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Projectile Motion Goal: To better understand projectile motion by predicting where a projectile will land. Lab Preparation To prepare for this lab you will want to make sure you understand the basic concepts behind projectile motion: specifically what happens in the x and y directions and how do these relate to one another. You should also review and understand how to do projectile motion problems in which the projectile is launched horizontally. Equipment A photogate timing system will be used to measure the speed of a ball. The photogates consist of an infrared light emitter and detector pair pointed at each other (this is often used on garage doors as a safety device). An electrical signal from a photogate indicates if the infrared beam is being blocked by an object that is passing through the photogate. A computer can record the amount of time it takes an object to travel from one photgate to a second photogate. Each photogate is also equipped with a red light emitting diode (LED) on top of the gate that lights up indicating when the gate is blocked. Procedure In this lab you will let a ball roll down a track to give it a horizontal speed before it leaves the table (see Figure 1). Once the ball leaves the track it will be in projectile motion and we can predict where the ball will land. Your grade on this lab will be based in part on how successful you are in putting the projectile in the tube - so be careful in your measurements and calculations. Figure 1

I. Velocity measurement Using the distance between the photogates and the measured time the ball takes to travel between the gates, you can find the average velocity of the ball at the bottom of the track. Distance. First you need to determine the distance between the two photogates. The final segment of the track is horizontal so you want to set the photogates up on that part of the track. The photogates should be at least 10 cm apart. Careful consideration is needed to find the true distance between the photogates. Consider Figure 2. Photogate Photogate Track Locate ball when each gate is triggered d far m apannm Figure 2. As the ball enters the first photogate its leading edge breaks the beam and starts the timer, and as it enters the second gate it stops the timer. Thus, if one measures d, and d, they can determine the true distance between the photogates. Once you have a measurement open the Gate2Gate file and follow the instructions to enter this distance. Time. Next, you need to determine the time it takes for the ball to travel between the two photogates. First click on the "Start Collection" button. The computer and photogates are set up to start timing when the first photogate is blocked. The computer will stop timing when the second photogate is blocked. Release the ball from the top of the ramp to check that things are working properly. You will want a reliable technique for letting the ball go from the top of the track. Once you have a good technique make ten trials to find the speed of the ball at the bottom of the track. Find your average speed and calculate the percentage difference between your maximum and average velocity. Make sure you do not move your track for the rest of the experiment.

II. Predicting projectile motion If you are given a tube of height L, how far from the track's end (R) should you put it for the ball to be caught in the tube when it is launched from the top of the track? You need to develop a relationship that finds the distance R in the above diagram. Your relationship should have variables that you can measure. So it should have v (the average speed that you found above), H (which you can measure), L (which will be given on the tube), and g (which is a constant). So basically, this is a horizontal launch projectile motion problem that has vox (the same as found above) and 4y (which is L-H) as your knowns. Once found, show your general formula to your instructor. If it is correct, your instructor will give you a tube of length L to use for the next part. Calculate the predicted range R of the projectile for and also for . IV. Alignment and testing the prediction Having a prediction of how far away to place the tube, there still remains a critical issue of placing the tube in exactly the right location. These tubes (as you may notice) are not very wide. Even if the tube is at the correct distance, a slight misplacement to either side from the correct location and the ball can scatter off the edge of the tube and miss. Aligning direction. By making preliminary launches without the tube present you can determine the direction the ball travels. Launch the ball from the top of the ramp and note roughly where it first hits the floor. Near that location puta sheet of white paper and tape it in place. Put a sheet of carbon paper on top of the paper and launch the ball twice more. Lift up the carbon paper and you should have two nearly overlapping marks showing where the ball landed. Repeat this process, but launch the ball from about 1/3 the maximum height of the ramp. You should now have two points that define the direction the ball travels.

Distance. By using a plumb bob, you can locate the point on the floor directly beneath the end of the track. Put a piece of tape on the floor below the plumb bob and mark the location beneath the end of the track (Be careful not to move your track). This point can be used as an origin for measuring distances. Now, mark the predicted location for your tube with a paper bull's-eye taped on the floor. Testing your prediction. Put the tube at the predicted location to catch the ball. You have five attempts to launch the ball into the tube. Your lab instructor should witness every attempt until the ball goes into the tube. If your first attempt misses you can do one of the following. a) Continue launching without any changes. b) Re-visit your calculations and/or measurements to find any errors. If there was an error, state clearly what the error was. Once you have a new corrected position change the placement of your tube and launch again. c) Move the tube at most one centimeter from your original prediction before trying again. Continue launching until the ball goes into the tube. After each miss you should record how much you missed by and what corrections you made for the next launch When finished with your lab return the tube to your lab instructor. Remove any paper, tape, and any marks you have made. Leave your equipment neatly organized on the lab table. Homework 1. In part I you are asked to measure the distance between the photogates and that the measured value is at least 10 cm. Why is this important? In other words, what is so significant about the measurement having a value of 10.1 cm compared to 9.8 cm? 2. Determine the velocity (magnitude and direction) of the ball just as it reaches the tube. Make sure you show all of your work and draw a diagram showing the velocity just when it reaches the tube.