3 Projectile motion. Experiment objectives: Experiment introduction:

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1 3 Projectile motion Experiment objectives: 1. Understand the independence of the motion in the horizontal and vertical direction for projectile motion 2. Calculate the horizontal and vertical components of a velocity vector 3. Calculate the horizontal and vertical travel for projectile motion 4. Cultivate the habit of keeping all experimental data in a well-organized manner Experiment introduction: Projectile motion Projectile motion is a form of motion in which an object is launched near the earth's surface, and it moves along a parabolic trajectory under the force of gravity only. Of course, in reality there exists air resistance, but for some cases, such as small objects with relatively low velocity, air resistance is negligible. Projectile motion is a 2-dimensional motion, which can be separated in the horizontal and vertical direction for independent analysis and calculation. For objects in projectile motion, the only force, gravity, exists in the vertical direction, so the only acceleration exists in the vertical direction as well. Therefore, if we break down the curved projectile motion into vertical and horizontal, the vertical is free fall motion, and the horizontal is motion of uniform velocity. To facilitate the following discussion, horizontal is denoted as the x direction; vertically upward is denoted as the +y direction. For the horizontal, if we know the starting position x i and the x component of the initial velocity v i, x, the final position x f is x f = x i + v i, x t (1) where t is the flight time. Similarly, for the vertical, if we know the starting position y i and the y component of the initial velocity v i, y, the final position y f is y f = y i + v i, y t 1 2 g t2 (2) where g = 9.81m/s 2 is the gravitational acceleration of the earth. Please note that the sign of each term in Equation (2) is critical for calculation. Based on the motion shown in Figure 1, since we already chose vertically upward as the +y direction, v i, y is positive, and the acceleration term is negative. In this experiment, you need to assign correct sign to each term accordingly based how you choose the positive direction. Page 1

2 For an object in projectile motion, as shown in Figure 1, its velocity vector can be decomposed to x and y components with trigonometry. If the velocity vector makes an angle θ above the horizontal, the components are v x = v cos(θ) v y = v sin(θ) (3) y v y vԧ θ v x Figure 1: The parabolic trajectory of a projectile motion and decomposition of the velocity vector. Initial velocity In this experiment, we will roll a racquetball down a track, as shown in Figure 2, and determine where it lands on the floor. After the ball leaves the track, its motion is projectile motion. Therefore, its exit velocity at the end of the track is the initial velocity of the projectile motion. We can place a smart gate at the end of the track to measure the magnitude of the exit velocity; and the launch angle θ can be obtained using trigonometry. As seen in Figure 2, one just needs to measure the three sides of the dashed triangle, and use trigonometry formulas either cos(θ) = adjacent/hypotenuse or sin(θ) = opposite/hypotenuse to calculate the angle θ. Tilted track x θ Racquetball Figure 2: The parabolic trajectory of a racquetball rolling off a tilted track Page 2

3 Exploration: During the Exploration, roll a racquet ball down a tilted track on the lab table, and 1. Calculate its landing spot on the floor 2. Experimentally measure the landing spot and compare it to the calculated value 3. Repeat steps 1 and 2 with at least 2~3 different tilt angles and at least 2~3 different exit speed Exploration grade: 20 points Please draft one or two sentences along with your measurement data and/or calculation results to answer the following questions. Some of the questions may appear in the post-lab quiz. Your instructor will randomly check your answers. 1. How many different angles and exit speeds have you tried? 2. When you compare the calculated and experimental landing spots, how close are they? 3. It is usual that difference exists between calculated and measured results. Is there a trend for the difference? i.e. is the measured landing spot consistently shorter or longer than the calculated value? Or does the difference appear random? Please also present the following to your instructor for a grade: 1. The positive direction you picked for calculation. 2. The Equation (2) with correct signs of each term based on your choice of positive direction 3. Calculated and measured landing spot for all trial runs, with corresponding exit speed, tilt angle and difference between calculated and actual landing spots. 4. Relevant calculation. Please note that points will NOT be marked down if any of the above is wrong; however, points will be deducted based on the following guideline. More than half of the materials are missing, illegible and/or poorly organized; results cannot be understood. Exploration notes: No deduction Some but less than half of the materials are missing, illegible and/or poorly organized; efforts have to be made to understand the results. Everything is legible and well organized; instructors can easily understand the results. The figure below shows the equipment setup for this experiment. You can place two meter sticks on the track to keep the ball rolling along the central axis. Smart gates racquetball Track To capture the exit speed, place the smart gate as close as possible to the track end. Also adjust the gate height accordingly to capture motion. Page 3

4 Connect the smart gate to its cable, then to your computer through the USB Link, as shown below. Check the pins in the smart gate plug and socket; forcing the plug in will damage the pins. Smart gate Application: In the Application part, your instructor will use a projectile launcher to eject a ball at a given initial speed v i = 3.12~3.22m/s but at a randomly assigned launching angle to your group. You need to determine the landing range through calculation. Inform your instructor once you have confidently calculated the landing point. Your instructor will launch a ball to compare your calculation to the true landing point and determine your Application grade. Application Grade: 20 points Please present your measurement data, relevant calculation and the determined mass to your instructor for a grade, which will be determined based on the following guideline: The true landing spot is outside of the ±3.0cm ±5.0cm ±7.0cm ±9.0cm ±11cm > ±11cm calculated landing range. Points Additionally, points will be deducted based on the guideline below No deduction Some but less than half of the materials are missing, illegible and/or poorly organized; efforts have to be made to understand the results. More than half of the materials are missing, illegible and/or poorly organized; results cannot be understood. Everything is legible and well organized; instructors can easily understand the results. Page 4

5 Lab 3 Report Rubric writing abstract The abstract of a technical document serves as a summary, which presents the work done, the results achieved in the complete document. It is usually one short paragraph, and does not include mathematical equations, footnotes, references, graphics, or tabular material. In other words, an abstract briefly summarizes what has been achieved, what method has been used, and how it was done; and the language of an abstract should not be technically specific so that readers of general background can easily understand it. In the report for this lab, please write an abstract, which will be graded using the following rubric (The rubric is adapted from the abstract requirement of a physics journal, Applied Physics Letter). The sample abstract attached may be helpful. Format Item 0 points 2 points Paragraph spacing The abstract is not double spaced. The abstract is double spaced. Abstract length The abstract is either too short or too long. The abstract is one paragraph of no more than 250 words. Font Non-standard font used for report. Regular Times New Roman font of size 12 is used for abstract. Grammatical tense Lab activities are not reported in past tense. All lab activities are reported in past tense. Content Item 0 points 3 points Lab topic The lab topic is not summarized. The lab topic is briefly summarized. (What physics did you work on in this experiment?) Lab results The results are not summarized. The results are summarized. (What quantities did you compare in this experiment, how did they compare?) Lab method The lab method is NOT described. The lab method is described. (How did you determine the results?) Language Informal language with more than 8 grammar errors Formal language with fewer than 3 grammar errors Don t forget to attach a copy of this rubric to your lab report, otherwise 5 points will be marked down. Page 5

6 Sample with comments: (The abstract below came from the scientific journal Applied Physics Letters.) What is the new technique? What is the method to verify the new technique? the results obtained with the new technique were consistent with those of other approaches. The mechanical properties of ultrathin films synthesized by atomic layer deposition (ALD) are critical for the liability of their coated devices. However, it has been a challenge to reliably measure critical properties of ALD films due to the influence from the substrate. In this work, we used the laser acoustic wave (LAW) technique, a non-destructive method, to measure the elastic properties of ultrathin Al 2 O 3 films by ALD. The measured properties are consistent with previous work using other approaches. The LAW method can be easily applied to measure the mechanical properties of various What has been achieved? There is challenge for traditional approaches, an easy alternative technique is found to solve the challenge. Page 6