15 “Study of the flight distance-angle of departure relationship”

Laboratory work 2 “Study of the flight distance-angle of departure relationship”

Equipment:

1) ballistic laboratory gun;

2) measuring tape with centimeter scale;

3) two or three sheets of writing paper and one sheet of carbon paper;

4) scotch tape.

Theory.

When firing a projectile over a horizontal surface at different angles to the horizontal, the range of the projectile is expressed by the formula

From this formula, it follows that when the launch angle of the projectile changes from 90 to 0°, the range of its flight first increases from zero to some maximum value, and then again decreases to zero. The range of the projectile is maximal when sin2a has the greatest value (=1). This dependence in this work should be verifiedexperimentally by means of the ballistic gun shown in Fig. 13.1.

The gun is a spiral spring (1) with a rod along the axis, mounted on a bracket (2) with a protractor (3). On the rod is placed a special ball (4), which has a hole that fits around the rod. Afterplacing the ball, the spring is compressed and hooked in place so that the ball is behind the trigger at the base of the spring. If you push the protruding part (5) of the trigger, the ball is released and under the force of the spring moves along the rod in a given direction.

The magnitude of the initial velocity(launch velocity) the ball (v₀) is assumed to be the same for all experiments

On the table where the ball lands a piece of carbon paper should be fixed in place with two pieces of scotch tape.On top of this should be taped in place a piece of copy paper. When the ball hits the paper it will leavea mark.

Procedure

1. Construct a table in your notebook to record your results, measurements, and calculations (Table. 1).

Table 1

2.         Familiarize yourself with the launching device andhow it works.

3.         On the edge of the table secure the launcher with a clamp and use a protractor to orient the launcher at an angle of 45°. Without placing the paper, make a test shot and note approximately where the ball lands. Fix the strip of paper to the table so that when shooting at angles between 0° and 45° the ball falls at its far end, and tape a sheet of copy paper over the carbon paper (to mark where the ball lands).

4.         After mounting the gun at angles of 20, 30, 40, and 45°, take three or four shots at each angle. Mark each trace left by the ball on the copy paper by the carbon paper with the angle of launch.

5.         Move the launcher slightly to the side, and set it at angles of 50, 60, and 70°, and again take three or four shots. Mark each trace left by the ball on the copy paper by the carbon paper with the angle of launch.

6.         Measure the average distance of the ball’s flight for each angle. Record your measurements in the table.

Questions for analysis:

1.         At what launch angle should the flight range of the ball be the greatest?

2.         What are the launch angles at which the flight range is approximately the same? What is the sum of these angles? How does this agree with the formula that determines the range?