June 6 -10, 2005
The Little Red School House Approach: Solving Remedial Challenges KTeam and SCANS Institute
Measuring Acceleration Due to Gravity
Three basic linear (straight-line) equations of the form y = mx + b, having variables of distance, time, velocity and acceleration, are the following: vf = vo + at vf 2 = vo 2 + 2 ad d = vot + ½ at 2 where vo is initial velocity, vf is final velocity, d is distance, a is acceleration, and t is time.
Three basic linear (straight-line) equations… vf = vo + at vf 2 = vo 2 + 2 ad d = vo t + ½ at 2 Given any three of the five variables, the other two can be determined when vo is zero.
Three basic linear (straight-line) equations… vf = vo + at vf 2 = vo 2 + 2 ad d = vo t + ½ at 2 These equations can be used to demonstrate that an object, falling freely under the influence of earth’s gravity, undergoes constant acceleration.
1/ 2/ 3/ vf = vo + at vf 2 = vo 2 + 2 ad d = vo t + ½ at 2 When an object is dropped from a distance, or height h, acceleration “a” becomes “g” for gravitational acceleration during time t. If initial velocity is zero, Equation 3 becomes h = ½ gt 2
3/ d = vo t + ½ at 2 h = ½ gt 2 Using y = mx + b and graphing h versus t 2 give a straight line with slope equal to ½ g, so g equals 2 x slope
Time (sec) Time Squared Distance (cm) 0. 53 0. 2809 139. 5 0. 48 0. 2304 118. 2 0. 44 0. 1936 99. 1 0 0 0
h = ½ g t^2 Slope = ½ g g = 2 x slope
h = ½ g t^2 Slope = ½ g g = 2 x slope
Dropped Ball “Measured” Data "Measured" Distance Time^2 Calculated Distance (m) 0. 05 0. 10 0. 01 0. 049 0. 45 0. 30 0. 09 0. 441 1. 24 0. 50 0. 25 1. 226 2. 39 0. 70 0. 49 2. 403 3. 99 0. 90 0. 81 3. 973 4. 91 1. 00 4. 905 5. 85 1. 10 1. 21 5. 935 8. 1 1. 30 1. 69 8. 289 19. 4 2. 00 4. 00 19. 620
“Measured” Video Frame Data
“Measured” d vs Time Squared Slope = 1/2 g Correlation Cofficient = LINEST(D 3: D 11, F 3: F 11) = 4. 84 g = 2 x 4. 84 = 9. 68 CORREL(D 3: D 11, F 3: F 11) = 0. 99997
Dropped Ball “Measured” Data "Measured" Distance Time^2 Calculated Distance (m) 0. 05 0. 10 0. 01 0. 049 0. 45 0. 30 0. 09 0. 441 1. 24 0. 50 0. 25 1. 226 2. 39 0. 70 0. 49 2. 403 3. 99 0. 90 0. 81 3. 973 4. 91 1. 00 4. 905 5. 85 1. 10 1. 21 5. 935 8. 1 1. 30 1. 69 8. 289 19. 4 2. 00 4. 00 19. 620
“Measured” d vs Time