Calculating kinetic energy

Law of Conservation of Energy Quick Review…. Law of Conservation of Energy Energy cannot be created or destroyed – it can only transform Kinetic Energy Energy of things in motion Potential Energy Energy of position or condition Stored energy PEgravitational = mgh

Quick Review…. To give an object kinetic energy, you have to hit it, kick it, push it, pull it, shove it, drop it, launch it, etc.

Explore… Get a stack of books, a ruler with a groove, an expo marker, a wooden ruler, a stopwatch, and 3 marbles for each group. Set-up your experiment like this duct tape loop

Design a mini-experiment… Design suggestions: Measure the start time when the marble hits the end of the ramp. (Might be a good idea to have 2 timers) Make sure to catch the marble as it falls off the edge of the table. Answer this question using a scientific method: What are the effects of the starting height of a marble on the time it takes the marble to travel 1 meter? Hint: try 2 cm and 8 cm

Do It! Conduct several trials at 2 cm and 8 cm until you are confident in your claim. Make sure to record your measurements in a data table, then plot the points to analyze.

analyze It! Now think back to the moving- cup-experiments. There we found out that a ball released at 8 cm would have 4 times as much energy as one released from 2 cm. This tells us that when a marble is moving twice as fast, it has 4 times as much energy. You results should show that when you moved 4 times as far up the ramp, the speed of the marble went twice as fast. (If it takes half the time, it is moving twice as fast, right?)

analyze It! If we repeated this experiment a bunch more times we would see that if the marble is released 3 times higher, it travels 9 times faster and if it released 4 times higher it travels 16 times faster. We call this a “squared relationship.” (22 = 4, 32 = 9, 42 = 16, etc.)

So what does this mean? What this data represents is the idea that the kinetic energy of an object depends on two things: the speed (velocity) of that object squared and the mass of that object We can write this scientific law as a math equation: KE = 1/2(mass)(velocity)2

KE= 1/2mv2 So what does this mean? We use letters to stand for measurements in Physics equations like this: m =mass of the object falling, measured in Kilograms v = speed of the object, measured in meters/second (there is a difference between speed and velocity, but for now, we will say they are the same thing) When the letters are next to each other, it means multiply them together (notice that velocity is the only measurement which is squared) Find this equation on your yellow reference page and put a little star by it.

So what does this mean? KE= 1/2mv2 If we had a graph of this data, it would look like this: Notice that the line is curved, because we have a “squared” term in the equation

Let’s do a practice problem… What is the kinetic energy of a 85.7 Kg downhill skier traveling at a velocity of 3 meters per second ? (Write down this practice problem in your notes.)

Let’s do a practice problem… What is the kinetic energy of a 85.7 Kg downhill skier traveling at a velocity of 3 meters per second ? (Write down this practice problem in your notes.) Step 1 – Draw a diagram

Let’s do a practice problem… Step 2 – Determine what you want to know What is the kinetic energy of a 85.7 Kg downhill skier traveling at a velocity of 3 meters per second ? (Write down this practice problem in your notes.)

Let’s do a practice problem… Step 3 – Write down what you already know What is the kinetic energy of a 85.7 Kg downhill skier traveling at a velocity of 3 meters per second ? (Write down this practice problem in your notes.)

Let’s do a practice problem… Step 4 – Find an equation What is the kinetic energy of a 85.7 Kg downhill skier traveling at a velocity of 3 meters per second ? (Write down this practice problem in your notes.)

Let’s do a practice problem… Step 5 – Replace the letters with numbers you already know What is the kinetic energy of a 85.7 Kg downhill skier traveling at a velocity of 3 meters per second ? (Write down this practice problem in your notes.)

Let’s do a practice problem… Step 6 – Multiply using a calculator What is the kinetic energy of a 85.7 Kg downhill skier traveling at a velocity of 3 meters per second ? (Write down this practice problem in your notes.)

Let’s do a practice problem… Step 7 – Round the answer to the accuracy of measurements What is the kinetic energy of a 85.7 Kg downhill skier traveling at a velocity of 3 meters per second ? Did you get 400 J ?

Let’s do another practice problem… What is the kinetic energy of a 5 gram bullet shot from a gun at a speed of 200 meters per second? (Write down this practice problem in your notes.) Follow all 7 steps…

Let’s do another practice problem… What is the kinetic energy of a 5 gram bullet shot from a gun at a speed of 200 meters per second? (Write down this practice problem in your notes.) Remember that you have to convert g to Kg Did you get 100 J

One last logic problem… If two identical cars are passing each other on the freeway, but one is going triple the speed of the other, how will their kinetic energies compare? (Write down this practice problem in your notes.) Write your answer as a sentence and use math to give evidence for your opinion.

One last logic problem… If two identical cars are passing each other on the freeway, but one is going triple the speed of the other, how will their kinetic energies compare? (Write down this practice problem in your notes.) The faster car will have 9 times the KE of the slower car because v2 of 3 is 9 times larger than v2 of 1