Marble Drop Game Category: Physics Type: Make & Take Rough Parts List: 1 1 2 1 1 Large piece of wood Small piece of wood Long pieces of wood Box of nails Roll of wire or rubber bands Screws Paint Marbles Tools List: Hammer Drill Saw (jigsaw) Pliers Screwdriver Pencil Ruler Wood glue Sandpaper T-­‐square (optional) Video: http://youtu.be/i0B8Sg7Ca4U How To: Here we’ll show how to make a full regular array of nails. You can also make a random array, or some other pattern and see different results. Cut a piece of wood for the game board. Sand the edges. © 2013 Fresno Community Science Workshop. All Rights Reserved worldwide. When linking to or using FCSW content, images, or videos, credit MUST be included. Paint the front and back. Decorate it any way you want. Cut a strip of wood the same length as the board. Make sure the length of wood is flush with the edge of the board and nail or screw it into place. Do this for both sides of the board to create a border. Divide the bottom of the board into nine even spaces and mark with a pencil. Using these marks, use a T-­‐square or ruler to make straight lines down the length of the board. © 2013 Fresno Community Science Workshop. All Rights Reserved worldwide. When linking to or using FCSW content, images, or videos, credit MUST be included. Starting 1” from the bottom make a horizontal mark at 1” intervals along the length of each line. Mark new lines half-­‐way between the first set of lines, and starting 1.5” from the bottom. Mark 1” intervals along the line. Hammer a nail into each intersection. Write the scores in the 9 sections at the bottom. Here’s a suggestion: 3,5,7,0,10,0,7,5,3. To separate the scores, put screws or nails halfway in at the points marked earlier on the board as well as at the edges. Loop a wire or rubber bands around the screws and the first nail of each row to make compartments. Squeeze the wire together as shown. Mark a triangular stand for the board. The size shown here is a triangle of 5”x 9”. © 2013 Fresno Community Science Workshop. All Rights Reserved worldwide. When linking to or using FCSW content, images, or videos, credit MUST be included. Use a jigsaw or scroll saw to cut the stand. Decorate as desired. Secure the stand to the board with wood glue. Or use screws to connect the stand to the gameboard. Drop a marble into the top of the gameboard and watch it move through the board! Fine Points: → To make the borders you can use wood or plastic, just make sure it is straight edged. → Try to hammer the nails in as straight as possible. → If making with young children, softer material such as corkboard or foam core with pushpins could be used to make the gameboard. Concepts Involved •
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Gravity pulls everything down. Moving things continue to move in a straight line unless a force acts on them. When a falling marble hits a nail, it has some probability of bouncing off to one side, and some probability of bouncing off to the other side. When it passes many nails, the end result is the sum of all those probabilities put together. Focus Questions: 1. If you release a marble from the center, do you think it has a greater chance of reaching the bottom near the center or toward the edge? 2. If you release a marble toward the edge, do you think it has a greater chance of reaching the bottom near the center or toward that same edge? 3. Do you think the tilt of the board will make any difference as to where a marble will reach the bottom? © 2013 Fresno Community Science Workshop. All Rights Reserved worldwide. When linking to or using FCSW content, images, or videos, credit MUST be included. A Closer Look: The marble drop game is a maze consisting of rows of nails. The marble falls because the earth’s gravity is pulling on it, just like it pulls on everything. Actually gravity attracts all objects towards each other, and so it is more accurate to say that the earth and the marble are pulling on each other. The earth is much bigger though, so the earth doesn’t rise up much at all to meet the marble. The moon on the other hand is much bigger than the marble, and the earth does move appreciably as it and the moon swing around each other. In this project, gravity pulls the marble down into collisions with the nails and it moves randomly down the course. If it doesn’t hit a nail, it continues to fall straight, an example of Newton’s first law of motion: Objects in motion tend to stay in motion, and objects at rest tend to stay at rest, both until a force acts upon them. Although the marble travels straight, it is accelerating, that is, going faster and faster as it falls. Technically you’d say its speed is not constant but rather increasing. This is because the force of the earth’s gravity continues to act on it. This is an example of Newton’s second law, which says that the acceleration an object depends on the force acting it. The project is also an example of probability. When the marble hits a nail exactly straight from the top of the nail it has an equal chance of falling to the left or to the right. If it hits the outer boundary, the marble will fall in a direction that allows it to remain in play. If a marble hits a nail from an angle, this will change the probability for the sides. It is a rule of probability that you can add the probabilities of consecutive events to end up with a total probability for the series of events. You can’t really measure the probability of each event here, but you can get a rough idea of what the total probability is that a nail will fall in any given compartment by releasing many marbles – maybe 20 – and watching where they tend to land. In general, there will be a distribution with one compartment having the most marbles – meaning the largest probability – and others having less on either side of it. The ones with no marbles have a very low or zero probability. Links to k-­‐12 CA Content Standards: Grades k-­‐8 Standard Set Investigation and Experimentation Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other strands, students should develop their own questions and perform investigations. Grades k-­‐12 Mathematical Reasoning: 1.0 Students make decisions about how to approach problems: 1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. 1.2 Determine when and how to break a problem into simpler parts. 2.0 Students use strategies, skills, and concepts in finding solutions: 2.1 Use estimation to verify the reasonableness of calculated results. 2.2 Apply strategies and results from simpler problems to more complex problems. 2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and © 2013 Fresno Community Science Workshop. All Rights Reserved worldwide. When linking to or using FCSW content, images, or videos, credit MUST be included. models, to explain mathematical reasoning. 2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. 3.0 Students move beyond a particular problem by generalizing to other situations: 3.1 Evaluate the reasonableness of the solution in the context of the original situation. 3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems. 3.3 Develop generalizations of the results obtained and apply them in other circumstances. Grade 2 Standard Set 1. Physical Sciences. The motion of objects can be observed and measured. As a basis for understanding this concept: 1.e. Students know objects fall to the ground unless something holds them up. Grade 8 Standard Set 2. Forces. Unbalanced forces cause changes in velocity. As a basis for understanding this concept: e. Students know that when the forces on an object are unbalanced, the object will change its velocity (that is, it will speed up, slow down, or change direction). © 2013 Fresno Community Science Workshop. All Rights Reserved worldwide. When linking to or using FCSW content, images, or videos, credit MUST be included.