# Gain in Kinetic Energy And Momentum Of A System.

Extracts from this document...

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.

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.

Conclusion

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.

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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