|
|
This is only a preview of the paper
Click here to register and get the full text.
Existing members click here to login
|
|
|
Pearls in Air 1. Abstract 2. Introduction 3. Data Analysis 4. Conclusions Abstract After receiving 3 photos on droplets acting as projectiles, I took measurements of horizontal and vertical displacements and scaled them up to real values. Next, the two sets of measurements were plotted against time to examine the relationships between the variables. The horizontal velocity was calculated by finding the gradient of the best fit line for the graph. It was: The acceleration of the droplets (taken upwards) was found by taking the second derivatives of the functions of the 3 graphs; also by plotting vertical displacement against time squared and doubling the gradient. The latter method was used to find the following acceleration: Additionally, the initial vertical velocity was found by considering the symmetrical nature of the parabola that the water takes. Combining the 2 perpendicular components produced an angle and magnitude for the initial velocity. This was found to be: Then, the information calculated was put to further effect by using it to plot a ‘simulation’ of the water’s path. To do this, I deduced the equation of a parabola. Introduction 1. The Experiment This consisted of a jet of water projected from a nozzle at a certain height and angle of elevation. A vibration generator that was connected to the pipe had a frequency of 44.8Hz. Strobe lighting was shone on the jet of water. This light had the same frequency as the vibration generator, and so gave the effect of a frozen projection of water. In the background was a 5cm square grid. This allowed me to take reasonably accurate readings from the 3 photos subsequently taken. 2. Aim The aim of the investigation was to use the raw data to find out more about the nature of the experiment. This would include vertical and horizontal velocities, the acceleration of free fall on the droplets and the initial velocity of the water. 3. Theory The drops of water move along a parabolic path. The motion vertically and horizontally can be considered separately, since these components do not affect each other. Vertical motion Horizontal motion Both components Vertically, the droplets are being accelerated, due to the force of gravity acting downwards on their masses. The vertical velocity of a droplet increases in magnitude at a constant rate. Horizontally, the force of gravity does not affect the motion, and so it has no acceleration. This means the horizontal velocity of a droplet is constant. The 2 perpendicular components can be combined to find the resultant motion, using Pythagoras and trigonometry.In general, Also likely to affect to motion is the resistive force called drag, which increases as the square of the velocity does. I predict that the horizontal motion will show constant velocity because there is no acceleration acting. I also predict that the vertical droplets will have varying velocities, but will accelerate downwards at approximately 9.81ms-2. This is because acceleration due to gravity pulls the drops towards the earth’s centre of mass. Data Analysis 1. Method First, the displacement of the droplets was taken directly from the photo. This was measured in mm about an origin, which was the crossing of the lines directly above the nozzle.
Approximate Word count = 2098
Approximate Pages = 8.4
(250 words per page double spaced)
|
|
|
|
|
|