3. Projectile Motion GOALS 1. Observe the general path of a projectile 2. Compare the times of fall for a projectile and an object in free fall. (Part A) 3. Determine how mass and horizontal speed affect the time of fall for a projectile (Part A) 4. Apply the equations of motion to the horizontal and vertical motions of a projectile (Part B) 5. Predict the horizontal range of a projectile (Part B) BACKGROUND A projectile is an object in motion that was given an initial thrust, and then is affected only by gravity. The path of a home run baseball is an example of projectile motion. In this lab we will use small, smooth objects, and air resistance will be negligible. Projectile motion will be analyzed by considering the horizontal and vertical motions separately. Your physics text probably has the relationship between displacement, initial velocity, time and acceleration: (Equation 3.1) d = Viniit + 2 at2 where d is the displacement, v, is the initial velocity, t is the time, and a is the acceleration. Horizontally, once a projectile is started, it moves at a constant speed and the acceleration is zero. In this case the last term in Equation 3.1 drops out: (Equation 3.2) horiz = Vhoriz where dis the horizontal distance, ,or is the horizontal velocity, and t is the time. Vertically, the projectile accelerates at the constant rate of gravitational 13acceleration, - 9.81 m/s2. While the initial vertical velocity is often not zero, in this lab it is. This eliminates one term in Equation 3.1 and it PROCEDURE becomes: Note: Both parts of this lab should be performed on a table or counter top. There needs to be about one meter of clear space on the counter (Equation 3.3) dver = 2 812 for the marble to roll across before it falls to the floor. where d is the vertical distance, g is the acceleration of gravity, and t is time of fall. Equation 3.3 can be solved for time by rearranging it and Part A [Qualitative) Figure 3.1 taking the square root. 1. Place a ruler near the corner of a table, so that (Equation 3.4) 1 2 = - 2d vert one end extends over the g edge of the table about 5 cm. Place one penny on (Equation 3.5) 2d vert the end of the ruler that g extends over the floor. In Part A of this lab you will discover how the times of fall for a Place the second penny on projectile and an object in free fall are related. In Part B you will work the table next to the ruler quantitatively with the two components of the motion. and about one penny's diameter from the edge of the table. See Figure 3.1. Materials and Equipment 2 . You will shove the ruler sideways to make both pennies fall to the Book* Stopwatch* floor at the same time. The penny on the ruler should fall straight Nickel or quarter* Tape, masking* down as the ruler moves quickly out from underneath it. The penny Pennies* (2) Tape measure, metric on the counter will shoot off the counter when the ruler hits it and Ruler* Tube, clear plastic, 15 cm then fall to the ground as it moves away from the counter. Steel sphere 3. Put one finger firmly on the end of the ruler that is on the counter so the ruler can pivot. With the other hand, apply a quick, but soft push against the side of the ruler near the penny, causing both pennies to fall to the floor. Which penny hit the floor first? 4. Repeat Procedure 3 several times with about the same force so you are sure of the results. What can you conclude about the time of fall for the two coins? How does a slow horizontal velocity affect the time of fall?5. Repeat Procedure 3 using more force on the ruler so that the coin 10. Using Equation 3.1 in the Background to calculate the horizontal will travel further horizontally. Which penny hits the floor first? velocity along the table top. Remember, this is also the horizontal Repeat this procedure several times with the greater force to be sure velocity as it falls through the air as a projectile. of the results. What can you conclude about the time of fall for the two coins? What affect does a faster, horizontal speed of the penny have on its time of fall? Answer questions 1 and 2 in the Results 11. Use the measurement of the height of the counter and Equation 3.5 section. in the Background to calculate the time of fall. 6. Place a coin of greater mass (nickel, quarter, etc) on the ruler and replace the penny on the table. Try the experiment again. Repeat 12. Use Equation 3.2 in the Background to calculate the predicted this several times. How does increasing the mass affect the time of range, (the horizontal distance along the floor measured from the fall? Answer questions 3 and 4 in the Results section. bottom of the counter). Part B [Quantitative] 13. Write an "x" on a small piece of masking tape and mark the spot on Note: You may need a partner for this activity. the floor that you just calculated. Now roll the steel sphere and see if it hits your predicted spot. Mark where the steel sphere landed, 7. Place the plastic tube on a book to form a ramp for the steel sphere and measure the distance from your prediction. to roll onto the table. Position the ramp so that the steel sphere can roll about one meter before falling to the floor. Secure the tube to the book and to the counter with masking tape. See Figure 3.2. About 1 m Stee Clear plastic sphere tube book Table or counter top Figure 3.2 3. Measure and record the distance the steel sphere will roll along the horizontal surface. . To release the steel sphere, place it on a teaspoon at the level of the tube, and gently tip the spoon to slowly put the steel sphere in motion. Time the roll along the horizontal table. Catch the steel sphere before it falls to the floor. Repeat this twice and average the horizontal rolling times.3. RESULTS, Projectile Motion Part B Part A Table 3.1: Horizontal rolling time along the counter top. 1. What can you conclude about the time of fall for the two coins? Trial Time, Seconds 2 3 2. How does a slower and faster horizontal velocity affect the time of fall? Average 5. Rolling distance along counter = cm = m 3. How does increasing mass affect the time of fall? 6. Use Result 5 and the average time from Table 3.1 to calculate the horizontal velocity. 4. What can you conclude about your observations for time of fall of the coins? 7. Height of counter = cm = m 8. Calculate free fall time from the height of the counter and Equation 3.5 from the Background. 199. Calculate predicted range from the horizontal velocity and the answer to Result 8, above. 10. Measure the actual range = m 11. Calculate the per cent of error