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Experiment to calculate spring constant of 2 springs

Extracts from this document...

Introduction

Experiment to calculate spring constant of 2 springs

This experiment is concerned with comparing the theoretical period of a trolley tethered between two springs and the actual value calculated by experimentation.

The theoretical period of the trolley can be calculated using the equation:

image10.png

Where m is the mass of the trolley and image11.png and image22.png are the spring constants of the two springs the trolley is tethered between.

In order to do this, the spring constants for the two masses must be calculated. This is done by attaching one of the springs to a force sensor and measuring the force at distances of regular intervals away from the force sensor. From this, a force against extension graph can now be produced, and the s[ring constant can be calculated using the gradient of this line. This is repeated for each spring in order to calculate the spring constant for both springs. The line given for the graph is of the formimage12.png, and can be compared to the equation image13.png in order to calculate these spring constants.

In the second part of this experiment, the trolley is tethered between the two springs used above and is displaced from its equilibrium position a certain distance each time.

...read more.

Middle

image13.png:

image12.png

image13.png

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:

image14.png

Using this equation, the spring constant of this spring can now be calculated:

image15.png

Spring 2

image16.png

As shown before:

image17.png

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

image18.png

Spring 2

image19.png

Part 2

Mass 1 = 0.273112kg

Time (s)

0.7544

0.7543

0.7544

0.7543

0.7543

0.7544

0.7543

0.7543

Random Uncertainty

1.3x10-5

Average:

0.7543

Mass 2= 0.523828kg

Time (s)

1.0317

1.0318

1.0317

1.0319

1.0316

1.0316

1.0314

1.0310

Random Uncertainty

1.1x10-4

Average:

1.0316

Mass 3= 0.775805kg

Time (s)

1.2476

1.2477

1.2481

1.2476

1.2468

1.2464

1.2464

1.2461

Random Uncertainty

2.5x10-4

Average:

1.2471

...read more.

Conclusion

Mass 1

image30.png

Experimental image23.png

Mass 2

image31.png

Experimental image25.png

Mass 3

image32.png

Experimental image27.png

Mass 4

image33.png

Experimental image28.png

Mass 5

image34.png

Experimental image29.png

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.

...read more.

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