A tilted plane as a gravitational field model

Abstract

Gravitational models have been widely used to study the effects of fields on particle motion. The advantages of such models are: (1) They are often easier or cheaper to construct and use than the system which they represent. (2) Particle motion is readily seen and may be photographed. (3) Events lasting for a fraction of a microsecond as, for example, with electrons moving in electrostatic fields, may be demonstrated in models as events which take a few seconds. The article describes the use of a tilted plane as a two-dimensional, uniform gravitational field. It has been used successfully as a sixth-form physics experiment to demonstrate the motion of projectiles fairly close to the Earth over a limited range. Thus it shows the motion of artillery shells (ignoring air resistance) but not of artificial satellites or long-range rockets, for which a simple uniform field model is not valid.

Trajectory of an object sliding across an incline

“…The result in figure 2(b) was obtained by launching the top in an approximately horizontal direction. The x, y coordinates could be fit accurately with cubic functions, giving x = 0.064 + 1.158t − 1.889t 2 + 1.103t 3 and y = 0.255 + 0.086t − 1.566t 2 + 1.292t 3 over the time interval 0 < t < 0.6 s. The accelerations in the x and y direction therefore varied with time, with a x = −3.78 + 6.62t and a y = −3.13 + 7.75t.…”

“…Several experiments have been described in this journal involving motion of a ball that rolls across an incline [3][4][5]. Golfers are familiar with the problem since a golf ball tends to follow a curved rather than a straight line path when rolling on a sloping green.…”

Trajectory of a ball on an inclined plane

“…which describes a parabola. Several papers have described this result [1][2][3][4][5], although the effects of friction tend to complicate the problem. Nevertheless, it is essential to include friction when calculating the acceleration of a ball that rolls straight down an inclined plane, as explained in R Cross most introductory physics textbooks.…”

“…If it is projected at an angle as shown in figure 1, then its path is essentially parabolic, in much the same way that a ball follows a parabolic path when it is thrown at an angle in the air. In that respect, an inclined plane provides a more convenient method for studying trajectories, since the coordinates of the trajectory can be measured on tracing paper, or on misted glass or with a video camera [1][2][3]. In the air, the main force on the ball is the vertical gravitational force, mg. Air resistance is usually negligible at low ball speeds.…”

Projectile motion on an inclined misty surface: I. Capturing and analysing the trajectory

“…The projectile, which is a steel ball, slides and leaves a trail as it passes. Although there have been many diverse studies on the subject of projectile motion in physics education literature (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14]), we are not aware of any student experiment that uses a similar technique.…”