Practical Investigation into the Horizontal motion of a Projectile

Safety

With an experiment of this nature there are not many safety factors to consider. However, I ensured that I conducted the experiment where nobody could slip on the paper on the floor, and attached all apparatus such clamps to the table securely.

Hypothesis

To create a successful mathematical model of this scenario, I will not consider the air resistance of the particle.  Air resistance would not be very significant due to the fact that I am using a ball bearing of fairly high density.  This is exemplified by the equation:

F=ma

Where:         F = Force (N)

                 m = Mass (Kg)

                a = Acceleration (ms^-2)

However, the trials from higher starting points up the ramp may be affected.  This will be due to the fact that the ball is moving faster, thus creating more air resistance in comparison to it’s mass and momentum.

This illustrates that providing that mass is constant, force is proportional to acceleration.

The particle begins its measured journey at the highest point of the projectile path.  At this point the particle's vertical velocity is zero.  However it has a downward vertical acceleration of g, 9.8ms^-2.

Mathematical Diagram:

                   

Known quantities are:        a = 9.8ms^-2

                                s = 24m

                                u = 0ms^-1

Where:                         a = Acceleration

                                s = Distance (Height, H)

                                u = Initial Velocity

Using:                   s = ut + ½ at^2

               

0.8 = 0 x t + ½ x 9.8 x t^2

               

t^2  = 1.6/9.8  

                       = 0.163265306

                

    t  = 0.404061017

                       = 0.40 seconds

The time taken to reach the floor is 0.40 seconds.  This will be the same for all trials due to the fact that the ball bearing is always moving downwards with the same velocity, it is just moving horizontally simultaneously.

Horizontal motion must be considered to find the horizontal distance traveled.  There is no horizontal acceleration once the particle leaves the ramp, so the horizontal velocity will remain the same from that point.

So:                Distance Traveled = Horizontal Speed x Time

It would have been extremely difficult to measure the horizontal speed of the projectile accurately.  However, we can calculate this using the distance results.

Results

Using 0.100m as an exemplar:

                        Horizontal Speed = Distance Traveled

                                                         Time

                                                 =  0.273

                                                 0.40

                                                =  0.6825

                                                =  0.68ms^-1

Analysis

Both graphs illustrate a strong relationship between the starting height and the average distance of the projectile.  At first glance the relationship doesn’t look particularly strong.  However, if you discount the last three results, the points are in an almost completely straight line.  These differing results may have been a result of the air resistance becoming more significant with the increase in speed.  The only way of avoiding this is to either use a ball bearing with the same mass but smaller surface area, or to conduct the experiment in a vacuum.  Another factor that may have affected the results is the 2cm length of table that the ball bearing rolls across before falling.  As the ramp is not curved, there will be a rapid change of direction.  Much like the air resistance, this shouldn’t make sufficient difference to disguise any trends.  However, as the speed of the particle increases, the opposing force of the table will also become larger.  This may result in the ball bearing’s motion being disrupted.  For example, it may bounce, which would cause the time of flight to vary.

Conclusion

Overall, the investigation has successfully proved my thesis that there is a relationship between the horizontal motion of a projectile, and it’s vertical starting height on a ramp.  This was also supported by the mathematical equations of motion.  Though under some circumstances it is possible to neglect factors such as air resistance, I would definitely consider it If conducting the experiment again.