Projectile Motion. Equipment: Ballistic Gun Apparatus Projectiles Table Clamps 2-meter Stick Carbon Paper, Scratch Paper, Masking Tape Plumb Bob

Transcription

1 Purpose: To calculate the initial speed of a projectile by measurin its rane. To predict how far a projectile will travel when fired at different anles, and test these predictions. To predict what anle will produce the maximum rane for a projectile fired off the table onto the round, and test this prediction. Equipment: Ballistic Gun Apparatus Projectiles Table Clamps 2-meter Stick Carbon Paper, Scratch Paper, Maskin Tape Plumb Bob 1 of 7

2 Part I - Measurin Initial Speed Today you are oin learn about projectile motions by shootin miniature cannons all evenin. There are three thins that determine how far the projectile will o once it leaves the cannon: 1. The initial speed of the ball, written as v o, 2. The heiht of the launch point above the round, written as h, 3. The acceleration due to ravity,. Recall that is you drop a projectile from a heiht h, then the projectile will free fall, with distance and time related by: 1 h = t 2 2 Solvin for time t, you et: 2h t = Now if you fire the ball horizontally at a speed v o instead of droppin it, it will travel a horizontal distance R (for rane) iven by R = v o t, where t is the time from the free fall equation above. So if you fire a projectile horizontally from a heiht h, with a speed v o the distance it will travel is: 2h R = vo. Equation 1 Prelab question 1: Would increasin the heiht of the launch point from the round increase or decrease the projectile s rane? Why? Prelab question 2: Will increasin the projectile s initial speed increase or decrease its rane? Why? 2 of 7

3 Prelab question 3: Which would cause the rane to chane more: doublin the initial speed or doublin the heiht of the launch point? Show your reasonin. We can rewrite the equation 1 in a way that lets us calculate the initial speed by measurin the rane: v o = R Equation 2 2h We ll use this equation with the measurements you re about to take to determine the speed at which your projectile leaves the launcher Follow these steps to make your measurements: 1. Clamp the cannon to the ede of your table with the muzzle pointin away from the table. Make sure that the cannon is completely horizontal. Also make sure that you aren t pointin toward any humans. 2. Your cannon is sprin loaded, with three different settins. Toniht, you should use the lowest settin. Load the projectile into the cannon by pushin it in until you feel a click. If it clicks twice, you have one too far! Fire the cannon by pullin up on the release lever, and pay attention to where the projectile lands. 3. Tape down a piece of scratch paper on the floor where the projectile landed, and tape a piece of carbon paper, carbon side down, on top of the scratch paper. Now when you fire the cannon the projectile will strike the carbon paper and make a mark. 4. Load and fire the cannon ten times. 5. Use a plumb bob to mark the spot on the floor directly below the cannon muzzle. 6. Pull up the carbon paper, but leave the scratch paper on the floor. Use the twometer stick to measure the distance from the launch point (that you found with the plumb bob) to each mark on your scratch paper. Record your measurements in the table below. Trial Number Rane (R) Trial Number Rane (R) Calculate the averae rane of the projectile. Averae R Meters Uncertainty R (max min)/2 meters 3 of 7

4 8. Measure the heiht of the cannon muzzle above the round. Heiht meters 9. Use equation 2 alon with your answers from steps 7 and 8 to calculate the initial speed of the projectile. Show your work here V 0 Meters/Second Part II - Predictin and Measurin Rane for Different Launch Anles Durin part one, we were launchin the projectile from the table onto the floor. We were also launchin it horizontally each time. If, we launch the projectile so that it lands on the table instead of the floor, we can use this equation to calculate its rane. We can even predict how far the projectile will o when we fire it at an anle instead of just shootin straiht. In this case, the Rane equals the horizontal component of the velocity (v x ) multiplied by the time in the air, so R = vxt Understandin how v x and t relate to the firin anle q (theta) and the initial speed v o requires a bit of trionometry, so we ll leave out the derivation here. However, you can see that the time in the air also depends on the vertical component of the velocity, and the steeper the anle, the loner the projectile will spend in the air! However, there is a bit of a compromise, as the horizontal component of the velocity ets smaller with steeper anles. 4 of 7

5 The final equation for the rane as a function of initial velocity and firin anle is: 2 vo sin 2θ R = Equation 3 The symbol θ in this equation stands for the firin anle of the projectile. Without makin any calculations, what firin anle do you think will produce the lonest rane? 1. Usin equation 3 and your answer to question 9 in part I, predict the rane for several different anles and record them in the column labeled Predicted R on the table below. Show your work for at least one anle here. Before you calculate sin(2θ), do a quick check of your calculation skills and make sure that sin(30 o ) = 0.5. If not, then your calculator needs to be set on deree mode. θ Predicted R 2. Point the cannon so that the projectile will land on the table. Set the anle to fifteen derees and fire once to see where the projectile lands. 3. Tape down a piece of scratch paper on the table where the projectile landed, and tape a piece of carbon paper, carbon side down, on top of the scratch paper. 4. Fire the cannon three times. Lift up the carbon paper and measure the distance from the cannon muzzle to each mark on your scratch paper. Record your measurements in the table below. 5. Repeat steps 2-4 for all the other anles. 6. Calculate the averae rane for each anle and enter it in the final column 5 of 7

6 θ Rane Trial 1 Rane Trial 2 Rane Trial 3 Averae R 7. Copy the results from the last two tables into the table below, and calculate the percent difference between your measurements and your predictions for each anle. θ Predicted R Averae Measured R Percent Difference 8. How close were your measurements to your predictions? 9. What anle produced the maximum rane? Was it the anle you predicted 6 of 7

7 Part III - Launchin from the table to the floor at an anle The last thin we ll do toniht is turn the cannon around so that it is firin onto the floor aain. Instead of firin it horizontally, we will fire it at an anle. What launch anle do you think will produce the maximum rane? Why? 1. With the cannon facin away from the table, launch the projectile at an anle of 35 and measure the rane. Repeat for launch anles of and 55. θ Rane 2. Which anle had the hihest rane? Does this match your prediction? 3. Now that you have finished the lab, write approximately two pararaphs discussin what you did, how you did it, what you learned and how you would interpret your results. 7 of 7