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Gain in Kinetic Energy And Momentum Of A System.

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Introduction

Gain in Kinetic Energy And Momentum Of A System

Experiment

Below is a diagram of the experiment.

Here, a trolley of mass 1kg was released at the top of a slanted runway. To pull the trolley down the runway a falling mass was attached to the trolley. Card of 200mm length was also attached to the trolley so that it would break a light gate further down the runway. This enabled the maximum velocity of the trolley and the falling mass to be found.

With the first test the mass was varied in 100g intervals with the height of the mass kept constant at 80cm.

Here I would expect that with the more weight pulling the trolley the kinetic energy of the trolley will increase and so the velocity of the trolley will increase also.

Overleaf is a results table for this experiment.

Weight in g

Velocity1 mm/s

Velocity2 mm/s

Velocity3 mm/s

Velocity4 mm/s

Average mm/s

100

1286

1129

1161

1167

1185.75

200

1817

1589

1614

1486

1626.5

300

1878

1850

1757

1874

1839.75

400

2116

1988

2018

2045

2041.75

500

2283

2430

2294

2240

2311.75

600

2387

2548

2407

2392

2433.5

700

2564

2497

2472

2418

2487.75

800

2601

2670

2635

2597

2625.75

Here the graph produced a curve with a positive correlation. This showed that there was not a linear relationship and that it could possibly be a y = x² graph.

...read more.

Middle

Force (Newtons)

Time (Seconds)

1

1.33

2

0.98

3

0.83

4

0.75

5

0.69

6

0.65

7

0.62

8

0.60

Here the graph produced a curve with a negative correlation. This was expected as the more weight pulling down on the trolley, the faster the trolley will move and therefore the shorter the time taken for the mass to reach the ground.

To calculate the impulse acting on the system in Newtons seconds I used the following formula:

Impulse Acting = F X t

Where F is the force acting on the system and t is the time in seconds.

The momentum gain of the system should be equal to the impulse acting on the system and so this allowed me to check the values found.

To calculate the momentum gain of the system I used the following formula:

Momentum Gain = v[M+m]

Below is a table of all of the calculated data from the first test.

Force (Newtons)

Time (Seconds)

Impulse Acting on System

Momentum Gain of System

1

1.33

1.33

1.30

2

0.98

1.96

1.95

3

0.83

2.50

2.39

4

0.75

2.99

2.86

5

0.69

3.46

3.47

6

0.65

3.92

3.89

7

0.62

4.36

4.23

8

0.60

4.80

4.73

Here the impulse acting on the system and the momentum gain of the system values were very close to each other which helped to validate the results.

...read more.

Conclusion

7">50

1586

1617

1594

1623

1605

40

1762

1441

1524

1892

1654.75

30

1193

1285

1460

1259

1299.25

20

1016

1052

1041

1027

1034

10

686

751

677

699

703.25

Here, the graph produced a curve with a positive correlation. The curve showed that as the height increases, the rate of change of speed of the trolley decreases.

To calculate the work done for this second test the following formula was used:

Work Done = F X S

Where F is the net force and S is the distance the mass was dropped.

To calculate the kinetic energy gain of the system the following formula was used:

K.E. Gain = ½ v²[M+m]

Below is a table of this calculated data for the second test made.

Height in cm

Speed in mm/s

Work Done in Joules

K.E. Gain of System

Time

Force

80

1649.4

14.97

156.8

3.74

4

70

1627.4

14.00

137.2

3.50

4

60

1443.8

12.96

117.6

3.24

4

50

1294

11.83

98

2.96

4

40

1331.8

10.58

78.4

2.65

4

30

1045.4

9.17

58.8

2.29

4

20

831.2

7.48

39.2

1.87

4

10

564.6

5.29

19.6

1.32

4

Conclusion

By calculating the different data from the results using a spreadsheet I have been able to find numerous relationships.

These include:

  • Distance is proportional to Time squared
  • Kinetic Energy is proportional to the mass of the falling load
  • The Kinetic Energy is proportional to the Gravitational Potential Energy
  • Weight of falling load divided by Net Force is proportional to Acceleration squared.

...read more.

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