Two Dimensional Motion

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1 Catherine Kimball Mary Young Physics Institute 2003 Two Dimensional Motion 2 x 2 Pegboard High School 2 x 2 Plywood 4 X 2, _ inches thick piece of plywood behind slope at the top and in front and behind slope at the bottom helping to form the tray 2 x 2 piece of plywood to form a tray 4 x 10 piece of plywood with a 10cm slope Line tray with felt 2 x 2 base to set the boards on Materials 2 x 2 Plywood/Pegboard Lowe s $4.00 (Lowe s will cut for free if necessary) Marble/ Ball bearing available at school 3-1 _ pipe straps Lowe s ~ $ wood golf tees Wal-Mart ~ $ _ x 19 piece of sticky felt Hammer and nails, Screw driver and screws, Scroll saw, sand paper on hand Plywood x 2 both _ inch thick scrap wood Plywood x 2 both _ inch thick scrap wood Plywood 1-4 x 10 _ inch thick scrap wood *To build beginning to end takes 1-2 hours.

2 The Concept When a traveling object is projected horizontally, its horizontal velocity will be unaffected as gravity pulls the object toward the Earth over a period of time. So if we roll a ball off a slope we should be able to determine the path at which it will fall. Frameworks IV. Force, Motion and Mechanical Energy Grades 5-8, A. 1-3 Grades 9-12, A.1, B. 1-2 Student Misconceptions Having several years of teaching experience between Mary and I, we came up with our own student misconceptions. It is interesting to note that Rosalind Driver, et al., in Making Sense of Secondary Science (1994) came up with similar misconceptions in their research. Gravity will pull a projected object straight down. An object will continue out in a straight path until gravity pulls it to the ground. The rate at which an object falls depends on its mass/weight. Students do not think that an object that is dropped and on object tossed horizontally from the same height will hit the ground at the same time. Students feel that the horizontal force affects the vertical motion of the object. The Demonstration At this level, students aren t prepared to solve this problem mathematically. This project will probably be set up as part of a much larger lab dealing with inquiry based activities on acceleration, gravity and motion. Students will first predict what they think the path of the ball will be once it is released form the top of the slope. They will then draw a picture of their prediction.

3 Once their predictions are made they will then be allowed to explore and test their predictions. They will do this as follows: 1). They will place the pipe strap, holding it in place with golf tees, in the highest position where they think the ball will fall through. 2). They will test this by rolling the ball down the slope. 3). Once they find the actual spot it falls through they will mark that spot with a sticky dot. 4). They will then repeat this procedure doing the next position where they think the ball will fall threw, again marking the actual spot. 5). This will be repeated until they reach the bottom of the apparatus. 6). They will draw a picture of what actually happened and compare it to their prediction. 7). Students will try to determine what causes this to happen. High School Students will be given the scenario of a stunt person flying off a cliff while skiing. They will be asked to guess where the stunt crew should place the air mat for the stunt person to land on. After predictions are made and a few drawn on the board, the teacher will get the apparatus to show two-dimensional motion. (Make sure that you have figured this ahead of time to work out the kinks.) The marble/ball bearing will represent the skier and be released from the tallest point on the slope. The clay will represent the air mat. To enhance this, have students calculate where the skier will be at each tenth of a second. Place Linch pins on the board where they calculated the skier would be and retest the skier (marble). There should be a constant horizontal speed (represented by equal distances from the board and the rings) and an accelerating vertical speed (represented by the increasing intervals between the rings).

4 How does doing this demonstration provide an example of the scientific concept? The students should be able to measure the distance between the board and each ring/sticky dot and see that gravity will not have an effect on the horizontal speed of the ball. What prediction would the students make? Students at the middle level will predict that the ball will do one of two things: 1. The ball will drop straight off the slope with very little horizontal displacement. 2. The ball will travel straight out at a horizontal distance, then drop to the bottom. Students at the high school level will predict that the ball will accelerate in both directions, horizontally and vertically. Roles What is the role of the teacher? In this situation, the role of the middle school teacher is to discuss the effects of gravity on acceleration and motion of objects. Answers questions when needed and finally provide a safe opportunity for students to conduct various mini labs that have been set up around the room. Each lab will have a set of instructions for them to follow such as: make a prediction, draw a picture, perform experiment, etc.

5 High School At the high school level, this demonstration and lab will follow a discussion of two-dimensional motion and homework involving equations on two-dimensional motion. The role of the teacher is to allow the students to use the apparatus to discover that horizontal and vertical motions are truly independent of each other. Students will be asked to describe any situation where they might encounter this type of movement. What is the role of the student? The initial role of the student is to listen to lecture, ask questions when needed and take notes. They will then work in small groups to make predictions, draw pictures and perform experiments. Afterwards, they need to draw a picture of the final outcomes and give possible explanations for that outcome. The lab station should then be left as they originally found it. High School The role of the student is to test the concept of independent vertical and horizontal movement in the lab. After an initial demonstration, students will measure the horizontal and vertical distances moved each tenth of a second and finally they will calculate speed at each of these time intervals. They will then test these calculations using a speed device and the apparatus. What is the role of the docent in the hallway exhibit? In our hallway exhibit, we will have various cartoons that depict a variety of cartoon characters that run off a cliff, go so far out horizontally and then fall straight down. Above that will be the caption: ONLY IN CARTOONS! The docent will be there to lead the student through the experiment, they will start by asking question about gravity and acceleration based on the ideas we have because of cartoons and TV. They will then allow the student to actually perform

6 the experiment. The docent will need to keep track of the pins and the marble/ball bearing so they aren t lost between class periods. Outcomes What do we hope the students will learn from this demonstration? Even though we have different age groups, our hopes are very similar. First, we hope that both groups learn that objects do not fall from a moving target straight to the ground. Secondly, we hope a definite arc or parabola is formed as the object falls. Thirdly, we hope that students see that horizontal acceleration is not dependent on gravity while vertical acceleration is. Fourthly, students at the high school level should be able to use this device to measure the speed of the ball as it passes through each ring showing that it increases at equal rates. Finally, we hope that all students can take this information and relate it to events in real life. Assessment Question: The United Nations needs to drop a care package off to a refugee camp that is located between two fences. Draw a picture of where the airplane should be when it drops its package, the path the package will take as it falls and then give an explanation for your drawing. Fence 1 Fence 2

7 Answer: The airplane and package should be drawn before fence 1 at a reasonable distance, with an arc pattern for the care package drop. Reason: the package is being pulled down by gravity however, it is traveling at the same velocity (direction and speed) of the airplane. Therefore, it travels forward as gravity pulls it down. High School Question: A band of outlaws wants to invade a neighboring castle. The cannon has been placed on a hill that is 50 meters high and the castle is 125 meters from the base of the cannon. d = _ at 2 h = 50 If the charge gives the cannonball a velocity of 32 m/s, will it hit the castle? If your answer is no, what can the outlaws do to reach the castle? d = 125 m Answer: t = s, horizontal d = 102 m so the answer is no. What can the outlaws do to reach the castle? Use a larger charge to give it a higher velocity or angle the cannon upward.