# Experiment of acceleration down a slope

### Introduction

If an object moves in a variable velocity way, it will have acceleration which was used to describe the rate of change of velocity (Lowe & Roance, 2000).

a = v / t

The acceleration is uniform if the velocity changes the same at same interval of time.

If the velocity of the body increases from u to v in a period of time t, then the acceleration a is:

a = change of velocity / time taken = (v-u) / t (Pople, 2000)

Accelerations are equal at any slope of any velocity-time graph.

If a ball (has mass) fall down a slope, then the acceleration could be calculated from the distance the ball travelled and the time it rolls. The equation is written like this:

S = ut + ½ at2

(a is the acceleration, u is the initial velocity, S is the distance and t is the time)(Duncan, 2002)

The u would equal 0 if the ball is starting from rest, the equation is written like this:

S = ½ at2

The aim of this experiment is measuring the relationship between S and t2 to investigate uniformly accelerated motion and calculate the acceleration.

### Method

At the beginning, the slope which was 80 cm was set up at an angle in order to take a minimum of 2 seconds, but the length of the slope was not long enough, so the longest distance was 0.8 m. Next, on the slope, six points at different length were signed from the top to the end of the slope. The lowest point was 0.3m to the end of the slope and the intervals between each two points were 0.1m. After this step had been done, the time t taken from rest for the ball was measured from the top of the slope through a distance S to one of the marks on the slope. The time t was measured three times in order to ensure that the results were as accurate as possible. Different distances were repeated ant the values of S and t were recorded.

### Results/Findings

The results of the six measurements are shown in the figure 2. Column1 shows the distance measured in meters. Columns 2, 3 and 4 shows the time measured in seconds which the ball takes from the top of the slope to the end. Column 5 shows the average value of time and the column 6 shows T².

L(m) |
Tٕ(s) |
T2(s) |
T3(s) |
Ave. of T(s) |
T² (s²) |

0.8 |
2.40 |
2.35 |
2.00 |
2.25 |
5.06 |

0.7 |
2.12 |
2.05 |
2.18 |
2.12 |
4.49 |

0.6 |
2.20 |
1.80 |
1.90 |
1.97 |
3.88 |

0.5 |
1.74 |
1.69 |
1.67 |
1.70 |
2.89 |

0.4 |
1.60 |
1.40 |
1.50 |
1.50 |
2.25 |

0.3 |
1.35 |
1.40 |
1.10 |
1.28 |
1.64 |

### Discussion

L(m) |
T²(s²) |
a(m/s²) |

0.8 |
5.06 |
0.32 |

0.7 |
4.49 |
0.31 |

0.6 |
3.88 |
0.31 |

0.5 |
2.89 |
0.35 |

0.4 |
2.25 |
0.36 |

0.3 |
1.64 |
0.37 |

The figure 3 shows the relationship between the L (m) and T² (s²). The acceleration is equals to 2S/t². The average of acceleration is 0.34 m/s². The figure 4 contained a line which is showing a line which is almost linear shows the relationship between the T^2 and the distance, but the line still has some points which are not fit for the graph. These accelerations are not equal with each other. That means there are some errors happening in this experiment, such as resistance of air and the coarseness of the slope, but the resistance is too small that it would not cause too much trouble. Besides, some errors were made by people themselves. Some wrong manipulations can also make the results wrong. For example, the time which is measured by people is not really exact. The time will be longer or shorter then it should be. Besides, if the experiment can be taken for several people, then they can get more than one series of result. Moreover, the experiment can be taken as many times as people can. Then the result should be more exactly.

Another reason for the errors is that the displacement might be longer then it should be. The ball might not run in a straight line so the distance is longer and the time the ball takes would be longer. Therefore, the results might be getting some trouble.

### Conclusion

The ball was moving with constant acceleration which was equal to 0.34m/t². The figure 4 has proved that the distance is proportional to the square of time. Within the errors in this experiment, the object is move with a uniform acceleration. To make the results better, the researchers can measure many times and use an electronical stopwatch to measure the time the object taken. The best way to solve the time question is using two sticks which are smooth and glossy. The sticks should be parallel with each other. This method would help to avoid the distance problems.

### References

Duncan,T. (2000). Advanced physics. London: Hodder Murray.

Lowe,T.L. and J.F.Rounce(2000). Calculation for A-level Physics (5th Ed). Cheltenahm: Nalson Thornes.

Pople,S. (2000). Advanced Physics though diagrams. Shanghai: Oxford University Press.