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Name Lab Date ID Lab Group TA Name Day of the Week: M T W R F Partners' Last Names EXPERIMENT 3 Projectiles SAFETY: Be careful not to fire the projectile when anyone is in the line of fire and not paying attention. However, do have someone in your group prepared to stop the projectile after it has hit the ground a few times to insure nobody else slips on a rolling, plastic ball. Always wear your safety glasses when firing the projectile. Objective: 1. To model motion in two dimensions using the concept of vector quantities. 2. To determine the initial speed and angle of a projectile by measuring the horizontal displacement and the time of flight. Apparatus: Pasco apparatus, computer, and interface. Theory: The velocity and acceleration of an object are both vector quantities. Once the velocity and the (constant) acceleration have been reduced to their respective components, an equation of motion can be independently written for each of the x and y directions. This allows for the current position of an object, with an initial position, initial velocity and acceleration, to be calculated at some time, t, later. These general equations are 2 2 1 0 0 2 2 1 0 0 ( ) ( ) y t y v t a t x t x v t a t y y x x ? ? ? ? ? ? By definition, an object in projectile motion is subject to acceleration due to gravity alone. Thus there is no acceleration in any other direction. The equations of motion of a projectile are therefore given by (with ay = -g) x x v t ? 0 ? 0x 2 2 1 y y0 v0 t gt ? ? y ? These can be used to find the initial velocity components (assuming an angle of ?0 counterclockwise from the +x-axis) t x x v v x 0 0 0 0 cos ? ? ? ? gt t y y v v y 2 0 1 0 0 0 sin ? ? ? ? ? as well as the initial velocity and the launch angle, if t, x, x0, y, and y0 are measured. 2 0 2 0 2 0 x y v ? v ? v x y v v v v 0 0 0 0 0 0 0 cos sin tan ? ? ? ? ? Question 1: An object has a velocity of 5.0m/s and is travelling 30º above the +x-axis. Find the components of velocity. Question 2: An object has an acceleration of 15m/s2 directed 25º clockwise from the +y-axis. Find the components of acceleration. Question 3: What assumptions can be made (if any) about the value of the following quantities for an object in projectile motion: a) vx b) vy c) ax d) ay Relevance to the Experiment: In this experiment, the time-of-flight, t, is measured by the computer, and x, x0, y0, and y are measured with a metre rule. Using the equations above, v0 and ?0 are found. PRELAB CHECKPOINT Mark: __________ Get your TA’s initials before proceeding onto the next part. ____________ Procedure: Part 1 – Data Collection (First Launch Angle): 1. Make sure that nothing is plugged into the two USB ports on the front or right side of the computer. 2. Turn on the computer and allow it to boot up. Log-on as Guest. 3. Start the DataStudio program (the icon is on the desktop) and open the DataStudio workbook C:\64-140\Experiment 3 WB.ds. 4. Look at the workbook pages by clicking the triangular arrows on each side of the page number at the bottom of each page. The workbook will show you the apparatus and the names of the parts that you will use. 5. Connect the two photogate heads to one photogate port, and connect the time of flight pad to the second photogate port. 6. Plug both photogate ports into the USB links, and plug the USB links into the USB ports. 7. Clamp the base of the projectile launcher to the edge of the table, pointing it towards an open space. 8. Set the launcher to fire approximately horizontally, and measure the angle using the plumb bob and angle scale. Note this angle. ? 0 = __________ ± __________ 9. Measure the height above the lab floor of the launch position of the ball. This will be indicated on one side of the launcher. Enter this value below as y0 . 10. Measure the height of the centre of the ball above the ground when it is placed on the timeof-flight pad. This is most easily done with the pad on the table. Enter this value as y. 11. Estimate the errors in the height measurements. y0 = ? y = ? 12. After checking that nobody is in the way, test fire a ball using the middle range position on the launcher to see where the ball lands, and place the time-of-flight pad at this position. Test fire again to ensure that the ball lands near the centre of the pad. 13. Click the Start ( ) button, fire the ball, note exactly where the ball lands on the pad, and click the Stop ( ) button. 14. Measure the horizontal distance travelled by the ball and enter this value as x ? x0 in the table below, together with t and v0 which are measured by the computer and shown in the workbook table. 15. Repeat these measurements three times. 16. Calculate the average values for x ? x0, t and v0 for the chart and use these averages to fill in the section that follows. 17. To calculate the error values, use the given excel spreadsheet. Shot # x ? x0 v0 t 1 2 3 4 Average Standard Deviation Standard Error y ? y0 = ? ?0 ? y?y = ____________ t x x v x 0 0 ? ? = x v ? 0 = gt t y y v y 2 0 1 0 ? ? ? = y v ? 0 = Derive the error formulas for v0x and v0y using (1.7) from the Lab Manual Intro document. Verify the error in v0x and v0y using the excel sheet provided. 2 0 2 0 2 0 x y v ? v ? v = v0 = ____________ 0 ? v = v0 = __________ ± __________ x y v v 0 0 0 tan? ? = ? 0 = ??0 = ? 0 = __________ ± __________ Question 4: Compare this value of ? 0 with the value you measured setting up the launcher. Do the two values agree within experimental error? Explain any disagreement below. CHECKPOINT 1 Mark: __________ Get your TA’s initials before proceeding onto the next part. ____________ Part 2 – Data Collection (Second Launch Angle): Set the angle of the launcher to approximately 30º. Measure the angle. ? 0 = __________ ± __________ Repeat all the measurements of Part 2. Measure the height of the first photosensor above the ground. y0 = ? Make four shots using the short range firing position and measure the quantities as before, entering the data in the table below. To calculate the error values, use the given excel spreadsheet. Shot # x ? x0 v0 t 1 2 3 4 Average Standard Deviation Standard Error y ? y0 = ? ?0 ? y?y = t x x v x 0 0 ? ? = x v ? 0 = v0x = __________ ± __________ gt t y y v y 2 0 1 0 ? ? ? = y v ? 0 = v0y = __________ ± __________ 2 0 2 0 2 0 x y v ? v ? v = v0 = _________ 0 ? v = v0 = __________ ± __________ Question 5: Compare this value of v0 with the average value of the computer measurements in the chart from Part 1. Do the two values agree within experimental error? Explain any disagreement below. x y v v 0 0 0 tan? ? = ? 0 = ??0 = ? 0 = __________ ± __________ CHECKPOINT 2 Mark: __________ Get your TA’s initials before proceeding onto the next part. ____________ Part 3 – Data Collection (Third Launch Angle): Set the angle of the launcher to approximately 60º. Measure the angle. ? 0 = __________ ± __________ Repeat all the measurements of Part 2. Measure the height of the first photosensor above the ground. y0 = ? Make four shots using the short range firing position and measure the quantities as before, entering the data in the table below. To calculate the error values, use the given excel spreadsheet. Shot # x ? x0 v0 t 1 2 3 4 Average Standard Deviation Standard Error y ? y0 = ? ?0 ? y?y = t x x v x 0 0 ? ? = x v ? 0 = v0x = __________ ± __________ gt t y y v y 2 0 1 0 ? ? ? = y v ? 0 = v0y = __________ ± __________ 2 0 2 0 2 0 x y v ? v ? v = v0 = _________ 0 ? v = v0 = __________ ± __________ x y v v 0 0 0 tan? ? = ? 0 = ??0 = ? 0 = __________ ± __________ CHECKPOINT 3 Mark: __________ Get your TA’s initials before proceeding onto the next part. ____________ Question 6: A ball is kicked from a rooftop that is 5m above a level soccer field. The ball travels 20m horizontally before it hits the ground. This could be shown by the diagram below. If this entire process takes 5 seconds to occur, indicate on the diagram the position of the ball 1s, 2s, 3s and 4s after the ball was first kicked. Be sure to justify your answer below. CHECKPOINT 4 Mark: __________ Get your TA’s initials before submitting the report and leaving the lab room. ___________