Mark Riley 3107631608

CONTENTS

Introduction and Aim PAGE 1

Materials and Procedure PAGE 2

Results and Calculations PAGES 3-8

Discussion and Analysis of Results PAGES 9-10

Conclusion PAGE 11

Answers to questions from TASK 2 PAGES 12-13

Mark Riley 3107631608

PAGE1

The Conservation of Energy

Introduction Hooks’ Law states that the force needed to stretch or compress a spring is

directly proportional to the distance the spring is stretched or compressed. The

stretching and compression of a spring is referred to as deformation. Therefore

the amount of deformation of a spring is directly proportional to the force

causing the deformation. Energy that is stored in a stretched or compressed

spring can be calculated using the equation EPE= ½kx2. The k value represents

the “spring constant’ for any particular spring and tells us about the stiffness of

the spring. The greater the value for k the stiffer or stronger the spring. This

experiment aims to determine the k value of a particular coil spring. By applying

forces to a spring, measuring the extensions(x) and plotting these results in a

graph, K can be calculated by the gradient of the trend line. The energy stored in

a spring can also be calculated by the work done to compress or stretch the

spring. In this experiment EPE is found by calculating the work done by

Gravitational Potential Energy (mgh with h being calculated from when the

hanging spring is in it’s natural equilibrium position, and is also equal to x).

Aim To derive a k value for a coil spring and use this value to determine the EPE using

the equation ½kx2. Determine if the loss of Gravitational Potential Energy of a

falling 1kg mass is equivalent to the gain in Elastic Potential Energy of the

spring.

Mark Riley 3107631608

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Materials

Coil spring

Retort stand

Clamp

Metre ruler

Hooked mass set with increments of 100g

Procedure

Clamp retort stand to bench and hang the coil

spring from retort stand.

Use ruler to measure the height from the floor to the bottom of spring whilst the spring is

hanging stretched at its natural equilibrium position.

Be sure that all measurements are made by the same person.

PART I

Add a 1kg weight to the spring and use the ruler to measure the minimum

height(maximum extension) that the bottom of the spring reaches and minus

that from the original height measured in the previous step.

Repeat this ten times recording the results to find an average for x.

PART II

Add weights from 100g to 1.00kg in increments of 100g to the spring.

Carefully use the ruler to measure the extension caused by each of the weights

being added and record the results.

DIAGRAM 1

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DISCUSSION AND ANALYSIS OF RESULTS

We used units of millimeters and grams for this experiment. When we convert grams

and millimetres to kilograms and metres we are able to use 3 significant figures in

our calculations. We used the value for gravity as 9.81m/s2 (accepted value for this

region) in order to preserve the accuracy of 3 significant figures as far as possible

through the experiment.

We established that all energy changes that occurred during this conservation of

energy were of values that were negligible except that of Gravitational Potential

Energy(GPE) and Elastic Potential Energy(EPE). Therefore any work done by GPE

should just about have all transferred into EPE. Some of the negligible energies

ignored are heat loss, friction(eg air resistance) and sound.

We analysed the spring TABLE2a. and calculated the spring constant (K) to be 28.9J

CALC3a. using the gradient of a Force Applied vs Extension graph. GRAPH B We then

used the average maximum extension of the spring from the 1kg weight which was

0.507 metres CALC1a. and used both values in the equation ½kx2 to calculate that

there was 3.71J of EPE at the average maximum extension of the spring from the 1kg

weight CALC4b. We then calculated the loss of GPE over this extension to be 4.97J

CALC4a.

RESPONSE TO Q6 These two energies should be the same but there are obvious discrepancies between

the two energies calculated with the results from our experiment CALC5a. This

cannot be blamed on measurement uncertainty/ error because the uncertainty in

measurement of the distance was 0.71% CALC1c. whilst the difference in the EPE &

GPE energies in relation to GPE was 25.4%.CALC5b. Therefore this discrepancy must

be due to the miscalculation of the EPE because we used the equation ½kx2.

RESPONSE TO Q7 The expression EPE = ½kx2 was derived using the area under a Force vs Extension

graph. This is based on the assumption that a spring has ideal elastic properties and

the area under the graph is a triangle. The results prove that this does not apply to

the spring used as when we added the first 2 masses of 0.100kg then 0.200 kg there

was no extension TABLE2a. meaning that the relationship between Force and

Extension was not directly proportional. GRAPH A. Ignoring these first two pieces of

data, the remainder of the data was plotted in a graph and although all the

remaining points were linear, GRAPH B the trend line did not pass through the origin

(0,0) meaning that Force and Extension are not directly proportional and the area

underneath was not a triangle. The results show that y = mx + c or F = kx + F0 in

this case F=28.9x +2.58.CALC7b.

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DISCUSSION AND ANALYSIS OF RESULTS (continued)

The total value of error when determining a relationship between F and x was

overcome by accounting for the spring not having ideal elastic properties(not

passing through the origin). The actual relationship was found to be F=28.9x

+2.58.CALC7b. Because the area under a Force applied extension graph equals

the work done on the spring or the stored potential energy of the spring, we can

use this new relationship between F and x and substitute this relationship in

terms of area into the equation EPE = ½kx2 so it becomes EPE = ½kx2 + Fox. With

this new equation, the EPE was calculated as being 5.02J. CALC9a. This value for

EPE is in excellent agreement to the work done on the spring by GPE which was

4.97JCAL9b. with the difference as a percentage in relation to GPE being

1.03%.CALC9c. The accuracy of these results can be proven further by taking into

consideration, the limitations in precision of the ruler and weights, and the

percentage uncertainty of the measurements of the maximum extension of the

spring by the falling 1kg weight which was 0.71%.CALC1c.

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CONCLUSION

The results from the experiment successfully verify to some extent, the law of The

Conservation of Energy. We must consider that even if the experiment was

conducted in a closed system with an ideal spring, the work done on the spring by

Gravitational Potential Energy will never 100.00000% completely transfer into

Elastic Potential Energy.

The biggest flaw in this experiment is the way in which we measured the springs

extension of the falling 1kg weight. The maximum extension was only reached for

a miniscule period of time and was measured next to a ruler only by eye. Even

though an average was found after ten trials, the measurement was highly

susceptible to human error. Taking this into consideration we can justify why our

final calculation which should have been slightly less than the work done on the

spring by GPE was actually slightly more.

Other flaws in this experiment were mainly to do with measure and the fact that

the spring we used to conduct the experiment did not have the properties of an

ideal spring. These other flaws which created errors in our results were

calculated, accounted for, mostly overcome and had very little effect on the final

results.

As stated in the discussion, some of the Gravitational Potential Energy will be

transferred into other energies other then Elastic Potential Energy. This loss to

other energies is assumed to be such a minute value in this experiment that it

was ignored.

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TASK 2

Plot a graph of force (in N) against extension x (in m)

SEE GRAPH A ON PAGE 3 AND GRAPH B ON PAGE 4

Q1. Calculate the average of the ten measurements of the distance x to give the best estimate

of x.

Best estimate (average) of x= 0.507 metres

REFER TO CALCULATION CALC1a. ON PAGEON PAGE 5

Q2A. Calculate the uncertainty in x (∆x).

∆x = ± 3.6mm

REFER TO CALCULATIONS CALC1b. ON PAGE 5

Q2B. Express this uncertainty as a percentage of the best estimate of x.

Percentage uncertainty = 0.71%

REFER TO CALCULATIONS CALC1c. ON PAGE 5

Q3. From the graph determine the spring constant (in N/m).

Spring constant = k = the gradient of a Force applied vs extension(x) graph.

k = 28.9J

REFER TO CALCULATIONS CALC3a. ON PAGE 6

Q4a. Loss of GPE of the falling 1kg mass.

Loss of GPE= 4.97J

REFER TO CALCULATIONS CALC4a. ON PAGE 6

Mark Riley 3107631608

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Q4b. The gain in EPE using the expression EPE= ½kx2

EPE gained =3.71J

REFER TO CALCULATIONS CALC4b. ON PAGE 6

Q5a. The difference (in Joules) between the two energies.

GPE-EPE =1.26J

REFER TO CALCULATIONS CALC5a. ON PAGE 6

Q5b. Express this difference as a percentage of the gravitational potential energy.

Difference = 25.4%

REFER TO CALCULATIONS CALC5b. ON PAGE 7

Q6. THIS QUESTION HAS BEEN ANSWERED IN PARAGRAPH 4 OF THE DISCUSSION (PAGE 9)

Q7. THIS QUESTION HAS BEEN ANSWERED IN PARAGRAPH 5 OF THE DISCUSSION (PAGE 9)