• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11

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.

This student written piece of work is one of many that can be found in our AS and A Level Fields & Forces section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Fields & Forces essays

  1. Marked by a teacher

    Experiment to determine gravity from a spring using digital techniques

    3 star(s)

    It also confirms Hooke's law, that F=k?x for a spring experiencing a force F and extension ?x. This experiment also calculated a value for gravitational field strength as being . Evaluation Overall, this experiment can be seen as a success, with the value calculated for gravitational field strength being very close to the generally accepted value of 9.81Nk-1.

  2. Peer reviewed

    Investigating the forces acting on a trolley on a ramp

    5 star(s)

    experiment were recorded in a table with two columns; distance from light gate measured in millimetres and time taken to pass through the light gate, measured in milliseconds. Without taking friction into account, it was possible to take a rough estimate of acceleration due to gravity and hence it was

  1. Peer reviewed

    Energy and its uses

    3 star(s)

    dynamo with loss from friction and heat, it was then converted to electrical energy and transmitted through wires to the bulb where it was converted to thermal energy with losses due to electrical resistance and heat. 7. Battery drives lamps (stored electrical energy)

  2. Experiment to determine gravity from a spring using analogue techniques

    This is doubled, to 2.2% uncertainty in period squared, so: All uncertainty calculations were done as shown above, and the results were: Mass = 0.02kg Mass = 0.03kg Mass = 0.04kg Mass = 0.05kg Mass = 0.06kg Mass = 0.07kg Mass = 0.08kg Mass = 0.09kg Mass = 0.10kg Because

  1. The experiment involves the determination, of the effective mass of a spring (ms) and ...

    from the graph as shown below: From the equation it can be shown that: Gradient of line = 4?2 k ?k = 4?2 grad' To find the value of ms the intercept's on the y-axis and x-axis can be used can be shown that, on the y-axis where the x

  2. Investigating the relationship of projectile range and projectile motion using a ski jump.

    There are different things that I could change to improve the accuracy of the experiment. I can put a gate as a releasing barrier at the point of dropping the ball baring to ensure that it is being released at the same point every time.

  1. Measuring The Constant g; The Acceleration Due To Gravity

    One can also clearly see the relationship between distance and 1/2t(, linked by the acceleration constant g in the graphs drawn. The results to my second method are showing very strong consistency due to its small range, incredibly tight standard deviation showing only slight spread in the data, and also my almost negligibly small percentage uncertainty.

  2. To change the angle of a ramp and place a trolley 70 cm away ...

    The bigger the angle of the ramp the greater the distance the trolley travelled. We were running out of time to do our experiment so we decided to get the ramp angle up to 25 (using trigonometry to work out how many books we needed to do this)

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work