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I will investigate the change of velocity and acceleration of a laterally moving object attached by a string and pulley to a dropped object, when the mass of the dropped object is changed.

Extracts from this document...

Introduction

Investigation on converting Gravitational Potential energy into horizontal and vertical Kinetic Energy

Investigation on converting Gravitational Potential energy into horizontal and vertical Kinetic Energy

 - Leszek Swirski


P – Planning

Aim

I will investigate the change of velocity and acceleration of a laterally moving object attached by a string and pulley to a dropped object, when the mass of the dropped object is changed.

Method

Apparatus

  • Trolley
  • Piece of Card
  • Runway
  • Weights
  • 2 Light Gates
  • Weights
  • Pulley
  • Computer
  • LogIt 9000
  • Insight Timing
  • Appropriate cables

Diagram

image00.pngimage01.png

Set up procedure

This is how I will set up the experiment:image02.png

  1. Set up the apparatus as above, with Light gate A at 45 cm from where the centre of the piece of card (not trolley) will start to move from, and Light gate B at 45 cm further.
  2. Make sure that there is enough space between the pulley and light gate B for the piece of card to go through the light gate. If not, move the starting point of the trolley back, and the light gates accordingly.
  3. Plug Light gate A and Light gate B into the LogIt, and plug that into the computer.
  4. Start up Insight Timing on the computer

Then I am ready to start

Fair Test

I will make this a fair test by limiting the key factors:

  • Weight of trolley – I will use the same trolley every time to ensure the same weight
  • Distance travelled – I will keep this constant by releasing the weights from the same height and releasing the trolley form the same place every time. I will also not move the light gates
  • Friction/Air Resistance – Unfortunately, these cannot be avoided, however they will be minimal due to the equipment used, and will be relatively constant as I will not change apparatus.
...read more.

Middle

0.43

0.76

0.06

0.80

1.21

0.44

0.91

0.07

0.91

1.19

0.40

0.69

0.07

0.91

1.32

0.40

1.04

0.08

0.97

1.38

0.37

1.10

0.08

0.97

1.41

0.37

1.19

0.09

1.01

1.47

0.36

1.30

0.09

1.02

1.46

0.36

1.22

0.10

1.02

1.48

0.35

1.29

0.10

1.11

1.53

0.34

1.23

Repeat 3

Mass

Velocity A

Velocity B

Time

Acceleration

kg

m/s

m/s

s

m/s/s

0.00

0.00

0.00

0.00

0.00

0.01

0.31

0.46

1.20

0.13

0.02

0.48

0.72

0.77

0.31

0.03

0.60

0.90

0.61

0.48

0.04

0.70

1.04

0.53

0.65

0.05

0.78

1.15

0.48

0.77

0.06

0.84

1.23

0.44

0.88

0.07

0.91

1.37

0.41

1.11

0.08

0.96

1.42

0.39

1.17

0.09

1.02

1.50

0.37

1.31

0.10

1.07

1.59

0.35

1.49

From these results I can work out an average set of results:

Mass

Velocity A

Velocity B

Time

Acceleration

kg

m/s

m/s

s

m/s/s

0.00

0.00

0.00

0.00

0.00

0.01

0.28

0.41

1.30

0.10

0.02

0.47

0.68

0.78

0.27

0.03

0.59

0.86

0.61

0.44

0.04

0.70

1.00

0.52

0.58

0.05

0.77

1.10

0.47

0.69

0.06

0.83

1.20

0.44

0.85

0.07

0.91

1.29

0.40

0.95

0.08

0.97

1.40

0.38

1.15

0.09

1.02

1.48

0.36

1.28

0.10

1.07

1.53

0.35

1.34

Analysis

There are several pieces of information that can be extracted from the above table. The first two are the changes in Velocity at points A and B when the mass increases. The second is the change in acceleration as the mass increases. Also these values can be compared to the theoretical to show how outside factors (like friction) have affected the results.

The first that I will look at is the two velocities.

Here, I have put on a graph the two point’s velocities against the changing mass. As you can see, the velocities both increase with the mass, however they increase less every time.

Also, it shows how the velocity at B, further on (therefore at a higher height) is larger than the velocity at A (at a smaller height).image07.png

Theory backs both these remarks. Firstly, I shall consider the height’s influence. The formula for the velocity (squared) is:

v2 = 2m2gh

        m1 + m2

As h increases, its position makes it increase the amount in the numerator, therefore directly increasing the velocity. Therefore, as B’s height is larger than A’s, the velocity at B will always be higher that A. A notable exception is when m2 = 0, as then the height will have no effect as the numerator, and therefore velocity will have to equal 0.

Secondly, I shall consider the influence of the dropping mass. In the formula, removing the influence of the m1

...read more.

Conclusion

image11.png

Much worse anomalies come on the graph of acceleration. Problems due to friction and air resistance are obviously present, as the real graph is below the theoretical graph; however the real line is also, for lack of a better word, ‘wobbly’. The unsteadiness of the line makes it difficult to identify which points are actually anomalous, however by drawing a straight line of best fit (also shown), I approximate these to be at 0.01, 0.08, 0.09 kg.image12.png

The increased size of the anomalies may be due to the fact that the acceleration is calculated by using three measurements, velocity at A, velocity at B and the time, all of which can have slight mistakes which add up.

If factors such as friction and air resistance could not be eliminated, it might have been beneficial to measure them instead, and adjust the final results accordingly. Therefore, as further work, it would have been helpful to find out the co-efficient of friction of the runway, i.e. find the force needed to move the trolley (measured using a Newton meter, by pulling the trolley along the runway) and divide this by the force exerted upon the trolley by the runway (this being its weight, 0.5 kg, multiplied by the gravitational constant, 9.81, making it 4.905 n). Air resistance could also be mesaured, by Stokes law which says that air resistance force is proportional to density of the air times the cross sectional area of the object times the square of the velocity of the object. image06.png

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...read more.

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