```Projectile Motion (or You Bet Your Grade)Roy Coleman                      Morgan Park High School                                 1744 W. Pryor Ave.                                 Chicago, Illinois 60643                                 312-881-5050Objectives:To calculate the initial velocity of a spring stretched a varying amount and fired vertically from a shooter and to predict, by calculations, where that spring will land when it is shot horizontally off of a horizontal platform.  As a additional objective, to learn that ALL data must be recorded but that data which is way out of the ordinary can be ignored when calculating averages and results. Materials Needed:The following materials are needed for each group of 2-4 students:  1) a spring with sufficient elasticity so that stretching it about 1 cm will      shoot it to a height of about 50 cm.  One end should have a paper clip      attached and the other should be bent into a loop which will hook over the      nail in the end of the shooter described below  (Primary level students      might use rubberbands instead but they are not as consistent.)  2) a 'shooter' made from a 1" by 1" by 18" piece of wood with a headless nail      driven into the end near the edge so that the spring may be hooked to it  3) several metersticks  4) graph paper  5) a section of a room with sufficient height where a spring's shot may be      marked and/or measured directly  6) optional - an apparatus which simultaneously drops one object while      projecting a similar object horizontallyOne of each of the following is needed for the entire class:    1) a securely mounted horizontal surface at a height of 1.5-2 meters above the      floor where the students will hold their 'shooters' for the You Bet Your
Grade part of the experiment  2) a low waste paper basketStrategy:INSTRUCTORS PREPARATION: 1) Mark the 'relaxed' position of the spring on the side of the shooter. 2) Stretch and shoot the spring vertically such that it goes to a height of about 50 cm.  Make enough shots so that you are confident of the measurements.  Mark this stretch on the side of the shooter and number it #1.  3) Stretch and shoot the spring so that it goes to the greatest height that you are going to use.  Again, make enough shots so that you are confident of themeasurements.  Mark this stretch on the side of the shooter and number it #6. 4) Measure the distance between the two marks (#1 and #6) and divide it by 5.Measure down from #1 a distance equal to the result and mark that point #2.  Repeat the measurement for points #3 and #5, intentionally skipping where #4 should be.  (A suggestion was made to drill holes at each of these points to allow a small nail to be inserted and the paper clip hooked on the nail.  Pulling the nail fires the spring.)CLASS ACTIVITIES: 1) Have the students fire the spring vertically from each of the indicated stretches.  They should record ALL of their data and decide which of the points are consistent and which are in error.  (Does the height get more consistent as the student gets more experience?) (Does it make a difference if a different person does the shooting?) 2) Plot a graph of height vs. stretch.  (Is this graph a straight line?) (Does it go through zero?)
3) Calculate the initial velocity of the spring (vo=sqrt(2gh)) for each of the stretches and plot a graph of the initial velocity vs. stretch.  (Is this graph a straight line?) 4) Demonstrate that a projectile fired horizontally will take the same amount of time to reach the ground regardless of its initial horizontal velocity.  This should demonstrate that the vertical acceleration of an object is independent of the horizontal acceleration with the resulting motion being the sum of the two.  5) Show the students the board you have mounted horizontally and how their shooter should be placed.  Also show them the waste paper basket that they will be shooting into. 6) Have the students predict, from their graphs, the initial velocity of their spring for a stretch equal to what would be #4. 7) Have the students calculate the time that it will take for the spring to fall from the board to the top of the waste paper basket.  (t=sqrt((2H)/g))  For a high school class, you might just tell them to calculate the time to fall and let them figure out that the spring doesn't fall to the floor but only to the top of the basket. 8) The students should then calculate where to place the basket.  (R=vot) 9) Place the center of the basket at the calculated place and have them try shooting.  (Did they hit it and how many tries did it take?)Expected Results:    The results for the first few shots should be somewhat inconsistent but, after 5-10 shots, they should improve greatly.  Generally the shots should group within about 10% of the average value for each stretch.    Changing the person doing the shooting usually makes a noticeable difference because each person has their own unique way of releasing the spring.  Using a shooter with holes and a nail release along the side should eliminate this difference.     The graph of height vs. stretch should, with the possible exception of the first point, be a straight line.  It will probably not go through zero since a spring is linear only from the point where all of the coils are separated and it usually takes some small initial stretch to completely separate all of the coils.    The graph of velocity vs. stretch should NOT be a straight line because of the square root used to calculate it but, for the small sample of points tested, it will probably be very close to a straight line.Evaluation:    A student's grade is based on how many shots it takes for the spring to land in the basket.  (First shot = A, Second shot = B, etc.)```