# Hunting Technology. The Potential Energy of a Bow

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1 Grade level: Upper level middle school and high school Subjects: science, math, physics Skills: comprehension, application, analysis, synthesis Teaching strategies: experimentation, observation, data collection, analysis Duration: minutes (flexible) Class size: any; students can work as a class or in small group depending on availability of materials Objectives: Students will: learn the difference between potential and kinetic energy. conduct an experiment collecting metric data graph the results of their experiment demonstrate their understanding of the graph by predicting how the results change as given variables change Materials: strung flat bow, 100 lb spring scale, meter stick, rope, graph paper, pencil Adapted by the University of Iowa Office of the State Archaeologist from Southworth s 1990 article, Potential Energy Analysis of a Bow (Physics Teacher, January 1990:42-43). Prepared with support of the Iowa Science Foundation. Background information on American Indian Archery Technology written by Tim Weitzel for the Office of the State Archaeologist Series in Ancient Technologies Hunting Technology The Potential Energy of a Bow Background Provide the students with the background information about American Indian archery technology (attached after the lesson plan). Tell them that this lesson will allow them to take on the role of experimental archaeologists. Experiments like these help archaeologists understand how prehistoric people did things. Procedure Go over the terms potential and kinetic energy (vocabulary list on next page). Explain to the students that the potential energy of a bow is transferred to an arrow as kinetic energy when the bowstring is released and the arrow is shot. The more potential energy a bow can store, the more kinetic energy the arrow will have at the time of release. The kinetic energy of the arrow combined with its mass determines the arrow s velocity and affects it flight and the force of impact. 1. Tightly secure the center of the bow to a post with rope. 2. Secure a meter tape or measuring stick (scale in feet and inches) horizontally from the post behind the bow. Position one of the number marks on the tape just below the center of the bowstring, this will represent zero for measuring. 3. Attach the spring scale to the center of the bowstring. 4. Pull horizontally on the spring scale and record the force (in pounds) and the distance of displacement (in feet) for a series of pulls. Pass out a Comparing Cultures worksheet to each student. Working alone or in pairs, have them fill in at least five categories of basic needs in the left hand column of the worksheet. 5. On a sheet of graph paper, plot force (f) as a function of displacement (d). Work (W) or potential energy (measured in foot-pounds) is the area under the curve of the line on the graph (between the curve and the displacement axis).

2 Mobile Museum Docent Guide Questions 1. What happens to W as the f increases? (The amount of work or potential energy increases as the force or pull on the bow increases.) 2. What does this suggest about the draw of the bow? (The more strength required to pull the bow string the greater the potential energy and the greater the kinetic energy when the arrow is released.) 3. Could different materials in the bow and bow string affect its strength and potential energy? (Yes, the stronger the bow and string the more force required to pull it. Also if the bow is brittle and breaks or the string stretches or breaks you won t be able to maximize the force to pull and the energy released. The length of the bow would also effect the amount of force required to pull the string.) 4. Would you expect to get different plots with bows made of different materials? (Yes, some kind of wood are softer and bend more easily than others requiring different forces to bend them. If the wood breaks when force is applied it would not be good for a bow.) Vocabulary Backed bow: a bow made of wood with hide or sinew laminated onto the back of it Composite bow: a bow made from horn wood, sinew or leather laminated together. The horn is on the belly, facing the archer, and sinew on the back of a wooden core. Sinew and horn will store more energy than wood for the same length of bow Experimental archaeology: a field of study which attempts to generate and test archaeological hypotheses, usually by replicating or approximating the feasibility of ancient cultures performing various tasks or feats. Kinetic energy: the energy of an object in motion Potential energy: the stored energy of an object Self bow: a bow made from a single piece of wood

5 The height and strength of the archer determines the ideal draw weight of the bow. A combination of the length of draw and the draw weight of the bow determines the cast (propelling force) of the bow. Adjusting either or both of these features allows the arrowhead to be made larger or smaller as needed. The draw weight of the bow also determines the ideal weight and diameter of the arrow shaft. Even a bow with a high draw weight can only throw an arrow so far. If the arrow is too heavy, it will not fly far or fast enough to be very useful. A shaft that is too thick or too thin will also lead to problems. It must compress enough to bend around the bow stave as it is launched by the string. If it does not bend, the arrow flies to the side of the target. If it bends too much, it will wobble (reducing the striking force) or even shatter. The length of the draw, also determined by the body of the archer, determines the length of the arrow. The maximum cast of the bow determines the maximum weight of the point. This is how we know that certain "arrowheads" cannot really have been used on an arrow, at least not to any good effect. A general rule of thumb is that a stone arrowhead will be less than 1 1/2-x-3/4-inch in dimensions and will generally weigh less than one ounce. Larger "arrowheads" probably would have been spear, dart, or knife tips.

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