Name:_________________________________ Date:___________________ Period:______ Name:_________________________________ Name:_________________________________ Chapter 6 Lab: Bull’s Eye! Introduction: If a marble rolled off the edge of a table in a universe without gravity or air, it would keep going straight without any change in its motion (same speed and same direction). vix dx (horizontal ) You could measure the horizontal distance that the marble travels with the simple equation: d = vit + 1/2at2 , but because there is no horizontal acceleration (a = 0), the equation is simply: d = vt To solve this equation for d you must know the initial velocity (v) and the time (t) the ball in motion. . .. In the real physical universe, all objects experience acceleration due to gravity in the vertical direction. The vertical motion of the marble would determine the time (t) it is in the air before hitting the ground. Its vertical motion is the same as falling straight down: dy (vertical) You can calculate the time it takes the marble to fall with the equation: d = vit + ½at2 , but there is no initial vertical velocity (vi = 0) so the equation is simply: d = ½at2 To solve this equation for time (t) you must know the vertical distance (d) fallen and a = g = –10 m/s2 . . Purpose: The actual motion of the marble will be projectile motion following a curved path with both horizontal and vertical motion. Separate horizontal and vertical problems must be solved to predict the exact place the marble will land. After calculating the exact location, you will place a cup to catch the marble. vix d (vertical) d (horizontal ) You will only get ONE CHANCE to hit the target, so calculate carefully! 1 Materials: - incline (two meter sticks spaced slightly) - 2 small textbooks - stopwatch - marble - catching can - 1 big textbook 80 cm (or 0.80 m) wall (1 big book) (remove when ready for one shot at target) incline (2 meter sticks) 2 small books d (vertical) catch cup or can Procedure: Do NOT let the marble fall OFF the table until your ONE TRY to catch it. Part I: 1. Set up an inclined plane (2 meter sticks slightly spaced forming a groove for the marble to roll down) at a height of 0.07 m (or 7 cm). (use 2 Physics textbooks for this height) 2. Line the meter sticks with the edge of the book so the exact length of the incline is 80 cm (or 0.80 m). 3. Hold your marble at the top of the incline at the 80 cm mark. At the same time you let go and allow the marble to roll down, you must click start of the timer. (catch the marble after it hits the wall) Record the exact amount of time that is required to go from 80 cm to 0 cm in Table 1. . 4. Repeat step 3 nine more times for 10 trials altogether recording all times in Table 1. 5. Calculate the average velocity and final velocity down the incline and record in Table 2. (This velocity is the initial horizontal velocity (vix) when the marble is launched off the table) Table 1: Time Time Time Time Time Time Time Time Time Time Average Time Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Trial 7 Trial 8 Trial 9 Trial 10 (t) of ten trials (s) (s) (s) (s) (s) (s) (s) (s) (s) (s) (s) Table 2: Average Velocity (vavg): Distance Time Average of incline t Velocity (average d vavg from data) (m) (m/s) Final Velocity vf (m/s) vavg = d t Final Velocity (vf): vf = 2•vavg 0.80 SHOW your WORK for calculating vavg and vf . 2 Part II: 6. Take only one of the meter sticks from your incline (do not move the other one as it must keep the same exact position. Use it to measure the vertical distance (d) (or height) from the top of the table to the top of the catch can. Record this measurement in meters (m) in Table 3. 7. Calculate the time (t) to fall and the horizontal distance (d) (or range) the marble will travel and record these answers in Table 3. 8. Take only one of the meter sticks from your incline (do not move the other one as it must keep the same exact position. Use it to measure the horizontal distance (d) (or range) along the floor from the table to the distance you calculated in Step 7. Place the catching can on the spot to catch the marble. 9. Ask your teacher to check your calculations BEFORE you use your ONE LAUNCH ATTEMPT. 10. You have ONE CHANCE to fire the marble into the catcher. You must place it at the 80 cm mark on your incline again and be certain that it is setup identically to your time trials. Remove the big book wall and release the marble for your one attempt. Pay close attention to where the marble lands. If it not in the can, you should measure how far away it lands so you can calculate % error and discuss in your conclusion what you could have changed. Table 3: (measured) (calculated) (calculated) Vertical Distance Time to Fall Horizontal Distance (height) (range) d t d (m) (s) (m) SHOW your WORK for calculating t and d (horizontal). Time (t): d = viyt + ½at2 (viy = 0) (a = g = –10) Range (dx): d = vixt + ½at2 (a = 0) 3 Questions: 1. Did your ball land in the cup on your first try? Yes or No If not, calculate your % error using the formula: (actual d – calculated d) x 100 = % error (actual d) or: (actual distance marble traveled – calculated distance marble should travel) x 100 = _____% error (actual distance marble traveled) show work and box answer: 2. What may cause the marble to miss the target? (list more than one possibility, even if you made it in) _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ 3. If you had rolled the marble from a taller incline (4 books) to get more horizontal launch velocity, the marble would have traveled less same more distance. (circle one) Explain: _________________________________________________________________________ ________________________________________________________________________________ 4. If you had rolled the marble from a taller incline (4 books) to get more horizontal launch velocity, the marble would have taken less same more time to fall. (circle one) Explain: _________________________________________________________________________ ________________________________________________________________________________ Conclusion: Write a paragraph discussing the lab’s purpose (refer to the first page) and what you observed and learned about the time and range for projectiles based on horizontal and vertical launch velocity. Include error(s). 4

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# Ch 6 Lab - Bull`s Eye!