the project packet and pick a Team Captain. That person will be responsible for making sure the project build goes successfully.

B ALLOON C ARS : Project build requirements: The car must go a minimum of 10 feet. The car must be made of recycled and/or repurposed materials. No kits allowed. The car must be only powered by one deflating balloon.

B ALLOON C ARS : The car will be raced in two separate events: Day One: RACE ‘A’: The quickest time in 10 feet (measured in seconds) Day Two: RACE ‘B’: The car that goes the furthest total distance (measured in feet and inches)

B ALLOON C ARS : HOMEWORK #1 Record your time for 10 feet for your team during Race ‘A’ HOMEWORK TONIGHT: Calculate the speed (or velocity) of the car in meters per second (or m/s). Take the distance the car travelled (in feet) and divide by the time it took for it to travel that distance (time is in seconds). This will give you feet per second (or ft/s). Then take the feet from this last calculation and divide by feet for conversion to meters. This will give you meters per second (m/s)

B ALLOON C ARS : HOMEWORK #2 ( EXTENSION ) Record your total distance from Race ‘B’. Count the tiles from the starting line straight down the middle of the “track” and then the number of tiles the car went off track (if it did at all). HOMEWORK TONIGHT: Using the Pythagorean Theorem, calculate the estimated straight-line distance of your car’s total distance run from Race ‘B’. Start Number of tiles (straight) Number of tiles to the side

B ALLOON C ARS : Now we’ll weigh the cars. Each team will come up and weigh the cars in grams. Convert the weight (mass) from grams to kilograms. Write down your car’s mass (weight) in kilograms in your packet.

B ALLOON C ARS : Now we’ve got to find the power to weight ratio for your car. To do this, we’ll need to calculate the horsepower for your car. In a nutshell, horsepower is a unit of power that is used to describe the equivalent power output of a machine to that of a draft horse. First used by James Watt to help him sell his newly designed steam engines so that he could show his customers the equivalent power output of his steam engine to that of what a draft horse could do.

B ALLOON C ARS The distance we found is in feet. To do this, we must use metric measurements. The conversion from feet to meters is: 1 foot = meters So to find the distance, multiply the distance in feet by to find the distance in meters * = meters

B ALLOON C ARS : We will be finding the power to weight ratio of Mr. Schmidt’s car Schandler. The car weighed.032 kilograms and it traveled 20.5 ft in 5.0 seconds.

B ALLOON C ARS : We’ll use the equation: P = F · v P = Power (in Joules/second) F = Force (in Newtons) v = velocity (in meters/second) To find the power, we need the force and velocity. To find the force, we need mass and acceleration. To find acceleration, we need time and distance.

B ALLOON C ARS : The first piece of data we need to find power is velocity, better known as a rate. D = r * t Which is the same as: D = v * t = v * = v This means the velocity is m/s

B ALLOON C ARS : We need to find the estimated acceleration of your car. We’ll do this from your best time and velocity numbers. You’ll need: Time it took for your car to travel that distance (in seconds) Velocity of your car traveled (in m/s)

B ALLOON C ARS :

B ALLOON C ARS So what does this mean? The acceleration of Mr. Schmidt’s car is m/s 2

B ALLOON C ARS : Second, we’re going to need to calculate the Force your car exerted when it was on it’s run. To do this, we’ll need to use the acceleration number from the last equation and multiply it by the mass of the car (weight – in kilograms).

B ALLOON C ARS : We’ll use the equation: F = m · a F = Force (in Newtons) m = mass (in kilograms) a = acceleration (in meters per second squared) We are solving for ‘F’ so with your other data, plug in your numbers and solve the equation.

B ALLOON C ARS : So what does this mean? The force Mr. Schmidt’s car exerts is N

B ALLOON C ARS : Third, we now have to use the number we solved for Force to find the Power output of the car. This will be the unit of measure that we’ll need to convert into horsepower. We’ll be using the number you got for “Force” for this equation.

B ALLOON C ARS : We’ll use the equation: P = F · v P = Power (in Joules/second) F = Force (in Newtons) v = velocity (in meters/second) We are solving for ‘P’ so use the data that we found for the velocity of the car muliplied against the number you found for the ‘Force’ of the car.

B ALLOON C ARS : P = F * v P = * P = This means the power of Mr. Schmidt’s car is J/s

B ALLOON C ARS : Next, we need to covert the Power unit from Joules per second (J/s) into horsepower (hp). To do this, we’ll need to multiply your ‘P’ number by a conversion constant. P · = the amount of equivalent horsepower your car had to move that distance in that time based on the weight of the car * = hp

B ALLOON C ARS : Lastly, we need to calculate the horsepower to weight ratio. For this, we’ll need to take your horsepower rating and divide it by the weight of the car in kilograms. This will give a unit rate of horsepower per kilogram. horsepower of car ÷ car mass (kilograms) = hp/kg /.032 = hp/kg

B ALLOON C ARS : Now we can plot the horsepower to weight ratio against some known factors: The Bugatti Veyron that we studied at the beginning of this unit weighs 1,888 kg and had 1,001 horsepower. It’s horsepower to weight ratio is: 0.53 hp/kg A Volkswagon Beetle (2012) has a rating of 170 horsepower and weighs 1,394 kg. It’s hp to weight ratio is: 0.12 hp/kg The Bugatti is nearly 5 times more powerful per kilogram than the VW bug!

B ALLOON C ARS : Now calculate Ms Jilek’s car’s power to weight ratio: Ms. Jilek’s car traveled 53 feet in 19 seconds and it weighed 30 grams.

B ALLOON C ARS : Graphing the race: Let’s plot the class’ horsepower to weight ratios against the furthest distance the car went. You’ll need your car’s horsepower to weight ratio Also the linear distance that you calculated using the Pythagorean Theorem If we’re going to graph this, which would be the depended vs. the independent variable?

B ALLOON C ARS : G RAPHING THE R ESULTS

B ALLOON C ARS : Questions: 1. What correlation did we see? Could we make a line of best fit that made sense? 2. What is the equation of the line? 3. What does it mean if the car is above the line? 4. What does it mean if the car is below the line? 5. What about the outliers? Can they tell us anything about the results? 6. What about those cars that went far but on less horsepower? 7. Using the equation of the line. What would be the expected distance if we took the highest performing car and gave it the horsepower of the most powerful car?