The value of K can be calculated from Slop = 4T2/k.
By plotting the above equation g is already involved from which can be calculated. The value of g can then be calculated from Hooks Laws equation for the spiral balance.
The equation g = Kb/m
Where: K = spring constant (k)
m = mass of the bob (kg)
b = length (m) of the spiral spring with mass (l) less the length of the spiral spring without the mass (lo).
b = (l-lo) m.
Results
Table 1: Time (s) taken for 20 swings of spiral spring balance
The value of each swing was obtained by dividing the average values of 20 swings by 20. The results of the experiment (Table 1 above) showed that time period (T) depends on the length of the string and mass have no effect on the time period of the pendulum. As the length of the string was increased the time period also increased.
Fig. 1 The plot of mean values of T2 (s) of 20 swings of spiral spring balance against mass of bob (kg).
The plot of T2 against distance (m) Fig. 1 above produce a straight line indicating that acceleration is constant.
Fig. 2 The plot of Mean and Standard Deviation
The values of mean and standard errors are below 0.002 within the expected range. This means the experiment was successful.
Calculations
The plot of T2 on vertical axis against l (m) on the horizontal axis as in fig. 1 above produced a straight line through the origin since T2=4π2xl/g with the gradient equals to 4π2/g. Hence the acceleration due to gravity g = 4π2/the gradient of the graph.
The gradient of the graph was calculated by dividing the change in ∆y values against change in ∆x values giving the gradient in m/s2
From fig. 1 the value of slop = 4.8729 m/s2
The acceleration due to gravity g = (4π2/4.8729) m/s2
g = 8.1016 m/s2
Discussion
The acceleration due to gravity on earth is widely accepted to be equal to 9.81ms-2 or 10 m/s2. The result of this experiment gave the value for the acceleration due to gravity of 8.1016 m/s2. The difference of the value of the acceleration due to gravity obtained from this experiment to the accepted value could be due to a number of reasons.
One of the major reasons for this difference in values could be due to sideways movement of the pendulum. The pendulum, when swung, was not always fully going in a horizontal plane, but there was also movement in the vertical plane. This could have caused acceleration of the pendulum to be lost due to this sideways motion.
The measurement of distance, counting of the 20 swings, starting and stopping of the stopwatch were done manually which could have introducing errors in the system and giving incorrect values of time period.
However the values of mean and standard errors are below 0.05 within the expected range. This means the experiment was successful despite the above conditions which could have introduced errors in the system.
If the experiment were to be performed again, longer distance (l) would be used since the time period (T) depends on the length (l) of the string. This could provide more time in counting the oscillation other than when the length of the string is short producing quick oscillation increasing risk of errors in counting time period.
