3B Scientific UE1030400 Inclined Launch Owner’s Manual
- July 18, 2024
- 3B Scientific
Table of Contents
UE1030400 | INCLINED LAUNCH
EXPERIMENT PROCEDURE
- Measuring the width of the trajectory as a function of the throwing angle and the initial velocity.
- Calculating the initial velocity from the maximum width of the trajectory.
- Point-by-point plotting of the “parabolic” trajectory as a function of the throwing angle and the initial velocity.
- Verification of the principle of superposition.
OBJECTIVE
Plotting the “parabolic” trajectories point by point
SUMMARY
The motion of a ball that is thrown upward at an angle to the horizontal in
the earth’s gravitational field follows a parabolic curve whose height and
width depend on the throwing angle and the initial velocity.
The curve is measured point by point using a height scale with two pointers.
REQUIRED APPARATUS
| Quantity | Description | Item Number |
|---|---|---|
| 1 | Projectile Launcher | 1002654 |
| 1 | Clamp for Projectile Launcher | 1002655 |
| 1 | Vertical Ruler, 1 m | 1000743 |
| 1 | Set of Riders for Rulers | 1006494 |
| 1 | Barrel Foot, 900 g | 1002834 |
| 1 | Pocket Measuring Tape, 2 m | 1002603 |
BASIC PRINCIPLES
According to the principle of superposition, the motion of a ball that is thrown upward at an angle to the horizontal in the earth’s gravitational field is the combination of a motion at a constant speed in the direction of throwing and a gravitational falling motion. This results in a parabolic flight curve, whose height and width depend on the throwing angle α and the initial velocity v0.
To calculate the theoretical flight curve, for simplicity we take the center of the spherical ball as the origin of the coordinate system, and we neglect the frictional drag of the air on the ball. Thus the ball retains its initial velocity in the horizontal direction
and therefore at time t the horizontal distance travelled is
In the vertical direction, under the influence of the gravitational field, the ball is subjected to gravitational acceleration g. Therefore, at time t its vertical velocity is
and the vertical distance travelled is
The flight curve of the ball has the form of a parabola, as it conforms to the equation
At time t1 given by
the ball reaches the highest point of the parabola, and at time t2 given by
it is again at the initial height 0. Thus, the height of the parabola is
and the width is
In the experiment, the flight curves of a ball are measured point by point as a function of the throwing angle and the initial velocity, using a height scale with two pointers.
EVALUATION
The maximum width of all the flight curves, smax, is reached when the throwing angle α is 45°. From this maximum width, it is possible to calculate the initial velocity. By using Equation 9, we get
Fig. 1: Flight curves for the smallest initial velocity and different throwing angles, measured experimentally, and calculated theoretically with air friction taken into account
MECHANICS | TRANSLATIONAL MOTION | Inclined Launch
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