WORKSHOP 5 PROJECTILE MOTION

Workshop Objectives –To compute the range, R, when a stone is launched as a projectile with an initial speed of 6 m/s at an angle of 60 o Software Version –Adams 2013 Files Required –Saved model from Workshop 4, or stone_completed.cmd –Located in the directory exercise_dir/mod_04_falling_stone/completed Problem Description –In this workshop you will use the stone that you built in Workshop 4 – Falling Stone.

Suggested Steps 1.Import file. 2.Build the plane. 3.Set up the initial conditions. 4.Create a measure for the projectile motion. 5.Run the simulation. 6.Find the time at which the stone makes contact with the plane. 7.Create a point trace of the projectile motion. 8.Find the Horizontal Displacement. 9.Save your work. 10.Optional tasks.

Step 1. Import File To import a file : a.Start Adams/View. b.From the Welcome dialog box, select Existing Model. c.Set the directory to exercise_dir/mod_05_projectile. d.Select OK. e.Find and select the model file projectile.cmd, which you completed in the previous workshop. f.Note that the model file is not in the current working directory. It is in the directory exercise_dir/mod_04_falling_stone. g.If you need a fresh copy of the model, import the command file stone_completed.cmd from the directory exercise_dir/mod_04_falling_stone/ completed/. h.Select OK. b c d f g c h e

Step 2. Build the Plane Build the plane: a.From the Settings menu, select Working Grid. b.In the Size: X text box, enter c.In the Size: Y text box, enter d.For both the X and Y Spacing text boxes, enter 50 and then select OK. e.Zoom out by typing a lowercase z, and then left-click and drag the mouse until the entire working grid is displayed on the screen. b c d e a

Step 2. Build the Plane (Cont.) a.To turn on the coordinate window, use View >Coordinate Window b.From the ribbon Bodies, select the Box tool. c.In the toolbox container: Select On Ground. Check Length, and then in the Length text box, enter 3500 mm. Check Height and Depth options, and then in the Height and Depth text boxes, enter 100 mm. d.Use the mouse to select the corner of the box at 0, -150, 0. e.The stone should appear balanced at the upper left corner in a front view. Note: the box will be white if it is on ground. If the box has a different color it is a new part and should be deleted. a e b c d

Step 3. Set Up Initial Conditions To set initial conditions to V x0 = 6000*cos(60°) = 3000 mm/sec V y0 = 6000*sin(60°) = 5196 mm/sec: a.From Model Browser, right-click the stone and select Modify. b.Set Category to Velocity Initial Conditions. c.Under Translational velocity along, check the X axis, and in the X axis text box, enter (6*cos(60d)(m/sec)) or (3000(mm/sec)). d.Under Translational velocity along, check the Y axis, and in the Y axis text box, enter (6*sin(60d)(m/sec)) or (5196(mm/sec)). e.Select OK. a b c c e

Step 4. Create a Measure for the Projectile Motion Create an object (part) measure to calculate the horizontal displacement, x g, of the stone’s center of mass (cm) marker when it is projected: a.From Model Browser, right-click the stone and then select Measure. The Part Measure dialog should appear. b.In the Measure Name text box, enter R_displacement. c.Set Characteristic to CM position. d.Set Component to X. e.Select Create Strip Chart. f.Select OK. g.The R_displacement strip chart should appear. a b c d e f g

Step 5. Run the Simulation To run a simulation for 1.5 seconds, using a sampling rate of 0.02 seconds: a.From the ribbon Simulation, select Run an Interactive Simulation. b.In the End Time text box, enter 1.5. c.Select Step Size. d.In the Step Size text box enter e.Select the Play tool. f.Adams/View runs the simulation and plots the corresponding data in the stripchart for the R_displacement measure g.When the simulation ends, click the Reset tool. f a b c e g d

Step 6. Find the Time at Which the Stone Makes Contact with the Plane To find the range (R): a.From the ribbon Result, select the Animation Control Dialog box tool. b.Select the Play tool. c.When the stone makes contact with the plane, select the Stop tool. d.Use the Step Forward and Step Backward tools to obtain the exact point at which the stone makes contact with the plane. e.Note the time at which the stone makes contact with the plane in the plot. (The time is displayed in the upper-left corner of the Adams/View window.) Use this to answer Question 1 in the Workshop 5, Review section, page WS5-16. f.Click the reset tool. e a b c d f

Step 7. Create a Point Trace of the Projectile Motion To create a point trace to view the trajectory of the projectile during an animation: a.Set No Trace to Trace Marker. b.Right-click the empty text box that appears, select Marker, and then select Browse. c.From the Database Navigator, select Stone.cm. The marker name should appear in the text box. d.Click the Play tool. e.As the projectile is simulated it should now trace its motion. f.Close the Animation Controls dialog box. e b d c b a f

Step 8. Find the Horizontal Displacement To find the horizontal displacement: a.Right-click a blank area inside the R_displacement stripchart, point to Plot: scht1, and then select Transfer to Full Plot. b.Adams/PostProcessor replaces Adams/View. c.Select the Plot Tracking tool. d.Because you want to know the displacement when the stone makes contact with the plane, move the cursor over the plot until the value of X is equal to the time at which contact was made. e.Note the value of displacement, Y. Use this value to answer Question 2 in the Workshop 5, Review section, page WS5-16. f.Compare this value of Y to the results given in the closed-form solution, which is shown in the Workshop 5, Review section, page 17. g.Click the Adams/View icon to return to model. a b d c e g

Step 9. Save Your Work To save your work (such that the file contains not only the model information, but also the results and plots): a.From the File menu, select Save Database As. b.In the File Name text box, enter projectile, and then select OK. c.Adams/View creates a binary file that contains not only the model information but also the results and plots. d.If you want to further explore the model, as suggested in the next section, leave the model open. Otherwise, proceed with the next step. e.Exit Adams/View. b b a

Step 10. Optional Tasks Save your work before performing these tasks. Do not save your work after performing these tasks. If you must save the model after performing these tasks, give the model a different name. To follow the stone during an animation: a.Zoom in on the stone. b.From the Results ribbon, select Animation Controls. c.Now change the reference frame while animating. d.On the Animation Controls dialog box, change Fixed Base to Base Part. Select the part to which you want to fix the camera. e.Go to the Adams/View online help and look up the Animation Controls dialog box to read about the other functionality available.

Workshop 5, Review Workshop Questions 1.At what time does the stone encounter the plane? _____________________________________________________ _____________________________________________________ 2.What is the range, R, of the projectile? _____________________________________________________ _____________________________________________________ 3.If a part’s initial velocity conflicts with a system constraint, which will take precedence during a simulation? _____________________________________________________ _____________________________________________________ 4.What modifications would be necessary to convert the stone into a pendulum? _____________________________________________________ _____________________________________________________

Workshop 5, Review (Cont.) Adams Results for Range –R = 3180 mm (can vary slightly depending on several factors, most likely the sampling rate.) Closed-form solution for Range –The analytical solution for R, the range covered by the projectile, is as follows: