Intro | Parameters | LRB | Timeline | Formulas | Pythagoras Graeme’s Cracker Revenge 2

1. Intro | Parameters | LRB |Timeline | Formulas | PythagorasGraeme’s Cracker Revenge2 Engineering 1 Kamiakin High School

2. Big Ideas • Use math, science, and technology to solve a problem • Vertical motion is independent of horizontal motion • Test a measurement many times for accuracy • Measure twice, cut once graemes_cracker_revenge

3. Introduction • You’ve been assigned a new project by your group’s manager. You are required to construct a scale model of a ramp from which a projectile will be launched • The project consists of: • Building a ramp and support structure • Use the Velocity formula to determine the final velocity of the projectile at the ramp’s bottom • Test many times to get an accurate average of velocity • Use the Time Formula to estimate time of travel by the projectile • Use the Distance Formula to estimate the horizontal distance the projectile will travel Velocity Formula Vf = 2d/t Time Formula t = (2h /g)1/2 Distance Formula d = v/t graemes_cracker_revenge

4. Parameters • Ramp length = 1 meter • Ramp angle = 45 degrees • Ramp material = balsa if provided by me or bring your own • Min R = 75cm/ • Min/max h = 75cm/260cm • Projectile = 2.54cm dia. steel ball • Projectile must leave the ramp horizontally • You must break the Graham Cracker • You only get one try graemes_cracker_revenge

5. Requirements • Teams of 2 or individual • Each student must maintain a Lab Record Book (LRB) with entries each day • Use tables for each test results • Include sketches and drawings graemes_cracker_revenge

6. Lab Record Book (LRB) • Brain storming ideas, sketches, formulas, predictions: getting started • Tables of collected data and results: as accomplished • Photos of activities: as they occur • Print one page with copy for each member of group • Cut and paste in LRB • Photo of final project: end of project • What you knew, what you learned, what you still need to know (KWL): end of assignment • Conclusions: end of assignment graemes_cracker_revenge

7. Timeline • Day 1 • Introduction and questions, begin brain storming • Day 2 • Continue planning, sketches approved • Discussion of Pythagorean Theorem • Day 3 • Create a Bill of Materials • Thickness, width and length of all structure members • Type of material (pine, sheet metal, etc.) • Where materials will be obtained (school/home) • Continue planning graemes_cracker_revenge

8. Timeline cont. • Day 4 (Fri) • Concept sketches and Bill of Material approval • Day 5-7 (Mon – Wed) • Begin collecting materials • Begin final scaled drawing (Multi-view or 3D) • Multi-view must have at least top and side • 3D of ramp and structure (by hand or computer • Must illustrate joints (blowups) and method of connecting members of ramp and structure • Begin final Bill of Material required • Thickness, width and length of all structure members • Type of material (pine, sheet metal, etc.) • Where materials will be obtained (school/home) • Day 8 (Thu) • Final drawing and Bill of Materials approved graemes_cracker_revenge

9. Timeline cont. • Day 8-12 (Thu-Wed) • Tower construction • Day 12 (Wed) • Demonstration of Vf (final velocity) formula • Testing Vf • Days 13-14 (Thurs - Fri) • Demonstrate time and distance formulas • Test time and distance • Day 15-16 • Break the Graham Cracker graemes_cracker_revenge

10. Project Formulas • PythagoraeanTheorem (for right triangles): • a2 + b2 = c2 • a = Side 1 (either of sides not the hypotenuse) • b = Side 2 (either of sides not the hypotenuse) • c = hypotenuse (the longest side) • Calculate how fast the ball drops on the ramp • Velocity Formula: Vf = 2d/t • Vf = final velocity (calculate) • d = distance (1 meter) • t = time (test) • Calculate the time it takes an object to fall a given distance • Time Formula: t = (2h /g)1/2 • t = time in the air • h = height of ramp bottom from floor • g = gravity • Distance Formula: • d = v/t (distance ball will travel) • V = velocity off ramp • t = time in the air (above) graemes_cracker_revenge

11. Pythagorean Theorem • Years ago, a man named Pythagoras found an amazing fact about triangles: • If the triangle had a right angle (90°) ... • ... and you made a square on each of the three sides, then ... • ... the biggest square had the exact same area as the other two squares put together! graemes_cracker_revenge

12. How Do We Use Pythagoras • Materials • 1 x Triangles • String: 3’ X 4’ X 5’ • Dry erase marker • Activity 1: Is the triangle a right-angle? • Measure 3” on short side and mark it • Measure 4” on longer side and mark it • Measure between the marks • What is the length? • Act. 2: Is a fence square to the house or property line? • 3 volunteers • Have volunteers take turns marking 3’ (a), 4’(b), and 5’(c) on the string • Tie the ends together • One person holds the start and 3’ mark vertically, another holds the string at the 4’ mark • The Third person holds a right angle at a-c • Does it make a right triangle? graemes_cracker_revenge

13. Pythagoras cont. If your ramp must be 1 meter, what will be the length of the vertical and horizontal sides? • a^2 + b^2 = c^2 • a^2 + b^2 = 1m If a and b are equal , which they must to be a 45 deg. Angle • a^2 = b^2 or • a^2 + a^2 = 1 • 2a^2 = 1 • a^2 = ½ • a = 1/2 graemes_cracker_revenge

14. More to Come • The rest of the formulas and discussion are in the next slide show graemes_cracker_revenge