Projectile Motion Experiment Objectives: Understand The Inde

Projectile Motionexperiment Objectives1 Understand The Independence

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 xi and the x component of the initial velocity vx,i, the final position xf is xf = xi + vx,i t (1) where t is the flight time. Similarly, for the vertical, if we know the starting position yi and the y component of the initial velocity vy,i, the final position yf is yf = yi + vy,i t + 0.5 a t^2 (2) where a = 9.81 m/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, since we already chose vertically upward as the +y direction, vy,i is positive, and the acceleration term is negative. In this experiment, you need to assign correct sign to each term accordingly based on how you choose the positive direction. For an object in projectile motion, as shown in Figure 1, its velocity vector can be decomposed into x and y components with trigonometry. If the velocity vector makes an angle θ above the horizontal, the components are vx = v cos(θ) (3) vy = v sin(θ) (4) where v is the initial velocity magnitude. In this experiment, we will roll a racquetball down a track, and determine where it lands on the floor. After the ball leaves the track, its motion is projectile motion. The exit velocity at the end of the track is the initial velocity of the projectile motion, which can be measured using a smart gate. The launch angle θ can be obtained using trigonometry by measuring the sides of the triangle formed by the track setup. This setup allows for calculating the launch parameters to predict the landing point, facilitating analysis of projectile motion principles through experimentation. The overall goal is to understand the independence of horizontal and vertical motion, and how to use initial velocity and launch angle to predict projectile landing points accurately in idealized conditions.

Paper For Above instruction

Projectile motion embodies a fundamental aspect of classical mechanics, illustrating how objects move under the influence of gravity. This experiment aims to reinforce understanding of the independence of horizontal and vertical components of projectile motion. By decomposing initial velocity into horizontal and vertical components, students can observe how each component influences the overall trajectory, which follows a parabolic path. The key principle is that horizontal motion occurs at a constant velocity, unaffected by vertical acceleration due to gravity, which causes vertical displacement. This separation of motions allows for independent calculation of each aspect and demonstrates the applicability of trigonometry and kinematic equations in predicting an object’s landing point.

In the experimental setup, a racquetball is released from a track at a known initial velocity and launch angle. The exit velocity is measured using a smart gate, and the launch angle is calculated through trigonometry by measuring the track dimensions. The theoretical trajectory is then computed based on these initial conditions, considering the equations of motion for horizontal and vertical components. The horizontal displacement is derived from the initial velocity and flight time, which can be calculated from vertical motion parameters, accounting for initial vertical velocity and acceleration due to gravity.

The experiment provides an empirical platform to test the principles of projectile motion. By conducting multiple trials with varied launch angles and initial velocities, students compare predicted landing points with actual measurements. Results typically show a close match, affirming the validity of the model, though some discrepancies may occur due to air resistance or measurement errors. Analyzing these differences enables discussion about the limitations of idealized assumptions and the importance of precise measurement techniques.

This experimental approach emphasizes key physics concepts: the independence of motion components, the use of trigonometry in resolving vectors, and the application of kinematic equations. Such understanding is fundamental in many real-world applications, from sports to engineering, where predicting projectile trajectories is necessary. The experiment also cultivates skills in experimental data organization, analysis, and critical thinking about physical models versus real-world conditions.

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