Projectile Motion with Examples in Physics I Study Guide | PHYS 244, Study notes of Physics

Download Projectile Motion with Examples in Physics I Study Guide | PHYS 244 and more Study notes Physics in PDF only on Docsity! Physics 244 Projectile Motion Introduction Previously, you studied motion in one-dimension by analyzing the vertical motion of a bouncing ball. Now you will examine both vertical and horizontal components of motion. For Part I of the experiment you will use the World In Motion software to examine two-dimensional projectile motion of an object thrown in the air. You will investigate the relationship between acceleration, velocity and position of the horizontal and vertical components. For Part II, you will track the motion of a parachute falling and observe the effect of air resistance and its relationship to the terminal velocity of the parachute. Materials World In Motion software, Excel Reference Giancoli, Physics 6th Edition: Chapter 3, sections: 5, 6, 7 Theory Part I: Theoretically, it is known that the motion in various directions is separable, i.e. one can analyze the vertical component separately from the horizontal component of the motion. If we throw an object on the surface of the Earth, then the downward acceleration should equal acceleration of gravity since it is in free fall. We should have no acceleration in the horizontal since gravity acts in the downward direction and thus: and (1) 2m/s8.9−=−= gay 2m/s0=xa Since acceleration is the slope of the velocity vs. time graph, the velocity versus time of the vertical and horizontal motions have different slopes. For horizontal velocity, the slope of the velocity vs. time graph should be 0 m/s2 so we expect a horizontal line. For the vertical velocity, the graph is a line with a slope of − 9.8 m/s2. Now we can write equations for the two different components of projectile motion. We know that the vertical velocity equation must have the slope of gay −= , therefore: gtvv yy −= 0 (2) Since the horizontal acceleration is zero: constant0 == xx vv (3) For the position vs. time graph of vertical motion we get the familiar equation: 200 2 1 gttvyy y −+= (4) Since the horizontal velocity is constant, the equation for the position vs. time must be linear since acceleration is zero and thus the squared term drops out. The slope of this graph is the horizontal velocity. We can then write the equation as tvxx x00 += (5) You will use these equations to analyze the video of a projectile in Part I. Part II: An object with a large surface area and low density behaves differently than objects in free fall because it is subject air resistance. For a falling object like a parachute, air resistance acts counter to the acceleration of gravity. A velocity vs. time graph will show increasing velocity over time until the point at which the velocity becomes constant, because the downward force of gravity is balanced by the upward air resistance. This velocity is referred to the terminal velocity. The force of air resistance is proportional to the square of the velocity of the parachute: airF α (6) 2v Initially, the air resistance is small but as velocity increases it will increase to a point where it equals the acceleration due to gravity. At that point, the net force on the object is zero and velocity is constant. This constant, maximum velocity is known as the terminal velocity and is related to the force of air resistance by a constant,κ , that depends on the shape of the object: mgvF termair == κ (7) Procedure Part I: Two-dimensional motion of a projectile 1. Click on the World in Motion icon on your screen; you may need to go to the Start bar and select Programs>World in Motion. 2. Once you have opened World in Motion, select Video Analysis to open the video file. Your instructor will tell you where it is located and which file to select. 3. Now, step through your video by hitting Step. Determine the best starting point at which to begin taking data. For example, if the object is launched from someone's hand, make sure you don't take data until after it has left the hand. Note the frame number and select Min Frame, enter the frame number for the starting point. Step through the video until