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Accelerationi is defined as the rate of change in velocity, where it can be calculated of how quickly the velocityi of an object is changing and its direction, over time. Therefore, being a vectori quantityi (The Physics Hypertextbook, 2019) from rest it is expected that a vehicle/object will be iaccelerating, as its velocityi will be changing from 0 (rest) to its ifinal velocityi. This data can be justified by measuring the vehicles displacementi over time period, to then determine its averagei iacceleration.

Tickeri timersi can be employed to measure the motioni of a vehicle because they are useful for measuring over short time intervals.

At every fiftieth of a second, the ticker timer releases pressurei and vibrates, creating an indentation/dot on the ticker timer tape. In order to measure the displacementi using this process, the ticker timer tape is threaded through the ticker timer and attached to the trolley which is in imotion. (Fod.infobase.com, 2019)

The idistance between the dots determines the speed of the object.

Constant spaces represent a continuous speed or increasing distances designate acceleration taking place. The displacement of each time interval is measured from the origin point to the specified time interval (spaces between each dot). Using the data, a displacement- time graph can be drawn, allowing methods of calculation to be used in order to find the iacceleration in ireference to the graph.

The car will be iaccelerating because its ivelocity is increasing from rest. Therefore, the graph is expected to have an increasing slope, iindicating the velocity is increasing.

This will include an ipositive, ilinear slope on a velocity-time graph, implying that there is a positive iacceleration. Using this info, the iaverage iacceleration of the car can be icalculated, either from the equation:

a=(v-u)/t

iWhere u is the iinitial ivelocity, found by calculating the igradient m=(y2-y1)/(x2-x1) of the itangent at the y-intercept, v is the final velocity, calculated by the igradient of the itangent towards the end of the graph, and t is the total time taken to reach its final velocity. Another way to idetermine iacceleration is through the equation of the graph, by doubling the A value of the quadratic value:

y=Ax^2+Bx+C

The aim of this investigation is to idetermine the iacceleration of a trolley. By using iticker itimers to measure the idisplacement of the vehicle over time and formulate displacement-time graphs via icapstone and excel, to calculate iacceleration using the two methods earlier stated.

**Materials**

- Car/Trolley
- Ticker timers
- Ticker timer tape
- Sticky Tape
- AC power adapter and extension cords
- Ruler

To begin the practical, the equipment was gathered, and set up. Ticker timers were connected to Power points and placed alongside the itrolley, whilst ticker timer tape was idistributed and ithreaded through the ticker timer. One end of the ticker tape was then iattached to the ivehicle with sticky tape and the other, iheld by the participant. It is vital that the ticker tape is isecured to the object and there are no twists in it, in order to ensure ieven imovement of the tape, also for an iaccurate ireading. Once in iposition the iticker itimers were turned on and ran for a couple of seconds before the ‘driver’ iaccelerated from irest, setting the vehicle in imotion.

As the car iaccelerated, iiparticipants then let go, for the tape to continue threading through the ticker timer. At the end of this step, the ticker timers were switched off and the tape was collected. It is important to note that before the car was in motion, the path is clear of any objects which may harm the driver or car, such as buildings, pedestrians etc. (Risks are outlined below in the safety risk assessment).

To record the results participants used rulers to measure (in mm) between 0-0.38 second at 0.02 increments, from the origin each time, using the dots created by the ticker timer. The origin can be located, where a mass of close dots occur indicating the origin, this represents the time before the car/trolley came into motion. This information was collected and plotted into a table and displacement measurements were converted into meters for calculation purposes. The displacement (m) and time were then graphed using a scatter plot graph via excel, and a trend line was created. Using these results calculations were used in order to determine acceleration of the vehicle.

A comprehensive risk assessment is crucial to mitigate potential hazards associated with the vehicle in motion and its surroundings. Ensuring the vehicle is roadworthy, maintaining clear paths, and the alertness of the driver are paramount safety measures.

**Table: Displacement of a Trolley Over Time**

Time (s) | Displacement (mm) | Displacement (m) |
---|---|---|

0 | 0 | 0 |

0.02 | 4 | 0.004 |

0.04 | 8 | 0.008 |

0.06 | 12.5 | 0.0125 |

0.08 | 17.5 | 0.0175 |

0.10 | 24 | 0.024 |

0.12 | 30.5 | 0.0305 |

0.14 | 37 | 0.037 |

0.16 | 46 | 0.046 |

0.18 | 54 | 0.054 |

0.20 | 62.5 | 0.0625 |

0.22 | 73 | 0.073 |

0.24 | 83 | 0.083 |

0.26 | 95 | 0.095 |

0.28 | 103 | 0.103 |

0.30 | 119 | 0.119 |

0.32 | 131 | 0.131 |

0.34 | 144 | 0.144 |

0.36 | 154 | 0.154 |

0.38 | 169 | 0.169 |

Based on the displacement-time graph generated, two methods were employed to calculate acceleration:

**Direct Calculation from the Graph**:- Using the slope of the tangent lines at the beginning and end of the graph.
- Equation: a=tv−u

**Quadratic Equation Method**:- Deriving acceleration from the quadratic equation of the graph.
- Equation: y=Ax2+Bx+C, where acceleration, a=2A

It was determined from the data gathered the car/trolley was accelerating at roughly 1.33ms^(-2), where two methods of calculation from the ticker timer graph (displacement-time) gave the same answer. These figures validate the velocity of the car is increasing, which increases the displacement of the vehicle over time, displaying a positive linear trend. This is granted the ticker timer was able to give an accurate calculation of the acceleration of the vehicle. The graph almost perfectly alluded to the trend line, as seen on the displacement time graphs with few points being above and below with a high R^2 value. This suggests that there were some irregularities to the data, which could have been affected by several different variables.

Nonconformities in the data, could be viable due to errors such as calculation error, inaccuracy of measurement, ticker timer accuracy or environmental factors such as bumps on the surface of the slope, friction, and drag implemented on the car. Human error becomes the most prominent factor in measurement and calculation error, where the use of a ruler can create many errors in measurement easily, such as movement, affecting the accuracy of the measurements from the origin points. Calculation errors such as converting mm to m and can add significant irregularities to the results as well as reading the measurements wrong. Hand drawn tangents leaves a very small window to be accurate, especially considering the graph contains many decimals. These limitations of human accuracy and lack of accurate/modern equipment impacts the accuracy of results, by including potential errors to the results.

Additional factors that impact the accuracy of the data collected can be drawn from environmental issues, which is inclusive of opposing forces to acceleration – e.g. air resistance/drag, weight and surface friction. These opposing forces can impact the rate of acceleration, where the force exercised to put forth motion, are slowed down by gravity, inflicting surface friction. These opposing forces can impact the rate of acceleration, where the force exerted to put forth motion, are slowed down by gravity, inflicting surface friction, and air causing drag. In such a short period of time, drag can become such a major influence to the results, which could explain the slight deviations to the data, especially during initial points of movement. Surface area such as bumps in the ground can also cause issues, where sudden movements to the ticker tape, can result in incorrect plotting of points, which affects the measurement stage of recording the results.

This Practical is also very limited to the apparatus used. Ticker timers are now very outdated, where there are huge technological advancements that bring new developments to machinery used to portray motion. Also using ticker tape can be quite unpractical, as it can get jammed through the ticker timer, and the ticker timer can miss a lot of movement between each fiftieth of a second. Instead of a ticker timer, other equipment can be used to organize more accuracy in results. LiDAR and RADAR are examples that can effectively measure the displacement of an object , over a certain period of time, for example LiDAR (Light Detection and Ranging) travels at the speed of light, where lasers continuously bounce back and forth from sensor to object, in order to record its displacement (Oceanservice.noaa.gov, 2019) over time. RADAR uses very similar techniques, though instead of lasers it uses radio waves to determine the position of an object. These devices can be a lot more accurate; this is because the recording gap is reduced significantly, therefore human error is limited as an effective variable.

To prevent these errors from occurring, the method of measurement should avoid the use of ticker timers and introduce more advanced means of technology to find the desired measurements and calculations. Otherwise, to ensure all measurements are accurate, and results are fair, class averages can be used, rather than individual results to limit the range in data. Larger scopes of data can also help to reduce variation in results, as the increase in data allows for further analysis and reading of results. This also allows a larger set of data that includes pure acceleration, where shorter periods can be inclusive of the driver slowing down to rest.

The concluding results show that the acceleration of the car/trolley was 1.33ms^(-2), which almost reflects the expected results of a positive acceleration in the form of a parabolic displacement-time graph. The Data claimed to be not quite accurate, showing some discrepancies to the expected results, this data was most likely affected by human error and environmental factors. These can be avoided with the use of more advanced technology, or through larger data sets or averages. Although there were plausible limitations, ticker-timers and the use of displacement graphs to determine acceleration, posed as reliable to determine an approximate value of acceleration.

- Fod.infobase.com. (2019). [online] Available at: https://fod.infobase.com/HTTP/180533.pdf [Accessed 5 Jun. 2019].
- Isaac Physics. (2019). [online] Available at: https://isaacphysics.org/concepts/cp_eq_of_motion [Accessed 5 Jun. 2019].
- Oceanservice.noaa.gov. (2019). What is LIDAR?. [online] Available at: https://oceanservice.noaa.gov/facts/lidar.html [Accessed 5 Jun. 2019].
- The Physics Hypertextbook. (2019). Acceleration – The Physics Hypertextbook. [online] Available at: https://physics.info/acceleration/ [Accessed 2 Jun. 2019].

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