• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Experiment to determine gravity from a spring using analogue techniques

Extracts from this document...

Introduction

## Experiment to determine gravity from a spring using analogue techniques

The aim of this first experiment is to examine simple harmonic motion exhibited a mass on a spring. Using data recorded in doing this, the spring constant for each spring can be calculated along with a value for gravity.

In the first part of this experiment, the relationship between the period of the oscillations of the spring and the mass of the spring is observed. The period of oscillation of mass on a spiral spring depends on the mass on the spring and the spring constant of the spring. This is given by: Where m is the mass on the spring and k is the spring constant of the spring. Since the period can be observed, and the mass on the spring is known, this part of the experiment is concerned with calculating k, the spring constant for each of the springs used.

The spring constant is different for every spring, and is defined as the mass needed to produce a unit extension of the spring (ref. 6). This is calculated by placing differing masses on the spring, extending the spring a certain distance from its equilibrium position each time and timing the time for 10 oscillations of the spring to occur. This is done by using an analogue stopwatch and a ruler to ensure that the distance extended from the equilibrium position was the same each time. The graph of period squared against mass can then be plotted.

Middle

3

6.8

4

6.7

Average time for 10 oscillations(s)

Random uncertainty (s)

2.90

0.05

3.58

0.025

4.20

0.05

4.70

0.05

5.05

0.05

5.45

0.025

5.80

0.05

6.05

0.025

6.43

0.025

6.73

0.05

Taking the average time for 10 oscillations, calculating the period and the period squared:

 Mass (kg) Time for 10 oscillations (s) Period (s) Period squared (s2 ) 0.01 2.900 0.290 0.084 0.02 3.580 0.358 0.128 0.03 4.200 0.420 0.176 0.04 4.700 0.470 0.221 0.05 5.050 0.505 0.255 0.06 5.450 0.545 0.297 0.07 5.800 0.580 0.336 0.08 6.050 0.605 0.366 0.09 6.430 0.643 0.413 0.10 6.730 0.673 0.453

So the graph of period squared against mass is: Since this graph is a straight line that should go through the origin, it can be seen that the period of the spring squared is directly proportional to the mass placed upon it. The equation for this graph can now be compared to to gain a value for the spring constant of this spring:  Since is the y value of the graph, and m is the x value of the graph, it follows that: The spring constant, k, can be found by substituting the value of the gradient of the graph into this equation: This is the value of the spring constant of the spring.

Uncertainties

To Calculate the Uncertainty in k

In order to calculate the uncertainty in k, a parallelogram is drawn around the extreme upper and lower points of the trendline, and the corner points of the parallelogram are recorded. The uncertainty in the gradient, and thus k, can then be calculated according to the equation: Where m(AC) and m(BD) are the gradients of the diagonals of the parallelogram and n is the number of points in the graph.

A(0.01, 0.10)  B(0.10, 0.46)  C(0.10, 0.445)  D(0.01, 0.08)   This uncertainty will be the same for k, because the other component’s involved it it’s calculation are all constants.

Therefore: To Calculate Uncertainty in Each Point

The main uncertainties are the random uncertainty, reading uncertainty and the calibration uncertainty. These can be combined using the equation , to give a total uncertainty for the period of the spring. This is then calculated as a percentage, and doubled, since the graph uses the period squared, and the total uncertainty for each period squared value can be calculated.

A sample uncertainty calculation is shown below.

Mass = 0.01kg

Random = ±0.05s

Calibration = 2% x 2.9 = ±0.058 As a percentage of 2.9, this is 1.1%.

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 all these uncertainties are very small, the error bars on the graph are too small to see.

### Spring 1 – Part 2

 Mass (kg) Extension (m) 0.005 0.002 0.010 0.006 0.015 0.011 0.020 0.015 0.025 0.020 0.030 0.024 0.035 0.029 0.040 0.032 0.045 0.037 0.050 0.042 0.055 0.046 0.060 0.051 0.065 0.055 0.070 0.060 0.075 0.064 0.080 0.068 0.085 0.071 0.090 0.076 0.095 0.081 0.100 0.086

Conclusion

Using LINEST, the value for the gradient is: This is combined for the uncertainty in g. So the value for g is: ## Discussion

### Conclusion

This experiment has shown the relationship for a mass m on a spiral spring with a period of oscillation T. Values for gravitational field strength were also calculated at and .

### Evaluation

This experiment can be seen as somewhat successful, with the values for gravitational field strength being close to the generally accepted value of 9.81Nkg-1.

The reading disk supplied was an accurate way of determining the distance extended, but the disk often slanted, which could affect measurements. In order to counter this, the distance was read at the same point on the disk each time, so this effect could be negated.

The stopwatch supplied was an analogue one, which only measured in increments of 0.1s. In future, a digital stopwatch would be used, which could measure in increments of 0.001s, in order to increase the accuracy of the time and reduce the uncertainty.

Due to the analogue stopwatch being used, the reaction time when pressing the stopwatch could interfere with the actual time, thus interfering with the results. There is no way this could be improved, as reaction time would vary each time, and this could be why the values obtained for gravitational field strength were further out than expected. In order to combat this, a digital way of determining the time could be used, and this is done in experiment 2.

Overall, this experiment can be seen as successful with problems overcome. Because the values for g were as close as could be expected due to the uncertainty in the reaction time, this experiment can be considered a success.

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

# Related AS and A Level Fields & Forces essays

1.  ## Experiment to determine gravity from a spring using digital techniques

3 star(s)

* The motion sensor is placed on a lab jack on top of a stool pointing upwards towards the mass on the spring. Instead of relying on the motion sensor sensing the distance from the bottom of the mass holder, a CD is attached to the mass holder, in order to increase the area that the motion sensor can sense.

2.  ## Investigating the forces acting on a trolley on a ramp

5 star(s)

This error can be partly compensated for by adding error bars to the graph, which incorporate values of v2 which may be higher than measured. The problem of the error is exaggerated by the fact that v2 is exactly that; squared.

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

seconds, Resolution 00.01 seconds, Sensitivity 00.01 seconds, Mean zero error 00.00 seconds, Uncertainty 00.10 seconds. (Masses have a percentage uncertainty of 5%) Trial Readings Mass in gram's Number of oscillations (x) Time for 'x' oscillations (xT) 1. Time for 'x' oscillations (xT)

2. ## Investigation to determine the viscosity of glycerol.

This strong bonding causes great friction between the layers of liquid and therefore gives glycerol its property of high viscosity. Glycerol has a high viscosity as opposed to other alcohols because, it has three -OH functional groups attached to it.

1. ## Viscosity Experiment. The aim of my investigation will be to analyse the relationship ...

After doing several online tests my reflex reactions averaged out to be 0.2 seconds. I was planning to use light gates at first, as this would have been much more accurate in measuring the time of the fall, but

2. ## Experiment to calculate spring constant of 2 springs

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.

1. ## An Experiment to Evaluate the Acceleration due to Gravity using a Spiral Spring

Figure 3, the gradient and therefore the value of k can be calculated using the following equations.

2. ## Design and conduct an experiment that graphically determines whether drag force is proportional to ...

Instead it increased by a factor of 1.5. When they were three coffee cups, the average time is 1.10 seconds with position of 1.54m. the drag force is .0320. The drag force tripled to that of the drag force in part one because the mass of the coffee filter increased by a factor of three. • Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to 