Calculating potential 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

Explore… Get a half-cup, a stack of books, a ruler with a groove, an expo marker, a wooden ruler, and 3 marbles for each group. Set-up your experiment like this duct tape loop “Start Line” mark on table

Design a mini-experiment… Design suggestions: Measure the marble height from the table straight up to the marble, NOT along the ramp. Measure the distance traveled by the cup from the starting center of the cup to the ending center of the cup. Answer this question using a scientific method: What are the effects of the starting height of a marble on the distance it will push a cup?

Do It! Conduct several trials at 3 very different heights until you are confident in your claim. Make sure to record your measurements in a data table, then analyze the AVERAGE data.

Design another mini-experiment… Design suggestions: Use the same start height, but try 1,2, and 3 marbles. Measure the distance traveled by the cup from the starting center of the cup to the ending center of the cup. Answer this question using a scientific method: What are the effects of adding more marbles rolling down the ramp on the distance it will push a cup?

Do It! Conduct several trials with 1, 2, and 3 marbles until you are confident in your claim. Make sure to record your measurements in a data table, then analyze the AVERAGE data.

Design a Third mini-experiment… Design suggestions: Pick one of your previous sets of data with the marble about ½ way up the ramp. Make these new trials at the same VERTICAL height. Add another book to change the angle. Answer this question using a scientific method: What are the effects of the ramp angle on the distance a marble will push a cup?

Do It! You only need to do 3 or 4 trials this time and just compare the data to your first mini-experiment as a control. Make sure to record your measurements in a data table, then analyze the AVERAGE data.

Summarize your outcome in a few sentences… One marble released about ½ way up the ramp pushes the marble about ½ as far as a marble released from the top of the ramp. Does your evidence agree?

Summarize your outcome in a few sentences… One marble released at the top of the ramp pushes the cup 3 times as far than when the marble is released about 1/3 of the way up the ramp. Does your evidence agree?

Summarize your outcome in a few sentences… For a given distance up the ramp, 2 marbles push the cup about twice as far as 1 marble and 3 marbles push the cup three times as far as one marble. Does your evidence agree?

Summarize your outcome in a few sentences… When you keep the VERTICAL height of the marble the same, regardless of the angle of the ramp, the marble pushes the cup about the same distance. Does your evidence agree?

So what does this mean? Scientists have done experiments like this millions of time, and it always turns out with the same relationship. In a graph, it would look like this…

So what does this mean? If we were to draw a “line of best fit” of this data, it would make a nearly perfect straight line. This is great new, it means there is a MATHEMATICAL relationship (or a law) that represents this experience.

PEgravitational = mgh So what does this mean? What this data represents is the idea that the gravitational potential energy of an object depends on two things: the height of that object above Earth’s surface and the mass of that object. We can write this scientific law as a math equation: Gravitational PE = (mass)(gravity constant)(height of object above surface) PEgravitational = mgh

PEgravitational = mgh 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 g = acceleration due to gravity (on Earth it is always 9.8 meters / sec2) h = height of the object above a surface, measured in meters When the letters are next to each other, it means multiply them together Find this equation on your yellow reference page and put a little star by it.

Doesn’t math make things easy ?! So what does this mean? PEgravitational = mgh Notice that if the mass is doubled (as in using 2 marbles instead of 1) mathematically, the energy is doubled. And if the height is doubled (as in starting the marble twice as far up the ramp) mathematically, the energy is doubled. This should coincide with what we observed during the mini-experiment, yes? Doesn’t math make things easy ?!

Let’s do a practice problem… What is the gravitational potential energy of a 0.004 Kg marble at the top of marble race tower which is 1.3 meters above the floor? (Write down this practice problem in your notes.) 0.004 Kg 1.3 m

Let’s do a practice problem… What is the gravitational potential energy of a 0.004 Kg marble at the top of marble race tower which is 1.3 meters above the floor? (Write down this practice problem in your notes.) Step 1: Draw a diagram and label it 0.004 Kg 1.3 m

Let’s do a practice problem… What is the gravitational potential energy of a 0.004 Kg marble at the top of marble race tower which is 1.3 meters above the floor? (Write down this practice problem in your notes.) Step 2: Write down what you want to know in this case, PE gravitational

Let’s do a practice problem… What is the gravitational potential energy of a 0.004 Kg marble at the top of marble race tower which is 1.3 meters above the floor? (Write down this practice problem in your notes.) Step 3: Write down what you already know (what was given in the question, or your measurements) Mass = 0.004 Kg Height = 1.3 meters g = 9.8 m/s2 (this is a constant)

Let’s do a practice problem… What is the gravitational potential energy of a 0.004 Kg marble at the top of marble race tower which is 1.3 meters above the floor? (Write down this practice problem in your notes.) Step 4: Find an equation on your reference page which contains what you know and what you want to know. Write it down. PE gravitational = mgh

Let’s do a practice problem… What is the gravitational potential energy of a 0.004 Kg marble at the top of marble race tower which is 1.3 meters above the floor? (Write down this practice problem in your notes.) Step 5: Replace the letters in the equation with the numbers and units that you know. PE gravitational = (0.004 Kg)(9.8 m/s2)(1.3m)

Let’s do a practice problem… What is the gravitational potential energy of a 0.004 Kg marble at the top of marble race tower which is 1.3 meters above the floor? (Write down this practice problem in your notes.) Step 6: Chug the numbers through your calculator PE gravitational = (0.004 Kg)(9.8 m/s2)(1.3m) PE gravitational = 0.05096 Kg m2/s2

Let’s do a practice problem… What is the gravitational potential energy of a 0.004 Kg marble at the top of marble race tower which is 1.3 meters above the floor? (Write down this practice problem in your notes.) Step 7: Round to accuracy of measurements PE gravitational = (0.004 Kg)(9.8 m/s2)(1.3m) PE gravitational = 0.05096 Kg m2/s2 = 0.051 Kg m2/s2

Which is the SI unit of energy measurement JOULES Notice those weird units? Kgm2/s2 That is equal to Joules Which is the SI unit of energy measurement A Joule is equal to the energy required to lift an apple 1 meter A light bulb uses about 100 J per second A person sprinting uses about 1,000 J /second slice of cherry pie contains about 2 million J – enough to drive a car for 20 seconds

Let’s do another practice problem… What is the gravitational potential energy of a 5.0 Kg book lying flat on the floor? (Write down this practice problem in your notes.)

Let’s do another practice problem… What is the gravitational potential energy of a 5 kg book lying flat on the floor? (Write down this practice problem in your notes.) No calculator required for this one – since the height is zero, and anything multiplied by 0 is 0, then the PE gravitational = 0 J (makes sense, since it doesn’t have the potential to fall)

Let’s do a third practice problem… What is the gravitational potential energy of a 500 gram rock which falls 0.4 Km from a tall cliff to the winding mountain road below? (Write down this practice problem in your notes.)

Let’s do a third practice problem… What is the gravitational potential energy of a 500 gram rock which falls 0.4 Km from a tall cliff to the winding mountain road below? (Write down this practice problem in your notes.) This answer requires a little “massaging” of the units before we can plug them in. Remember: *the mass must be in Kg *the height must be in m

Let’s do a third practice problem… What is the gravitational potential energy of a 500 gram rock which falls 0.4 Km from a tall cliff to the winding mountain road below? (Write down this practice problem in your notes.) Want to know: PE gravitational Know: mass = 0.5 Kg height = 400 m g = 9.8 m/s2 PEgravitational = mgh PEgravitational = (0.5 Kg)(400m)(9.8 m/s2) PEgravitational = 1,960 Kg m2/s2 = 1,960 J

Let’s do a Fourth practice problem… Aunt Jemimah raises a 1.75 Kg bottle of syrup above her head, to a total distance from the floor of 2.1 meters. How much potential energy has she given the bottle? (Write down this practice problem in your notes.)

Let’s do a fourth practice problem… Want to know: PE gravitational Know: mass = 1.75 Kg height = 2.1 m g = 9.8 m/s2 PEgravitational = mgh PEgravitational = (1.75 Kg)(2.1m)(9.8 m/s2) PEgravitational = 36.02 Kg m2/s2 = 36.02 J Aunt Jemimah raises a 1.75 Kg bottle of syrup above her head, to a total distance from the floor of 2.1 meters. How much potential energy has she given the bottle? (Write down this practice problem in your notes.)

Let’s do a theoretical problem… Compare these two potential energy situations: Player 1 hits a baseball 3 meters into the air along its trajectory to right field. Player 2 hits a baseball 6 meters into the air along its trajectory to left field. How much additional PE does player 2’s baseball have, compared to player 1’s baseball? (Write down this practice problem in your notes.)

Let’s do a theoretical problem… Compare these two potential energy situations: Player 1 hits a baseball 3 meters into the air along its trajectory to right field. Player 2 hits a baseball 6 meters into the air along its trajectory to left field. How much additional PE does player 2’s baseball have, compared to player 1’s baseball? (Write down this practice problem in your notes.) Even though I don’t know the exact mass of each baseball, I can still figure out this answer. First, I assume that the players used the same baseball, so it would be the same mass each time Then, I look at my equation PEgravitational = mgh If the second hit was twice as high, I can just add a 2 PEgravitational = mg2h So the second baseball would have twice as much PE as the first.