LAB: Kinematics and Projectiles Objectives In this lab you will determine the initial speed, travel time, and range of a projectile. Materials Theory Round object to roll Board for a ramp Blocks to change angle of ramp Table Stopwatch (phone or computer) Ruler, tape measure, or meter stick When a body moves equal distances in equal times, that body is said to be moving with a constant velocity. The average velocity throughout the time interval is defined as the displacement of the moving body per unit time. Vavg = ΔΧ ΔΕ When it is accelerating, the object will follow the kinematics equations. x=at² + vot + xo v = at + vo v+ Vavg = 2 (EQ 1) (EQ 2) (EQ 3) (EQ 4) (EQ 5) v² = v² + 2a (Ax) And when rolling down a ramp, the object will accelerate along ramp tilted at an angle of 0 to the horizontal, with a component of gravity: a = g sin 0 (EQ 5) For projectiles that do not land at the same height, we simplify the kinematics equations of motion. For a ball launched horizontally with x as the horizontal and y as the vertical displacement at time, as the initial speed (only in the x-direction), the equations of motion simplify to x = Vot y=gt² (EQ 6A & B) In this situation we assume the origin is at the ball's start position, with positives in the directions the ball is traveling - positive x is "forward" horizontally, and positive y is downwards (with gravity). Eliminating from these equations and solving for,, we have V= 2y (EQ 7) When comparing two measurements or values, percent error is used if one value is more likely to be correct and can be used as a "gold standard". Percent difference is used when you are uncertain which measurement is "correct". % Error = % Diff = Measured - Accepted Accepted | Measl - Meas2| xX 100% × 100% (EQ 8a & 8b) Average Projectile Motion = B: Sin'"' (22) Procedure a = h Part I: Kinematics tanb S= S = ½½ ah b S a 1. 2. 3. 4. Place the board on a table. h Set one end of the board on a block. This forms a ramp at a small angle. Measure the diagonal length (L) and vertical height (h) of the board and enter in Table 1. Use trigonometry to calculate the angle of the ramp relative to the floor/table, and record as "calculated angle".. Oheight base ③base ungth na taneb sine a+b⋅cose area: 2 5-ah-46² sin 20 g sin 0 Source for figure: Nolan & Bigliani "Experiments in Phyises", 2nd Edition. Smell test: Double check your calculated angle by placing your protractor flat on the table or floor, and sliding left and right until the diagonal length goes through the zero hole at the center of the circle. Record as "measured angle". Calculate the component of the acceleration due to gravity along the ramp (Equation 5), and enter into Table 1 as "predicted acceleration." Hold the ball or cylinder at the top of the ramp. Start the stopwatch as you let the object go. Stop the stopwatch as the object gets to the bottom of the ramp. Record time in Table 1. Repeat steps 7 and 8 for 2 more trials. Calculate the average time for the trials for each scenario and enter answer in Table 2. Use Equation 2 to calculate the measured acceleration. Use Equation 1 to calculate the average velocity for each scenario. 9. 10. 11. 12. 13. Use Equation 4 and the average velocity from the step above to calculate the final velocity for each scenario. 14. 15. Use Equation 6a to calculate the percent error between the two acceleration measurements, with the predicted value as "accepted". Use Equation 6b to calculate the percent difference for the two angle measurements, since you don't know which one is more likely to be correct. If any values are over 20%, repeat the experiment to try and eliminate errors. Part One: Kinematics Table 1: Constant Acceleration Measurements Length of ramp: Trial 0.6541 Height of Board 25 3/4 10 m Calculated (m) Angle (°) Measured Angle (°) Predicted Acceleration Time (m/s) (s) sinx = .09 ,6541 1 .09 x = 1 3 1105 Table 2: Constant Acceleration Calculations Average Time Measured Acceleration Average Velocity Final Velocity Acceleration Percent Error Angle Percent Difference (s) (m/s²) (m/s) (m/s) Part One: Kinematics Table 1: Constant Acceleration Measurements hort distance betw ** the angle in H = b Length of ramp. 541 25 3/4 10 m Trial Height of Board Calculated Angle (") Measured Angle ( 1 (m) 0.1143 QAB Predicted. Acceleration (m/s) Time (s) Sinx D 25° 0.1143 2 25° 0 01143 3 25° Table 2: Constant Acceleration Calculations Acceleration Angle Average Time (s) Measured Average Acceleration Velocity (m/s²) Final Percent Percent Velocity Error Difference (m/s) (m/s) (") (%)