Lab 2 Linear Motion

Lab 2 Linear Motion: Measuring g Value Objectives When you have completed this assignment, you will be able to: 1. Understand the concept of linear constant acceleration motion. 2. Measure the acceleration of free-falling objects 3. Calculate the acceleration due to gravity, g. Discussion A freely falling object is an object moving freely under the influence of the gravitational force only. Regardless of its initial motion, the freely falling object experiences a downward acceleration. This acceleration is constant. The motion of a freely falling object is the motion in one dimension under constant acceleration, only this motion is along the vertical. If we choose down-ward as the positive direction of y (a y = g = 9.8 m/s 2 ), the following equations will describe the motion: Velocity as a function of time: v y = v yo + g∙t [1] Velocity as a function of displacement: v y 2 = v y 0 2 + 2 ∙gy [2] Displacement as a function of time: y = v y 0 ∙t + 1 2 g∙t 2 [3] Displacement as a function of velocity & time: y = ( v y 0 + v y 2 ) ∙t [4] Equipment Computer with internet Procedures: Go to and open the Projectile Motion simulation. When it asks which section option you want to use, choose “ Intro .” Notice the following  the cannon (sitting on top left) can change its vertical height relative to the ground by dragging it up and down  the cannon ball angle can be changed by dragging and turning the cannon pipe.  the initial speed can be changed through the sliding bar on the bottom left.  different objects can be shot from the cannon, by selecting the object in the menu bar located top right.

 there are measuring equipment, such as a tape measure and the Time/Range/Height (TRH) device in the tool box next to the menu bar. Part I: Measuring Acceleration  Change the object/projectile to a golf ball (menu bar on top right)  sliding the initial speed to 0 m/s,  drag the cannon pipe and rotating to angle to -90° (straight down)  drag the cannon height to 4 m.  Record the golf ball’s mass and diameter in the data table 1.  Fire the golf ball by clicking on the fire button  Use the Time/Range/Height measuring equipment (TRH) to measure the time following the steps:  Use your mouse to drag the TRH out of the tool box into the large, blue area in the center of the window.  After clicking on the red “launch” button, notice the vertical path/trajectory line.  Place the TRH crosshairs at the end of the path and record the time of fall in table 1.  Repeat the steps for each of the height in table 1 by dragging the cannon up. Data Table 1 Mass of golf ball: [0.05] kg Diameter of golf ball: [0.04] m Height, h (m) Time, t (s) t 2 g = (2h)/t 2 4 m [0.09] [0.81] [9.88] 6 m 1.11 1.23 9.74 8 m 1.28 1.64 9.77 10 m 1.43 2.05 9.76 12 m 1.56 2.43 9.88 15 m 1.75 3.06 9.80

i) Type the data t 2 (x-axis) in the first column, and h (y-axis) in the second column. ii) High light the two columns, In the “Insert” menu tab, choose “Scatter” , a scatter plot will be drawn iii) Click on any data point on the scatter plot, and choose “Add Trendline…” from the drop-down menu. Choose “Linear,” and check “Set Intercept” and “Display Equation on chart.” Part II Measuring the distance.  Click on the yellow eraser button in bottom left of the window to clear the previous paths.  Leaving all other the same, initial speed=0, angle -90 (cannon pipe straight down).  Drag the cannon to a height of 15m, then fire the cannon.  Notice the vertical path/trajectory line. Upon very close inspection, you should notice there are “large” and “small” circles along the line, with a small circle every 0.1 s and a large circle every 1.0 s. ( Hint: you may need to click on the magnify button in the top left of the window to enlarge the image)  Place the Time/Range/Height measuring equipment (TRH) crosshairs at each circle of the trajectory path. Record the height for the first 10 circles in data table 2. Remember each circle is marked every 0.1 s. Data Table 2 n Elapsed time, t (s) Height, h (m) Measure from ground x n = 15.00 - h n (m) displacement from top Calculate the displacement using equation [3] 1 [0.1] [4.95] [0.05] [.049] 2 0.2 4.8 0.2 .196 3 0.3 4.56 0.44 .441 4 0.4 4.22 0.78 .784 5 0.5 3.77 1.23 1.225 6 0.6 3.23 1.77 1.764 7 0.7 2.6 2.4 2.401 8 0.8 1.86 3.14 3.136 9 0.9 1.03 3.97 3.969

n Elapsed time, t (s) Height, h (m) Measure from ground x n = 15.00 - h n (m) displacement from top Calculate the displacement using equation [3] 10 1.0 0.1 4.9 4.9 1. Show your calculation for displacement for n=3 or t=0.3s: Displacement: y = 1 g * t^2 2 Y = (1/2) * 9.8(0.3)^2 Y = 0.735 2. Find the percentage difference between your measure and calculated value for n=3. 3. Use the data table 2, plot X n (displacement) vs t on an excel sheet, then copy your graph below (again put t in the first column and Xn in the second column in the spread sheet, refer to “how to make graph” in Part I again if needed). [graph] Do you see a linear graph? [answer] Part III. Questions 1. What is free fall? [Free fall is an object that is falling under the sole influence of gravity] 2. Define acceleration. [Acceleration is the rate of change of velocity] 3. Why do you think the distance between each small circle increases while the time is the same 0.1 second? [answer] 4. Suppose there is a well and you would like find out how deep it is. You are given a stop watch and a small stone, will you be able to find out the depth of the well? Explain the procedure and find out a) the depth of the well if the time you get is 2s b) final velocity of the stone