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Making sense of data.

Extracts from this document...

Introduction

Coursework - Making Sense of Data

Introduction

The method used to collect the data was to fire projectiles from a launcher into a sandpit. The distance the projectile travelled was measured. For each projectile the angle of the launch was varied from 15 to 70o, from the horizontal. Twelve different angles were tested and three repeat readings were taken at each angle.

Five ball bearings with different diameters were used. The ball bearing was fired using a spring mechanism into a sandpit, which was at the same height that the ball bearing was launched from. The distance travelled was measured using a meter ruler.

Apparatus Diagram

Plan

  • From the raw results the mean distance travelled was calculated, giving an average reading using all the data.
  • From the diameter of the ball bearing the volume of the ball bearing was calculated - 4/3 * pi * radius3.  From this the mass can be calculated (using mass = density * volume).
  • The energy the spring provided was given as 0.1J. Using the mass this allowed the initial velocity to be calculated (initial velocity =sqrt (KE/0.5m)).
  • The initial velocity was divided into horizontal and vertical components using the sine and cosine rules combined with the angle of launch.
  • Knowing that the displacement vertically is zero, gravity is -9.8N/Kg and the initial vertical velocity the flight time can be worked out: time=2(initial velocity/gravity).
  • Assuming no air resistance the distance traveled should equal the time taken multiplied by the initial horizontal velocity. This allows a theoretical prediction of the distance travelled, which can be compared to the actual distance measured.
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Middle

θcosθ

This graph should also fall on a straight line. This is because U2 = (2*kinetic energy)/mass and by substituting it into the equation from graph 2 you get:

                   S =       (4Ke)        * sinθcosθ

mass *gravity

Therefore plotting S(y) and 1/mass (x) the gradient will be     4ke     *  sinθcosθ,

        Gravity

So if the angle remains constant the gradient will be constant, giving a straight line.

3. Distance-1/mass

e.g.

1/mass

4.  Estimated distance and actual distance against angle for a given diameter of ball bearing

This graph will show the difference between the actual results and the calculated distance using the energy (0.1J). It will be useful because, if the energy is correct, it will show how other factors including air resistance and measuring errors affect the results. Therefore the figures for estimated distance will probably be larger, i.e. the curve will be above the actual results as there is no air resistance.

Sample calculation

Launch Angle (o)

Angle (r)

Diameter of ball bearing(m)

Distance 1(mm)

Distance 2(mm)

Distance 3(mm)

15

0.26183

0.01

1395

1412

1418

Using the result:

  1. Average distance = (1395+1412+1418)/3 = 1408.3mm
  1. Volume of ball bearing = [4/3*Pi*r3]

     = 4/3 * 3.142 * (0.01/2 – radius)3

= 5.24E-07

  1. Mass of ball bearing     = density * volume

                                           = 8020 * 5.24E-07 = 0.004Kg

  1. Initial Velocities=
  •  Initial velocity = √(0.1/0.5*0.004) = 6.9ms-1
  •  Initial velocity vertically = 6.9 * sin0.262 = 1.786 ms-1
  •  Initial velocity horizontally = 6.9 * cos0.262 = 6.666 ms-1
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Conclusion

o and then decreasing again. However the actual distances are below what was expected. This may have been due to a number of factors (described below) or air resistance, which caused drag on the projectile, reducing its horizontal velocity.

Errors

        All the measurements recorded have a small degree of inaccuracy. For example, the distance the projectile travelled was measured with meter rulers to the crater formed in the sandpit, and the accuracy of this measurement is about +/- 1-2mm. This would not affect the results considerably as it is only a small percentage error - 2/2000 = 0.1%. Other small inaccuracies may have occurred with measuring the diameter of the ball bearing (+/- 0.1mm), adjusting the launch angle (+/- 0.5o) and aligning launcher at the same height as the sandpit (+/- 2mm). I feel the biggest error was in measuring the energy of the spring. This is probably why the calculated distance the ball bearing should have travelled is a lot further than the actual distance travelled. If this was the correct energy

provided by the spring air resistance would have reduced the distance travelled by almost 50%! (2380/4859*100 = 49%). Considering the experiment was conducted in a classroom without any wind this seems a very large value.

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