Procedure
Apparatus
- Trolley
- Two springs
- Force sensor
- Dynamics track
- Photo gate
- Mass bars
- Five pattern picket fence
- Computer with datastudio software
- Interface
Part 1
-
The interface was connected to the computer, and the data studio document P15 Prelab Oscillation.DS was opened up.
- The 1.2m dynamics track was then placed on a horizontal surface. In order the ensure that this dynamics track was horizontal, a spirit level was uses, and the adjustable feet of the dynamics track were adjusted until the spirit level showed that the track was exactly level. This needed to be done because if the track was on a slope this may interfere with results.
- The force sensor was connected to the interface and was mounted horizontally on a support rod and base. The trolley was placed on the dynamics track, and spring one was attached to it and the force sensor.
- The trolley was pulled 0.2m away from the force sensor, and the “tare” button of the force sensor was pressed, setting it to 0. In data studio, this was recorded as the 0 distance, and this value of 0 force was recorded by pressing the “start” button on the datastudio interface, in order for it to start recording data.
- This button changed to a “keep” button, and this was pressed in order to record the data. The trolley was pulled 2cm further away from the force sensor, and the “keep” button was pressed again. The trolley was now moved in 2cm increments, pressing the “keep” button each time, until it reached a distance of 24cm its starting position. Data was then stopped being recorded by pressing the “stop” button in datastudio. This was repeated for the other spring
- Using this data, a graph of extension against force could be created, in order to calculate the spring constant for each spring.
Part2
-
The photogate was connected to digital channel 1 on the interface. The datastudio document P15 Oscillation.DS was then opened up.
- End stops were placed on both ends of the dynamics track, and each spring was attached to one of these end stops. The other end of each spring was attached to the trolley, and the cart settled around the middle of the dynamics track. The five pattern picket fence was placed on top of the trolley, in order for it to break the photogate’s light beam.
- The photogate was attached to the photogate mounting bracket, and the photogate is aligned to the centre of the 2.5cm opaque band at the top edge of the trolley, so that this blocks the light beam created by the photogate.
- The trolley was then pulled 25cm from its equilibrium position. The “start” button on datastudio was now pressed, and the cart begins its oscillations, moving back and forth through the light gate. Datastudio now records the time for the picket fence’s opaque band to cut the light beam made by the photogate.
- After the cart has completed 8 oscillations, data recording is ended, by pressing the “stop” button on datastudio.
- The mass of an extra mass bar is recorded, and this part of the experiment is repeated for a range of masses.
Results
Part 1
Spring 1
Comparing the form of this line to:
Since the extension, x, is the x value of this graph, and the force, F, is the y value of this graph, it follows that:
Using this equation, the spring constant of this spring can now be calculated:
Spring 2
As shown before:
Calculating the Uncertainty in “k”
In order to calculate the uncertainty for each value for k, the LINEST function in excel was used.
Spring 1
Spring 2
Part 2
Mass 1 = 0.273112kg
Mass 2= 0.523828kg
Mass 3= 0.775805kg
Mass 4= 1.022271kg
Mass 5= 1.26856kg
Uncertainties
The reading uncertainty in each value can be taken as ±5x10-5 , because it is a digital timer used by the computer to time the oscillations. The random uncertainty is calculated for each value by taking the minimum value of the period and subtracting is from the minimum value, then dividing by the number of readings. In order to combine these values to provide a total uncertainty for the period, the equation is used, where Δx is the total uncertainty in the period, Δy is the random uncertainty and Δz is the reading uncertainty.
Mass 1
So the average period is:
Mass 2
Mass 3
Mass 4
As above, the reading uncertainty has become negligibly small compared to the random uncertainty, so the reading uncertainty can be taken as the total uncertainty in the period.
Mass 5
The reading uncertainty is taken as the total uncertainty again.
The theoretical period for each mass can now be calculated using the equation and this can be compared to the values obtained experimentally.
Mass 1
Experimental
Mass 2
Experimental
Mass 3
Experimental
Mass 4
Experimental
Mass 5
Experimental
Discussion
Conclusion
This experiment confirms Hooke’s law, F=-kx, because the graph of force against displacement exhibited straight line proportionality.
It also showed that the values for the actual period of the motion are very close to the calculated theoretical period.
Evaluation
This experiment can be seen as a success, with small errors and the experimental values obtained for the period of the motion were very close to the theoretical values calculated. The graph of force against displacement very closely resembles a straight line, so Hooke’s law is confirmed.
In order to ensure that the dynamics track sat exactly level, a spirit level was used and the adjustable feet of the dynamics track adjusted accordingly. This is because if the track had been on a slope, this slope would have affected results, leading to a less accurate experiment.
The results in part 2 of the experiment could have been improved by using less oscillations, because, particularly with the heavier masses, the last few oscillations were often significantly slower than the rest. This is due to friction, because if there were no outside forces, the trolley would oscillate at the same speed every time.
To increase the accuracy in part 1, the force readings could have been taken more often then every 2cm until 24cm. This would improve the accuracy of the graph slightly, but would not make a significant difference.
