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To do this I will investigate the input variable which is the factor we’re changing. I shall change the height of the slope, which therefore means the input variable is the gravitational potential energy (G.P.E) as the height moved affects it.

Prediction

I predict that the transfer of energy will be more efficient the steeper the slope gets. This is because as the slope gets steeper, the marble will rotate less and less (so less rotational energy) and make less and less contact , and when the slope has a gradient of 100%, the marble will not rotate at all, but just fall straight down.

The marble’s energy changes from G.P.E, as it falls vertically, to kinetic energy. However, as it comes down the slope it rotates. Some energy is lost as rotational energy.

G.P.E = K.E + Rotational Energy

Therefore I will need to measure the velocity at the bottom as there is no Kinetic Energy (K.

E) or rotational energy is at the top.

I will need to find out the efficiency of the energy transfer from G.P.E to K.E. The formula is:

Efficiency = Useful energy transferred (KE) x 100

Total energy supplied (GPE)

To work this out I need to know the G.P.E the marble has at the top (therefore the maximum G.P.E) and the amount of K.E the marble has at the end of the slope (therefore the max. K.E).

We can find G.

P.E by using the following formula:

GPE = mgh

m = the mass of the object in Kilograms

g = the acceleration due to gravity in metres per second squared

h = the height in metres.

We can find out K.E. by using the following formula:

KE = 1/2 mv2

m = the mass of the object in Kilograms

v = the speed of the object in metres per second.

To work out the average speed:

Avg. speed =_x_ = u + v

t 2

x = the length of the slope in metres

t = the time taken for the marble to roll down the slope in seconds

u = the initial speed of the marble

v = the final speed of the marble.

But as the marble will be stationary u = 0, so this means:

_v_ = _x_

2 t

If we bring 2 over to the other side this gives us a formula to work out the speed:

v = _2x_

t

So to work out the efficiency the formula can be rewritten as:

Efficiency = 1/2mv2 x100

mgh

The mass cancels out and so the mass of the marble does not have to be recorded.

Efficiency = 1/2v2 x100

gh

If I sub the formula for v I get the following formula:

Efficiency = 0.5(2x/t)2 x 100

gh

I shall use this formula as it requires only one calculation and still ends up with the same result.

Method

Apparatus:

* Clamp stand

* Marble

* Piece of guttering

* Ruler

* Stopwatch

* Book

The first thing I will do in the experiment is to set up all the apparatus as in the below diagram:

A ruler and a stopwatch will be used to measure the length and height and also to time how long it takes for the marble to roll down the slope. A piece of guttering is used as a slope because it is semi-circular and hollow. Therefore it prevents the marble from falling off halfway down the slope.

Then I shall measure the length of the piece of guttering (x). Next I shall set the height of the slope (h) and then record these lengths in a table.

The times will be measured to two decimal places. But the length and height will be measured to three decimal places.

After the lengths have been recorded, I shall let go of the marble at the top of the slope and start the stopwatch upon its release. When the marble reaches the bottom of the slope, I shall stop the stopwatch and record the time taken for the marble to roll down the slope into the table. I shall repeat this timing process 5 times for each height so that my results are reliable. I shall then calculate an average.

Then I will set the slope to a different height and time it again. The length does not have to be measured again because the same piece of guttering will be used each time.

To ensure that my timing is accurate, I shall put a solid book at the bottom of the slope. When the marble hits the object it will make a noise. When I hear the noise, I shall press the stop button.

I shall use the same marble each time to make the experiment valid because different marbles might have different masses and the mass will affect the speed of the marble. I should be the only person to record the time of the marble each time as different people have different reaction times.

The factors in this experiment are the height of the slope (h), the length of the guttering (x), the acceleration due to gravity (g), the mass of the marble (m), and my reaction time.

I can control the first factor by setting the height of the slope with the clamp stand and measured by a ruler.

The second and third factor will be controlled by using the same marble and guttering throughout the investigation.

I cannot control the acceleration due to gravity, but because this is constant and I know the value of it (approx 10), it will not affect my investigation.

I cannot control my reaction time, but by doing the whole investigation in one go, and not doing anything that affects my reaction time while doing the investigation (e.g. drink coffee which shortens reaction time), my reaction time should stay constant.

The length of the piece of guttering will be around 2 metres. The heights of the slope will be between 0.10 and 1.00 metres.

I shall measure the height (h) in metres to the nearest millimetre. I shall measure length (x) in seconds to the nearest 1/100th of a second and the time I will repeat the timing five times for each height and use the average of these five results. This will make the investigation reliable as it will reduce the effect of anomalous results.

When I record the time it will be made to two decimal places as the stopwatch limits me by only showing this amount of accuracy. For length and height it will be measured in metres to the nearest millimetre (three decimal places) because this is quite easy to see on the ruler. This is as accurate as the ruler will allow.

Before I do my actual investigation, I shall carry out a preliminary experiment in order to see if I need to make changes to my plan. The preliminary procedure will include three heights:

0.200m, 0.400m and 0.600m

I shall do 5 repeats for each and work out an average and the efficiency which should not exceed 100%.

Results for Preliminary Procedure

Height (m)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Time 4 (s)

Time 5 (s)

Avg Time (s)

Efficiency (%)

0.200

2.50

2.60

2.44

2.50

2.40

2.488

64.52

0.400

1.75

1.69

1.79

1.72

1.66

1.722

67.60

0.600

1.40

1.38

1.47

1.40

1.34

1.398

68.22

This shows what I expected as the efficiency increased each time. Therefore I should keep the same amount of repeats. However, I should do more measurements with a greater range (8 measurements) and smaller interval (0.100m). In my actual investigation I shall use the following heights:

0.100m

0.200m

0.300m

0.400m

0.500m

0.600m

0.700m

0.800m

Obtaining Evidence

Height (m)

Time 1

(s)

Time 2

(s)

Time 3 (s)

Time 4 (s)

Time 5 (s)

0.100

3.12

3.25

3.32

3.25

3.28

0.200

2.37

2.34

2.34

2.35

2.37

0.300

1.94

1.90

2.00

2.00

1.93

0.400

1.78

1.71

1.47

1.81

1.72

0.500

1.43

1.54

1.38

1.47

1.59

0.600

1.41

1.41

1.31

1.38

1.41

0.700

1.32

1.32

1.28

1.31

1.25

0.800

1.15

1.15

1.19

1.16

1.19

My results look fairly reliable as they all lie within a small range of each other.

Analysis

I need more information than the results obtained. I also calculated the average time and the efficiency which are shown here:

Height (m)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Time 4 (s)

Time 5 (s)

Avg Time (s)

Efficiency (%)

0.100

3.12

3.25

3.32

3.25

3.28

3.244

75.37

0.200

2.37

2.34

2.34

2.35

2.37

2.354

71.64

0.300

1.94

1.90

2.00

2.00

1.93

1.954

69.36

0.400

1.78

1.71

1.47

1.81

1.72

1.698

69.26

0.500

1.43

1.54

1.38

1.47

1.59

1.482

72.24

0.600

1.41

1.41

1.31

1.38

1.41

1.384

69.25

0.700

1.32

1.32

1.28

1.31

1.25

1.296

66.88

0.800

1.15

1.15

1.19

1.16

1.19

1.168

72.25

In order to show the results more clearly and make it easier to identify a trend I have drawn a graph.

My results show a slight pattern. This is shown by the curve of best fit which I have drawn. You can see that the efficiency decreases then increases. The lowest value is 69.25% while the maximum one has an efficiency of nearly 76%. Therefore the average efficiency could be directly proportional to the height.

Conclusion

Overall, the average efficiency increases as the height increases. This is because as the slope gets steeper there is less contact between the slope and the marble. Therefore, the marble rotates less so more of the gravitational potential energy is converted to kinetic energy. This also means less is wasted as rotational energy.

My conclusion completely supports my prediction because it uses the same idea as I stated in my prediction: that more gravitational potential energy is converted to kinetic energy as the slope gets steeper because less is converted to rotational energy.

My prediction is also supported by my results, because the graph shows that the efficiency does increase as the height increases.

Evaluation

The procedure I used was as accurate as possible with the apparatus I used. I recorded the results to the highest degree of accuracy as it limited me to do so. I also did five repeats for each height, which should have made my results very reliable.

Most of my results are in the pattern which I suggested they would be in when I wrote prediction. However, there is not a very strong trend and there is an anomaly. The first result for 0.100m is the highest result (nearly 76%) and it is supposed to be the lowest one.

This is probably because I was more alert at the beginning of the experiment and so my reaction time was shorter. Apart from this I cannot see any reason why the first readings I took were anomalous.

However, I do think that my evidence is valid because I kept all factors which could affect the experiment constant apart from the input variable of the height.

I do not think that I have collected enough evidence to fully support my conclusion. In order to do this, I must do the experiment again. Next time I shall use a larger range of heights so I can see if the trend continues. Also, if there is a larger range, an anomaly will not show up as obviously on the graph. I would not repeat the experiment any more than I did this time as more repeats wouldn’t affect the average much more.

I did not have many difficulties in this experiment except with the timing. If I were to do this experiment again, I would use light, motion or pressure sensors which are connected to a computer to record the times. I would do this because a computer’s reaction time is very accurate.

To obtain more evidence to support my conclusion, I would use a greater range of heights. Another way to do this is to shorten the intervals. The experiment would still have a range of heights from 0.100m to 0.800, but it is conducted every centimetre instead of every ten centimetres. This would make the trend much clearer. Therefore, this would make the trend and therefore my conclusion clearer.

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